# Talk:Depth of field/Archive 1

## Old junk previously not in a section

In photojournalism we went over "circle of confusion" again--and after hearing for the 3rd or 4th time, I think I finally understand it. It has something to do with the diffraction of light as it passes through a lens, causing blur b/c of overlapping on the negative. I think. Could someone who knows, not suspects, go through this again, maybe providing an image to help illustrate it? Thanks, Koyaanis Qatsi

The circle of confusion is due to refraction, not diffraction. Generally speaking, if you have a point source of light in front of an (ideal) lense, then refraction and the particular shape of the lense causes light rays from the source to meet in a single point behind the lense. If that point happens to lie on the film, the point will be in perfect focus on the photo. If the point lies before (or behind) the film, then the rays haven't completely met yet (or are already diverging again) when intercepted by the film. The precise circle on the photo results from the fact that the light rays, before hitting the lense, went through a diaphragm of fixed aperture; without the aperture, the bright region on the film would be much bigger, since a lot more light rays from the source would contribute. AxelBoldt, Saturday, May 25, 2002

Refraction, right. I had the right idea but wrote the wrong thing. What I don't understand, though, is why having a wider aperture results in shallower depth of field and a smaller aperture results in greater depth of field. I keep thinking I understand it, and deciding I don't. Which is why I thought a diagram and an explanation would be nice. Koyaanis Qatsi, Wednesday, May 29, 2002

Making the aperture smaller makes the circle of confusion smaller. Imagine the ideal case: a tiny tiny aperture, letting only a "single" light ray through. That light ray would be refracted at the lense, but would stay a light ray, and the circle of confusion would be a single point. Now a little larger aperture will let several rays through, these diverge a bit, the lense brings them together again, but the film intercepts them "too early", and you see a small circle. The larger the aperture, the more light directions get through, the lense tries to bring them together again, but they hit the film too early and you get a larger the circle of confusion.

Now, all the distances for which the circle of confusion is small enough will be more ore less in focus on the film. If the aperture is smaller, a larger range of distances will qualify. AxelBoldt, Wednesday, May 29, 2002

The explanations above about circles of confusion and how they are related to aperture could be more precise. To explain the principle more concretely you need to think about how light rays are bent in order to focus them to a point on film. None of the explanations above makes this point explicitly. When the aperture is wider, the light rays need to bend at a greater angle in order to meet the film plane at a point (it is important to note here that the distance from the aperture to the film plane cannot be changed for the purposes of this example). It is this greater angle of refraction, and this alone, that accounts for the reduced depth of field. I will try to use simple keyboard characters to illustrate the point; imagine that these characters represent the aperture, the light rays, and the film plane:

            o >|<


The "o" is the aperture, the "|" character is the film plane, the ">" character is the light rays being bent onto the film plane, and the "<" character is the light rays as they would continue on after meeting at a point. Consider the light ray that starts at the upper left and descends to the lower right; label this line AB (“A” at the upper left, “B” at the lower right). Now consider the light ray that starts at the lower left and rises to the upper right; label this line CD (“C” at the lower left, “D” at the upper right). Lastly, label the point in the center where the light rays meet as “F”; this point where the light rays meet is the only point where the light rays are in perfect focus. Ideally, point F lies directly on the film plane. However, many points of light do NOT line up directly on the film plane. Because of their varying distances from the camera, many points of light that form a real-life image are bent to planes that lie slightly in front of or behind the film plane. To illustrate this concept, imagine the lines AB and CD moving together as a group slightly to the right. Now the point of perfect focus is no longer on the film plane; now the point of perfect focus is behind the film plane. Also note this: now the "|" character representing the film plane no longer meets lines AB and CD character at one point. Instead it meets the lines at two points. Two points form a line. If you draw in this line you have now drawn in your circle of confusion. The point of light in the real-life image is now no longer reproduced as a point, it is reproduced as a circle. However, this circle might still appear as a point to the human eye, depending on variables such as the size of the reproduction and the distance from which the reproduced image is viewed. When the circle becomes so large that it no longer appears as a point to the human eye, then it begins to appear out-of-focus.

Now you must consider how changing the aperture changes the circle of confusion. When the aperture is made wider it looks more like this "0" than this "o"; if the film plane is kept at a fixed distance from the aperture, then the light rays need to bend at a greater angle in order to meet the film plane at a point. Draw a diagram and make the circle (aperture) greater and you will see what I mean. The angles here that concern us are angles AFC and DFB (you can ignore angles AFD and CFB). As the aperture becomes wider, both angles AFC and DFB become greater. To illustrate the effect this has on the circle of confusion, you should try drawing two extreme examples: draw the first example with a very small aperture, the second example with a much larger aperture (remember to draw the film plane at the same distance from the aperture in both examples). In the first example, angles AFC and DFB will be relatively small, in the second example angles AFC and DFB will be quite large. HERE IS THE CRUCIAL COMPARISON: if the film plane is 1.0 millimeters in front of or behind point F, then the circle of confusion will be larger in example 2. If the film plane is 2.0 millimeters in front of or behind point F, then the circle of confusion will be larger in example 2. If the film plane is 3.0 millimeters in front of or behind Point F, etc. etc. This is the core of the aperture/DoF relationship. WrathofAbsalom 01:28, 8 February 2006 (UTC)

Is it worth commenting on the depth of field of a pinhole camera? David Martland 07:28, 10 Dec 2003 (UTC)

Sure

Aren't the Df and Dn equations messed up? It seems if s>f then the equations as listed always give Df<Dn. Seems backwards.

I was conspicuous too. Therfore I searched trough some other sources. And there I saw our notion is correct. I didn't ever collaborate in a wiki before but I took the liberty to change the two equations and add another notation which is more readable for me. Is the righthand-notation better for everybody? Or is the lefthand used for a particular purpose? If so can somebody make the choice for me? --!nok 15:37, 14 October 2005 (UTC)

The equations were slightly wrong before, but even more incorrect after !nok's change. I have replaced them with the correct equations. Note that there are two different mathematical definitions of hyperfocal distance (they differ by a +f term at the end), and it's important to use the correct depth-of-field equations for the particular hyperfocal distance formula being used. I've also refactored the equations slightly, bringing the "S x" term down to make it a bit more obvious how the equations are structured... I hope. Doug Pardee 19:57, 6 March 2006 (UTC)

I was browsing through my old photos when I came upon this. I was experimenting with my camera's macro function while reading "The Camera" and I came up with this. When I found it, I thought it would be perfect for this article. Number one, speaking technically, it more clearly demonstrates "Depth of field" than the original photograph, and it's also larger, clearer, and sharper. And secondly, it adds a little humor to the article as well, because the words "depth of field" are within the sharp area of the DOF itself! The first sentance in the article states "In film and photography, the depth of field (DOF) is the distance in front of and behind the subject which appears to be in focus." and I believe my picture shows this vividly. PiccoloNamek 05:30, August 31, 2005 (UTC)

That's a great picture -- thanks for putting it in the article! The only thing that would make it better would be if the text read "A long time ago, in a galaxy far away..." :-)
Atlant 11:52, 31 August 2005 (UTC)
Agreed - love the picture - makes this article super-stylish. --DreamsReign 04:36, 17 May 2006 (UTC)

The article provides several photos for examples. The series of pictures under the flower are not a result of f-number change, but rather, of perspective distortion (the hitchcock zoom) I believe. The depth of field in all of those pictures are the same; the perspective distortion only makes the depth of field SEEM shallower as you progress down the pictures; but of course; this doesn't really matter, because the article describes these pictures as a result of f-number change or aperture change, which they are not. I may be wrong; so please correct me if I am.

Wouldn't the Cowslip photograph be more appropriate in the Artistic considerations section? JeffConrad 22:46, 15 October 2006 (UTC)

Agreed (it's my pic) and now moved - Adrian Pingstone 08:52, 16 October 2006 (UTC)

## On the other hand...

Actually, I believe the photos are not misplaced; now that I look at them closely, I think they are actually shallower and in fact a result of the aperture changing. This picture acts as a double-optical illusion; normally, it's easy to tell between perspective distortion and depth-of-field change... Sorry; I got the idea that somehow the background seemed to be getting bigger and bigger; as if it was a result of the hitchock zooming effect; when in fact, it was just getting more shallow (and because they got so blurry, sticks started "disappearing" in the background, as if they were distorting). So everything is fine -- the pictures do in fact get shallower; and they are a result of f-number change; instead of what I had previously posted above (a result of perspective distortion and optical illusions). Ironic that I had thought it was an optical illusion at first... and was in turn fooled by another optical illusion.

## An error and a suggestion

Error: text is missing below the first figure.

I don't see what you think is missing. What do you see it saying, and what would you suggest? Dicklyon 22:35, 2 June 2006 (UTC)

A suggestion: the discussion doesn't say that "N" in the equations stands for the f-number. Alison Chaiken 20:16, 2 June 2006 (UTC)

In the section "Depth of field formula" it says "Let H be the hyperfocal distance (calculated below from N, the f-number, and c, the circle of confusion for a given film format), ...". How would you recommend making it more clear? Dicklyon 22:35, 2 June 2006 (UTC)

## New equations 28 August 2006

I've revised the DOF equations to make them consistent in form, and have attempted to show how some of the approximations are obtained, and that all equations derive from the same basic assumptions, with simplifications under certain conditions. I eliminated expressions using hyperfocal distance from the close-up formulae under the assumption that hyperfocal distance isn't terribly meaningful for close-up work (they're simple enough to restore if someone thinks they are of value). The first two such formulae appeared to be incorrect: if

${\displaystyle H={\frac {f^{2}}{Nc}}+f}$,

the ${\displaystyle H-f}$ terms should appear in the numerator as well as the denominator. In any event, the other formulae presented seemed more than sufficient and more convenient to apply.

I also eliminated the center dots in the formulae: their inclusion seemed to be at odds with the Manual of Style, and certainly with conventional practice. I submitted a revision that kept the dots before making this change, so that they are easy enough to restore if someone feels they are absolutely necessary, though I think they served more to clutter than to clarify.

JeffConrad 02:40, 28 August 2006 (UTC)

Jeff, in a previous round of changes, I sought to use equations that are found in the literature and accurate enough, while being much simpler, and at the same time acknowledging the existence of more detailed equations whose accuracy is however limited by the factors they neglect such as pupil magnification.
I haven't really studied the new section carefully yet, but my impression is that by starting with the rather complex equations it will lose a lot of readers, before they get to the simpler ones. Think about it from that point of view and see if you think a different order of presentation could be made workable. I appreciate your effort on helping to clean this up, as you did with EV and LV and APEX system. Dicklyon 03:01, 28 August 2006 (UTC)
Dick, I had the same concern, and almost made a comment to that effect. Perhaps some simplification of the initial presentation is indicated, with more detail later to demonstrate that the basic equations weren't simply pulled out of the air. With this approach, I'd be inclined to keep the basic presentation even simpler than it was. The question is, "To what use would these equations be put, and which equations would be the most useful for that purpose?" A few equation candidates:
1. Total DoF?
2. Front and rear DoF?
3. Near and far limits of DoF?
4. Near:far DoF ratio?
5. Focus and f-number from near and far limits of DoF?
The last equations are almost the only ones that I've ever used, yet they possibly are the least common in the literature. It long has been my impression that DoF discussions concentrating on the object side of the lens are primarily academic exercises; in practice, the task of controlling DoF usually is much easier on the image side:
1. View camera users who calculate DoF usually use the focus spread (difference between near and far image distances) to determine focus and f-number.
2. Small- and medium-format users typically use lens DoF scales to accomplish the same task. At least they did with manual-focus lenses ... except for a few older Canon 35 mm cameras (with the Depth-of-Field AE mode), there is no easy way to control DoF with most autofocus lenses. It's possible, at least in theory, to use object-side relationships in conjunction with lens DoF scales, but the resolution on most AF-lens distance scales is so poor that it's difficult to set the distance with much precision (e.g., it's easy to calculate hyperfocal distance, but tough to set it).
That said, I think getting into the image side probably would lose almost all but the really hardcore readers.
My personal observation on practical control of DoF would be something like:
1. Determining DoF from focus spread or lens distance and DoF scales is reasonably straighforward for distances large in comparison with focal length; as noted, however, even this is no simple task with most AF lenses.
2. Determining close-up DoF with unit-focusing lenses is feasible in theory but quite a chore in practice. With most current small-format internal-focusing long-focus macro lenses that change pupil magnification, internodal distance, and focal length with subject distance, it's almost impossible.
In other words, great accuracy is not needed to determine DoF at moderate subject distances, if your camera will allow you to do it. Don't try to calculate close-up DoF at home ...
JeffConrad 06:18, 28 August 2006 (UTC)

## Larger formats -> smaller depth of field

I know that a larger aperture leads to smaller depth of field, but I don't quite see why longer focal length does the same - as written in the section Definition of "focus". Is it because the aperture has to be enlarged accordingly? Could someone spell this out to me? Perhaps I am just confusing the terms depth of field and depth of focus? Thursday, September 28, 2006.

Put simply, for the same subject distance, a longer focal length provides greater magnification, and to a first approximation, DOF is inversely proportional to magnification. Hence the reduced DOF. JeffConrad 08:03, 28 September 2006 (UTC)
Okay. Thanks for your quick reply. When I look at the f-numer equation
${\displaystyle N={\frac {f}{d}}}$,
i still get confused, however. I read several places that increasing the f-number N increases the DoF. From the equation it looks like increasing the focal length f would have the same effect on the f-number as decreasing the aperture diameter d, which would both lead to an increased DoF. From your reply it seems that this isn't true. Is there simple explanation why?
I should mention that I have no background in optics or photography. My interest is only out of curiosity. Bade, September 28, 2006.
The answer is simple: N is not the only variable in the DoF equation. Dicklyon 13:41, 28 September 2006 (UTC)
I can see that, but if I kept d constant, would a larger focal length f (and thus larger N) result in an increased DoF? In other words: does the DoF depend ONLY on the ratio N, or does it depend also on the absolute values of d and f. Does (for example) N = 50mm/1mm and N = 100mm/2mm (same ratio) give the same result (DoF-wise and otherwise)?
Plug some examples into the equation of your choice and see what happens. In general, no; increasing f will give you LESS DoF, not more, if you keep same aperture diameter d. As Jeff points out, the magnification view makes this easiest to see, but any form of the equations should give similar results. Dicklyon 15:14, 28 September 2006 (UTC)
The magnification (and hence the focal length) and circle of confusion scale with the format. See the reference Jeff Conrad's Depth of Field in Depth (PDF) under "Depth of Field and Camera Format" for a discussion of how this affects DOF. JeffConrad 23:33, 29 September 2006 (UTC)

## Depth of field versus format size

Dick, I got rid of the sentence

An 8x10 camera can be used to acheive the greatest depth of field and focus control, but at f-numbers such as f/64 the exposures can be extremely long.

because it didn't seem to make sense in the context in which it was used. Was the intent something to the effect of, "large-format cameras often can employ movements to achieve even greater DOF than smaller cameras"? If so, that probably should be mentioned. Of course, it also might be mentioned that a small camera can employ a tilt/shift lens to regain the advantage.

JeffConrad 07:58, 28 September 2006 (UTC)

I don't know the intent, as I didn't put that (I did edit it a bit). It does seem a bit narrowly put. I doubt that the movements were part of the intent, but that's also a good thing to mention. Dicklyon 13:41, 28 September 2006 (UTC)
So I see ... looks like it was Mr. Anonymous. Had I paid more attention to the history, I'd just have nuked the sentence without comment. Maybe it's best just to leave it out; it's contradictory to mention the greater DOF with smaller cameras and yet claim that the greatest DOF can be had with the largest image format. As the View Camera article mentions, using tilt or swing doesn't really increase DOF, but rather changes the plane of focus to better fit the DOF to the scene. We could add View Camera, Scheimpflug Principle, or Large Format to the "See also" section, but I'm not sure the treatment of movements in any of these articles goes far enough to explain how tilt or swing helps make up for the lesser DOF in larger formats. JeffConrad 22:44, 28 September 2006 (UTC)
What the heck ... I've added a two-sentence mention of movements and tilt/shift lenses to the end of the "Depth of field versus format size" section. I'm not sure that's where it belongs, but I can't think of where else to put it. An article on tilt/shift lenses remains a task for another time. JeffConrad 23:03, 28 September 2006 (UTC)

Isn't

"Consider formats that differ ..."

and the rest of the fourth paragraph a repeat of the previous paragraph? JeffConrad 22:37, 29 September 2006 (UTC)

In mentioning NIST Special Publication 811 in my last edit summary, I overlooked another obvious and more accessible source: the Wikipedia article on ISO 31-0. JeffConrad 22:59, 29 September 2006 (UTC)

Jeff, FYI, a Wikipedia article is never a source; they're OK for "see also", but not as references for sources. It's too transient, and needs to have sources of its own to be verifiable, so list a real source instead. Dicklyon 04:27, 11 October 2006 (UTC)
I chose my words in haste; I never intended to suggest the Wiki article as a "reliable source" in the formal sense, but rather as a guide to Wiki authors. NIST SP 811 obviously is an authoritative source in the USA; NIST SP 330 also is useful. The ISO 31 standards are the definitive references, but unlike the NIST documents, they aren't free. JeffConrad 04:54, 11 October 2006 (UTC)

### Edits of 14–15 October 2009

I removed

“A side effect of using the f-number in place of the absolute aperture width is the inability to compare DOF for a given f-number between formats. For example, an f-number of 2 in a compact digital camera will result in a much greater DOF than on a larger format camera at the same f-number; the actual aperture width would be smaller on the compact camera for the same field of view, thus giving a larger DOF.”

I think the editor meant to say essentially that when the same picture is taken in two different formats, setting each lens to the same f-number won't give the the DOF in both formats. To properly qualify the statement, however, we'd need to state the conditions given in the section DOF vs. format size, and this seems needless duplication to me. Moreover, the “in place of” would seem to invite the question, “So why don't we use absolute aperture diameter?” It would be simple enough to say

“The aperture diameter is normally given in terms of the f-number because all lenses set to the same f-number transmit approximately the same amount of light, simplifying exposure settings. A consequence of this ...”

but we'd be adding even more material not really related to the topic of this section. That two formats taking the same picture have the same DOF when the same absolute aperture is maintained is of theoretical interest as a format-independent index, but it's not commonly used in practical photography, so I think mention in the other sections is adequate coverage under WP:WEIGHT.

This article was already overloaded with math, but the DOF ratio of different formats, especially in terms of absolute aperture diameter, isn't covered in most sources, so it's arguably subject to challenge. Accordingly, I added a derivation and a link to that section.

That all looks great. Of course, by von Rohr's method, the result is trivial; you can get it from the picture instead of from the algebra. Dicklyon (talk) 04:38, 15 October 2009 (UTC)
I think it shows yet again that there's more than one way to do it; hopefully, at least one will be helpful to the reader. I thought you might add the ref, but included my derivation to make the treatment parallel to that for the more traditional relationship. In any event, I'd say it's adequately sourced. JeffConrad (talk) 05:00, 15 October 2009 (UTC)

I was just getting ready to save the ref format change when you already did it; see hnow easy it is? ;-) I put the space in the id tag because the templates seem to do it; it's probably of no consequence, but just in case we ever decided to use the templates ... The double mention of von Rohr seemed redundant, so I moved the cite to the beginning of the sentence. There's no way to have two WLs, so I added the WL to the article in the reference section; hope this is OK. This article also includes another WL to that article, so readers should be able to find it. My sources (Chicago) and a Google search for 'von Rohr' suggest that the particle is capped at the beginning of a sentence (but not in a reference list); change it if you know otherwise. JeffConrad (talk) 05:00, 15 October 2009 (UTC)

## Delete Circle of confusion computation?

I've listed Circle of confusion computation for deletion. Please take a look if you care, and leave a comment. Dicklyon 04:24, 11 October 2006 (UTC)

## Close-up DOF

There are two headings with the same name both starting:

When the subject distance s approaches the focal length

This is a great article but the redundency needs to be cropped out. I just added an image demonstrating close-up DOF. HighInBC (Need help? Ask me) 18:31, 16 November 2006 (UTC)

Take a look at [this diff] and see if you can think of a better organization. The idea was to have a first simpler presentation, and a later more gory derivation. Dicklyon 18:46, 16 November 2006 (UTC)

Hmmm The divsion does seem to make sense. Perhaps the names of the headings can be disambiguated. HighInBC (Need help? Ask me) 18:48, 16 November 2006 (UTC)

I had the same reservations when writing this, but redundancy is an unfortunate consequence of having both basic and detailed presentations. There are two other subheadings that appear in both the basic and detailed sections, but given the hierarchy of the subdivisions, I don't really see the ambiguity. The primary headings (or some qualifying adjectives) could be prepended or appended to the subheads to give unique names, but I find this cure worse than the disease. I think elegant variation would be similarly inelegant. JeffConrad 23:17, 16 November 2006 (UTC)

## Photo clutter

Is it just me, or does everyone want to add their own shallow-DOF photo to the article? The number of photos exhibiting the property is, for all practical purposes, infinite. Perhaps it would be better if we narrowed it down to a few less? Girolamo Savonarola 00:03, 17 November 2006 (UTC)

I did just add one, but I did so becuase I though an example of close-up DOF was needed. The related section has alot of text on the subject and no image. But mabye you are not refering to me hehe. HighInBC (Need help? Ask me) 00:06, 17 November 2006 (UTC)
Not you specifically; it's something that's been bugging me for a while. I guess the recent addition just sparked me finally commenting on it. The problem is that your image doesn't really show anything different from any other photograph with a shallow DOF - the first image in the article being a notable example.
The main problem, however, is that there are too many images period. I think that certain other ones may be worthy - such as an image progression showing the same image with different apertures. But beyond one or two examples, what else can you really show about DOF that is different? Let's decide what types of photos should be here and look for the best examples instead of adding photos which are good examples and trying to come up with a pretext for why it should belong to this article. Girolamo Savonarola 00:15, 17 November 2006 (UTC)
I completely agree with Girolamo—this isn't a photo gallery. The only justification for a photo in this article is its illustration of the concept. The best illustration of shallow DoF includes a photo of the same subject showing greater DoF (as do some of the first images submitted). I'm for weeding out the rest; they're gratuitous, detracting from the article rather than adding to it. JeffConrad 00:33, 17 November 2006 (UTC)
Well I am not to attached to the idea of the image being here. I don't mind if it is removed for housekeeping. HighInBC (Need help? Ask me) 01:27, 17 November 2006 (UTC)
Again, I agree with Giralomo that it isn't just your image. I'd also eliminate "A Cowslip flower ...," "Artistic effect ...," and possibly the kitten and the sequence below it. This may be going a bit too far, but again, the question is, "Does the image really illustrate the concept?" I think Paul van Walree's site is a good example of illustrative images that also happen to be well executed. JeffConrad 01:57, 17 November 2006 (UTC)
What many have failed to recognize is that the thumbnails have a whole lot more DOF than the full-size images, and thereby fail to make their point unless clicked on. We need examples that work in a small size. Dicklyon 06:43, 18 November 2006 (UTC)
Demonstrating rather conclusively that "apparent DoF" is redundant. It's tough to see what's sharp and what isn't in a small image (much like looking through the viewfinder of a small-format camera). The primary audience for images here probably are people relatively new to photography, so an illustration should be obvious: what is unsharp should be obviously unsharp, and what is sharp should be very sharp (preferably the result of a tripod-mounted camera). I think the images of the type, the butterflies, and the two white flowers make their points quite clearly; with the other images, the differences aren't as obvious. I think it's especially important for the differences in a sequence of images at different f-numbers to be obvious in the thumbnails, because it's awkward to move among the larger versions. JeffConrad 22:20, 18 November 2006 (UTC)

Although there hasn't been much response to Girolamo's original suggestion, no strong objections to reducing the number of images have been presented, either. It isn't possible to have this many images and still have them positioned near sections to which they relate. Unless someone has strong objections, I'm going to remove the Cowslip flower, the child, and the pen tip; I think the previous images adequately illustrate the concepts. I personally find the differences in the f/22 through f/2.8 sequence a bit subtle, but I'm inclined to leave them for now. JeffConrad 20:43, 15 December 2006 (UTC)

It would appear that, like the entropy of the universe, the number of images in this article cannot decrease. The process of culling the surfeit would seem unavoidably capricious; absent a strong consensus to the contrary, I'm going to leave things as they are. JeffConrad 22:14, 18 December 2006 (UTC)

I would say, if you haven't had any personal involvement with the creation of any of the images, delete whichever seem most appropriate. As for the sequence, perhaps it would be worth contacting one of the people in the image editing project so that they can be turned into a series of frames for an animation, thus saving the clutter of multiple images of the same thing. Girolamo Savonarola 22:19, 18 December 2006 (UTC)
Jeff, I'd go further and encourage you to "be bold" even if some of the photos are your own. You're the guy who has done the most to refine the content of the article, so there's no way your actions will be taken as anything but constructive. If someone objects to a removal, it can be negotiated, but I don't think anyone's likely to be too attached to their particular images here, or too touchy about trying to prune them. Dicklyon 00:17, 19 December 2006 (UTC)

I've removed the Cowslip flower, the child and the pen—I think some of the earlier images adequately illustrate the same concept. I would propose that we use the following criteria in considering whether to add images in the future:

• The image should clearly illustrate some concept relevant to the article.
• In this article, the differences between sharp and unsharp should be substantial, perhaps almost artificially so, because of the increased DoF of the thumbnails, but also to make the point readily apparent to someone new to photography. Ideally, this would not only make unsharp areas obviously unsharp, but also have sharp areas very sharp (i.e., tripod-mounted camera if possible).
• Ideally, an image also should be pleasing and well executed.

I have some reservations about the image of the Wolf spider. Although it's well executed, it's not obvious what is being shown. Those who have done insect photography probably will recognize the greatly increased DoF, but this improvement may be lost on others. I think the image would be far more instructive if the photographer were to include one of the individual images to show how limited conventional macro DoF is.

Girolamo's suggestion about the animation may have some merit (who to contact?). I also think the differences among the images could be somewhat less subtle. I'll see if I can come up with a more graphic illustration, but I'm not sure when I'll get to it. JeffConrad 18:29, 19 December 2006 (UTC)

## Edits of 11–12 December 2006

I agree with editor 208.104.120.140 that the second sentence under 'Aperture effects" was smoother without the parenthetical information. However, I also think that information is important, especially for newcomers or casual photographers, who often are confused by the inverse relationship between f-number and aperture size. The entire section probably would benefit from rewriting. JeffConrad 21:46, 11 December 2006 (UTC)

I've tried to put some of the more basic material closer to the beginning, and better group the images with the sections to which they correspond. Only so much is possible, however—as has been noted, there simply are too many images, several of which contribute nothing but clutter. JeffConrad 09:22, 12 December 2006 (UTC)

## Introductory paragraph

I'm somewhat baffled by the last sentence in the opening paragraph, and am inclined to remove it:

This region is greater behind the point of focus than it is in front, because the angle of the light rays change more rapidly; they approach being parallel with increasing distance.

Is there something obvious that I'm missing? JeffConrad 18:29, 19 December 2006 (UTC)

It could be made more intelligible. I think this is what it means:

This region is greater behind the point of focus than it is in front, because the angle of the light rays change more rapidly with distance closer than the focus point than with distance further; rays approach being parallel with increasing distance.

Dicklyon 19:15, 19 December 2006 (UTC)
Your take is much the same as mine. The angle between the marginal rays from the more distant point always is smaller than the angle between the marginal rays from the closer point; however, this does not establish that the DoF behind the subject is greater than the DoF in front of it. It's simple to construct a diagram showing the far DoF less than the near DoF; such a diagram would, of course, violate the lens conjugate equation.
It's impossible to construct such a contradiction if you ignore the conjugate equation and just draw the "outside-the-box" rays by Moritz von Rohr's method. And it's not that the angle behind is less, but that it's less different from the angle at focus. That angle difference translates to a COC, pretty nearly. But, it's a complicated explanation that hard to see easily. Dicklyon 22:42, 19 December 2006 (UTC)
Perhaps the DoF distribution still is worth mentioning, though I wonder if it's necessary in the opening paragraph. In any event, I think the explanation needs to go. I know of no way to show the DoF distribution other than mathematically; it's easy enough to add this if it's thought that the benefit outweighs the clutter of additional math. JeffConrad 21:49, 19 December 2006 (UTC)
I agree it doesn't belong in the lead, since it takes too much space to explain that the distribution goes all the way from symmetric in macro mode to infinitely more behind is distant mode, with everything in between. In my paper, I explained four regions, one of which is the region around which the popular "rule of thumb" of about twice as much behind as in front is actually nearly true. Should we add explanation of those four regions? Or we could use a picture to illustrate somewhat more behind than in front. I'll see what I have... Dicklyon 22:42, 19 December 2006 (UTC)
My initial reaction, which I didn't state very clearly, was that the conclusion was far from obvious to me without a diagram or some other explanation. A diagram might address that, but at that point we might as well add a derivation. At the very least, we need something to establish the near focused, and far distances from the lens. Although this could be done on either the image or object sides, the concept of DoF necessarily starts with an image-side blur spot, so I think an image-side derivation would be simpler and more appropriate for this article. It's certainly not difficult, though the article already is getting a bit long. It may be simpler to add a few equations; moreover, we've already pointed reader's to several derivations, including two online versions.
I had thought of covering the near:far DoF ratio, but again thought the article was a bit long. Perhaps a simple explanation would suffice; I tend to view the ratio as a continuum, ranging from zero at the hyperfocal distance to a limiting value of unity at high magnification. In particular, the distinction between you regions 2 and 3 seems a bit arbitrary. The continuum works only when using the "exact" equations for near and far limits of DoF; the approximate equations
${\displaystyle {\frac {\mathrm {near} }{\mathrm {far} }}\approx {\frac {H-s}{H+s}}={\frac {1-s/H}{1+s/H}}}$
would suffice for medium-to-far subject distances, but we'd need another equation, such as
${\displaystyle {\frac {\mathrm {near} }{\mathrm {far} }}={\frac {fm-Nc}{fm+Nc}}}$
(my Eq. 21, equivalent to your equations that follow Figure 3) for the macro region. I'll put something together in my user space to see if it's worth considering. JeffConrad 23:14, 20 December 2006 (UTC)
I have an expanded Basis of the DOF formulae section (which I've retitled) at User:JeffConrad/DoF equations. I think it addresses the issues raised, though I'm not convinced that we need all (or any) of it. Although it's convenient to have a self-contained derivation, the article keeps getting longer ... I am now convinced it is easier to show the near:far DOF distribution algebraically rather than with a diagram. Although it's easy to make a diagram showing greater DOF beyond the subject, it's not so easy to show that it must be so. JeffConrad 02:59, 21 December 2006 (UTC)
I'm against making an encyclopedia article too "mathy". You and I can follow all that and appreciate what it means, but to many readers it just becomes increasingly intimidating--a bigger chunk they have to skip and feel bad about. However, it might be good to summarize the result, that the 1/3-2/3 rule applies at H/3, and that the DOF is more symmetric when closer, more skewed when further. And I agree that it's easier to show the near:far ratio algebraically if you want to get quantitative, but I think it's easier to show diagramatically if you just want to show that it's greater on the far side. It takes a few words to motivate von Rohr's method, but then it becomes obvious, by construction, for whatever size circle you want to put in the field plane. Dicklyon 04:24, 21 December 2006 (UTC)
Depends on the article, I suppose, but as I said, I'm not convinced we need any of it. Quite frankly, I think the entire section Basis of the DOF formulae could be eliminated, pointing the mathematically inclined reader to any of the external links that cover this stuff in detail (I'd probably retain the image-side formulae for focus and f-number simply because they are among the few that actually are useful in the field). I see little reason to say anything about asymmetrical lenses except perhaps to mention that they aren't accurately described by the simple formulae. To my mind, the basic derivation would be far more useful (and less intimidating). In earlier edits, I simply retained many formulae that I probably would not have included in an article such as this.
One either gets into the mathematical detail or one does not, and when one does, the discussion gets quite lengthy, as both my paper and yours illustrate. The middle ground is tough to cover; I originally had a much shorter version, without formulae that I thought no one would ever miss. Of course, almost all the comments I got were about the formulae I had "overlooked."
It's easy to make a simple diagram using von Rohr's method, but really understanding it requires understanding the concept of projecting the image-side blur spot onto an object-side blur spot; easy enough, perhaps for Abbe, Kingslake, and von Rohr, but, to me, more difficult to grasp than the math, and definitely more obscure than the conventional image-side approach. The diagram on my page requires only first-year algebra and geometry, and the derivation certainly is no more complex than yours in the Circle of confusion article.
My original suggestion was simply to eliminate the last sentence of the introductory paragraph. Perhaps this could be tempered by adding a sentence elsewhere stating (but not demonstrating) something to the effect of
"The DOF beyond the subject is always greater than the DOF in front of the subject. When the subject is at the hyperfocal distance or beyond, the far DOF is infinite; as the subject distance decreases, near:far DOF ratio increases, approaching unity at high magnification. The oft-cited 'rule' that 1/3 of the DOF is in front of the subject and 2/3 is beyond is true only when the subject distance is 1/3 the hyperfocal distance."
Such a passage might be subject to challenge, of course, but that is always a possibility with a statement that is not supported. Again, however, the reader could be directed to one of the references or external links for substantiation. JeffConrad 07:50, 21 December 2006 (UTC)
OK, I'll let you worry about whether some simplification can be had by "overlooking" some formulae. I'll put von Rohr's method into his article, since it is, as you say, a rather unusual treatment for a mainstream DOF article. Dicklyon 16:16, 21 December 2006 (UTC)
I think putting von Rohr's method into his article makes perfect sense; perhaps the DOF article can include a link. Including the translation is a big help for those of us who retained little of our high school German.
I've revised the introductory paragraph, added a section Near:far distribution of depth of field, added the image-side equations to the DOF formulae section. I've left the derivation section for now, including the added material. See my further comments under that section on this page. JeffConrad 21:36, 21 December 2006 (UTC)

## Showing DOF in front and behind

Here's a drawing I made to show how near and far limits can be found, and why the distance to the far limit is more than the distance to the near limit, from the focused field plane:

This is essentially von Rohr's method, but with my angular COC parameter e; I hope it's more clear than his drawings (see Moritz von Rohr). The entrance pupil has diameter d and is at distance S from the focused field plane that is presumed to image exactly onto the focal plane. Dicklyon 22:55, 19 December 2006 (UTC)

Dick, no question about the conclusion, which follows using either the image-side or object-side approach. However, I think the conclusion is far from obvious without considerable additional explanation. Might it suffice simply to say that the DoF is greater beyond the subject and approaches a 50/50 split at close focus?
That might suffice. It shouldn't take many words to explain the picture. It's a lot easier conceptually than the image-side approach that requires invoking the lens equation. Dicklyon 05:36, 20 December 2006 (UTC)
Incidentally, I think adding the Dominic Groß translation would make the Moritz von Rohr diagram much easier to follow. JeffConrad 01:21, 20 December 2006 (UTC)
OK, I'll add that. Dicklyon 05:36, 20 December 2006 (UTC)

## Edit of 21 December 2006

I've added a brief discussion of the near:far distribution of DOF. I've also included the simplified image-side equations in the subsection Focus and f-number from DOF limits under DOF formulae.

### Derivation of the DOF formulae

I've retained the detailed treatment of the DOF formulae for now; if nothing else, it will be in the history if we decide to delete it and someone later wants to restore part of it. I've added the derivation of the equations for DOF limits, and a subsection on the near:far DOF ratio. I think the detailed coverage is helpful to the reader who wants the additional information; the section is essentially an appendix, so the reader who has no interest in the derivation can easily skip it (if the section is eliminated, the choice is eliminated for everyone). However, others may have different opinions. If the detailed treatment is too much, I think the entire derivation section can be eliminated without seriously hurting the article; only a couple of notes would need revision. JeffConrad 21:57, 21 December 2006 (UTC)

## Fancy Italic “f”

Dick, in this context, f is a quantity symbol, and as such, should be set in italics (see ISO 31-0 or NIST Special Publication 811). ANSI and ISO standards all follow this practice. JeffConrad 07:45, 25 January 2007 (UTC)

I don't find where it says that f in f-number is a quantity symbol. I thought it was just a name. Can you point me more specifically? And what about the long hooked f as used in f/#? Is that part of the standard? Dicklyon 02:57, 26 January 2007 (UTC)
I don't think there is any explicit statement, but it seems obvious that f is the symbol for focal length. ASA PH2.12-1961, Sect. 3.4.2, states
The symbol for relative apertures shall be f/ followed by the f-number.
The same statement appears in ANSI PH3.49-1971, again in Sect. 3.4.2. At least to me, it seems obvious that f/# indicates 'focal length divided by number', with f the symbol for focal length. I don't think there's really a long hooked f—it's simply an italic f. That this is so is illustrated in ISO 2720-1974, Sect. 3.1.2. ISO standards are set in sans-serif type; hence, f is simply in sans-serif italic (Actually, it's just oblique, because an italic front is both oblique and cursive. But this is getting a bit pedantic ...). JeffConrad 04:29, 26 January 2007 (UTC)
Jeff, my reading of the history is different. Long before the 1974 standard, the typographical standard of the long hooked f, not the oblique f, had been adopted for f-numbers as in f/8 where the f is literally focal length, but not at all standardized for the expression "f-number" where f is part of a name. I studied an awful lot of old books on this. I'm surprised to hear that the ANSI standard has an ordinary oblique f for both. Very strange. Dicklyon 04:58, 26 January 2007 (UTC)
Well, looking at books again, I must say the typography is much more varied and less regular than the simplified memory I just described. Still, I see no evidence that the f in f-number has ever been taken to be a quantity as it is in f/8. Some use a specifically different symbol, like F-number and f/8 (The Eye and Visual Optical Instruments By David A. Atchinson, George Smith). Dicklyon 06:02, 26 January 2007 (UTC)
Dick, your knowledge of photographic history far exceeds mine. No disagreement that actual practice is all over the map. Logically, though, I can't see how f-number derived from anything other than the quantity symbol for focal length, so I'd have to say that the folks on the ANSI and ISO committees got it right. They're also arguably fairly authoritative. Sidney Ray and Warren J. Smith also follow this practice, and they're fairly authoritative sources. I still wonder whether the long hooked f was anything other than just italics (which often produce a long hooked f, at least in serif typefaces). JeffConrad 06:31, 26 January 2007 (UTC)
Like this: ${\displaystyle f\mathrm {-number} }$. JeffConrad 09:40, 26 January 2007 (UTC)

## Principal planes

And principle planes are not the same as principal planes ... JeffConrad 22:13, 14 March 2007 (UTC)

## Aperture diagram (edit of 19 March 2007)

I agree with Girolamo—having the aperture diagram in the aperture article is more than adequate. JeffConrad 19:31, 19 March 2007 (UTC)

## Where is distance measured from?

The text below the Nikon lens' photo says this:

A 35mm lens set to f/11. The depth-of-field scale (top) indicates that a subject which is anywhere between 1 and 2 meters in front of the camera will be rendered acceptably sharp. If the aperture were set to f/22 instead, everything from 0.7 meters to infinity would appear to be in focus.

Now my question is: Is the distance measured from the front of the camera? I thought it was to be measured from the point in focus! Please correct me if i am wrong. 165.125.144.16 19:51, 19 March 2007 (UTC)

The measurements on the lens barrel (focusing/DOF scale) are normally taken from the camera's film plane. My old Canon SLRs have a symbol like this: -o- on the top plate of the camera indicating the position of this plane. (Quantities in optical formulas may refer to different origins, like the center of the lens.) -- Coneslayer 20:08, 19 March 2007 (UTC)
The formulae in the DoF article give object distance from the object nodal plane; at moderate-to-large subject distances, the distance between this plane and the image focal plane (i.e., the film plane) usually is negligible, but for close-up photography, the difference can be significant. JeffConrad 20:17, 19 March 2007 (UTC)
The important thing to note in practical applications, such as working as focus puller, is that lenses designed for film cameras give their focus markings from the film plane, while lenses designed for video markets, such as ENG, often tend to have focus marks measured from the front element of the lens. At the end of the day, though, this has no effect on the depth of field itself - only where the focus should be measured from. Girolamo Savonarola 18:10, 20 March 2007 (UTC)

## Imperceptible vs. acceptable blurring

Dick, is "acceptable" the right term in the introduction? In this context, I think it serves more to confuse than to enlighten. It would seem to me that in the general sense, "acceptable" could apply to any blurring that met the aesthetic requirements of a particular image, even one employing substantial selective focus. Isn't the concept of DoF that the CoC is a blur spot indistinguishable from a point? I recognize that "acceptable" appears several other places in the article, but in most instances, it means, essentially, "imperceptible". JeffConrad 00:32, 10 April 2007 (UTC)

Perhaps it is confusing in that sense, yes. But while the concept is usually "imperceptible", the actual values used are typically somewhat larger than a just-perceptible blur, perhaps by a factor of two, aren't they? In any case, different people choose differenet CoC values based on what is acceptable to them, like how close to have to look to notice blurring on a big print. Tieing this to perception is a conventional fiction, I think. Dicklyon 01:10, 10 April 2007 (UTC)
I certainly don't see any factor-of-two cushion. A Snellen chart is based on 30 cycles/degree, which is 6.875 cycles/mm at 250 mm. A Snellen chart is very high contrast, so the usual rule of thumb (see Ray 2002, cited in the Circle of confusion article) is to reduce this to 5 cycles/mm (equivalent to a CoC of 0.2 mm) to allow for the reduced contrast of normal subjects. The tools available to Snellen admittedly were limited in comparison to those available today; people at the Smith-Kettlewell Eye Research Institute in San Francisco tell me that resolution on the order of 35–37 cycles/degree to a high-contrast sinusoidal target is more typical. Even so, I still don't see the big cushion when allowance is made for normal-contrast subjects. I've seen some very optimistic claims on the net, but I've yet to see one with a credible explanation or citation of a reliable source.
I don't buy the theory that conventional CoCs are nothing but remnants of 1930s film resolution. The idea behind DoF is the perception of sharpness under normal viewing conditions, and not necessarily the maximum that film or an electronic sensor can capture. If the latter were true, a 4×5 would use the same CoC as 35 mm, and making an outdoor 4×5 image would be all but impossible. I don't disagree with Merklinger's math, but his illustrative examples employ magnifications seldom encountered by anyone but the CIA or David Hemmings. Even absent subject motion, the idea that a CoC can be reduced to any arbitrary value is far greater urban legend than imperceptible blur at DoF limits. Eventually, diffraction overtakes defocus blur, and a few simple calculations suggest that this happens at values not much less than conventional CoCs.
The basic concept of DoF always has been a zone in which everything is perceived as sharp. I agree that the choice of CoC is somewhat arbitrary, but if conventional practice is to be questioned, I don't think the introductory paragraph is the place to begin the attack. For the casual reader, the extra qualification is likely to confuse. JeffConrad 04:06, 10 April 2007 (UTC)
I'm OK taking it out of the lead, but I think it should be admitted that the conventional COC for "sharp" has crept over the years from about 1/700 to 1/1000 to 1/1500 to 1/2000 of the format diagonal. The latter for 10+ MP pixel peepers, of course. Dicklyon 04:29, 10 April 2007 (UTC)
I changed it (differently; tell me if you like it). But then I noticed the first section head is Definition of "acceptably sharp". So shouldn't that notion be in the lead? Dicklyon 06:48, 10 April 2007 (UTC)
Technically, I agree with the "specified" viewing conditions, but practically, I think the use of "normal or specified" still is confusing in the introduction. I've recast things a bit in attempt to avoid the problem; I've also moved the heavy stuff from the intro to the first section to be less intimidating. The intro now is a bit sparse, but everything I tried was little more than fluff. I'm not happy with "misfocus" (in the first section) but I'm afraid that "defocus" would be a bit much for many readers. See what you think ...
This article has been somewhat hijacked by a couple of still photographers; I hope we're still OK with the filming people ...
The topic of "CoC creep" would seem better suited to the Circle of confusion article. Of course, it would be interesting to see why the criteria have changed; I've seen many values cited over the years without much explanation. I don't suggest that the criteria I put in the CoC article are infallible, but at least they can be related to basic principles. For full-frame 35 mm, a 0.03 mm has been around since the 1930s, and is about 1/1440 of the format diagonal. It might derive from the assumption of enlargement to the long dimension of a 8×10 frame. The 1/2000 criterion is new to me ... JeffConrad 09:24, 10 April 2007 (UTC)

I think most of us agree that strictly, we speak of “acceptable” sharpness according to specified criteria. As I've mentioned before, though, this seems a bit technical for the first sentence. Strictly, “area” is probably applicable when applied to a two-dimensional image, but it’s somewhat at odds with the physical concept of DoF as a range of distances from the camera. In any event, reducing the number of words probably improves the readability, and to me, “Apparent sharpness” is less unwieldy as a section title than was “Apparent sharp focus”. See what others think. JeffConrad (talk) 07:08, 25 April 2008 (UTC)

“Portion of a scene” or something similar works for filming and photography but seems less suitable for something like photolithography; of course, “in front of and behind the subject” arguably had the same problem. We could say “the region of object space that appears sharp in the image”, but that seems a bit much for the first sentence. JeffConrad (talk) 22:09, 25 April 2008 (UTC)

## Camera Movements and DOF

I hate to add yet another section, but it seems better to introduce camera movements in one place rather than two. I've avoided the term "tilted plane focus" because it isn't standard (try a Google search to see what I mean), but I'm not sure there is a good term: "tilted focus plane" seems to be the winner of the obvious terms with 18 hits ... Good technical treatments of tilt and swing are few and far between, and the authors all seem to use different terminology: witness the term used to describe the axis about which the plane of focus rotates as the lens is focused: "counter axis" (Scheimpflug), "hinge line" (Merklinger) and "pivot point" (Wheeler). I usually call it a "pivot axis" or even "POF rotation axis" ... I've used "rotation of the POF" for the process because it seems most descriptive of what is happening; perhaps there is a more elegant way of stating it. JeffConrad 07:51, 24 April 2007 (UTC)

## Diagrams requested

{{reqdiagram}} This article would greatly benefit from diagrams illustrating the various formulas. -- Beland 18:56, 5 May 2007 (UTC)

I've indicated DOF in the diagram in the section 'Derivation of the DOF Formulae', and directed the reader to that section. That diagram illustrates most of the quantities discussed in the basic section, and the picture of the butterfly gives an alternative illustration of the concept. It's certainly possible to provide additional diagrams, but the article is already a bit cluttered. Perhaps others disagree, however. JeffConrad 00:49, 6 May 2007 (UTC)

## Edits of 5–9 June 2007

Try as I might, I cannot decipher the paragraph that was added to the Artistic considerations section (originally under Word of caution). Although I can think of several things that may be intended, I am guessing at best. Consequently, I cannot see what this paragraph adds to the article in its current form. Absent a clarification, I am inclined to remove it. JeffConrad 21:26, 6 June 2007 (UTC)

I think he was trying to say that the degree of blur of distant background is not determined by the DOF. But I agree it's a mess and hard to see how to fix, which is why I only took out the section head and waited for you to find it. Dicklyon 00:21, 7 June 2007 (UTC)
Actually, I held off waiting for you to make some cuts :-). If I knew how to fix it, I would do so. My guess was that the intent was to say that the amount of the background or foreground blur doesn't quantify the DOF. Perhaps the intent was simply that foreground/background blur is somewhat of a separate issue from DOF. I'm not sure why we would need this comment, though. When people attempt an attractive background blur, they don't usually give much thought to quantifying DOF (Merklinger's example of blurring a sign is special case). Perhaps the editor (WalrusJR) can clarify, but absent this, I think we should eliminate the paragraph. JeffConrad 01:43, 7 June 2007 (UTC)
I've tried to interpret the edit of 5 June 2007 and make the wording more comprehensible. Although, strictly speaking, the added paragraph is correct, we're really splitting hairs, and I wonder if the distinction merits this much space. I avoided the use of "nicely", because it could be taken to include bokeh. If it is felt important to cover the appearance as well at the amount of background or foreground blur, I suppose yet another sentence could be added, but I would wonder if we're getting too far off topic. JeffConrad 23:34, 9 June 2007 (UTC)

## DOF and camera movements—edits of 8 June 2007

There is no maybe about the near and far limits of DOF no longer being parallel when the POF is rotated, as the Scheimpflug principle article or any decent text on view cameras will show.

## Peer review and FAC?

Would any of the primary editors be interested in shepherding this article through the peer review and/or FAC processes? Girolamo Savonarola 20:50, 8 June 2007 (UTC)

If you think it's ready, and we get a couple more votes ... though I think a couple of minor details (discussed in the last few days) should be resolved first. JeffConrad 23:47, 8 June 2007 (UTC)
It can go into PR at any time, regardless of the state it's in. I would do it myself, except that I don't feel as familiar with the optics details nearly as much I'm certain a few people including yourself do. Girolamo Savonarola 00:22, 9 June 2007 (UTC)

## Foreground and background blur—edits of 10–16 June 2007

The ratio of background blur to background object size is very similar in concept to Merklinger's object field method, considered on the image side of the lens. The key difference, at least in the context of this article, is that, within the DOF, the blur is imperceptible, so although the ratio still holds, it is irrelevant. In the object field method, the ratio would still be important.

The difference in concept could be regarded largely as a matter of viewing conditions; most examples showing the benefits of the object field method are at much greater magnification than would normally be employed. Alternatively, the difference could be regarded as what the imaging medium is capable of recording rather than what is noticeable under standard "normal" conditions of enlargement and viewing.

A brief mention of some or all of this could be added to the article if people think it is important. However, unless lack of mention is likely to prompt the question, I'm inclined to omit it because the article is already quite long. JeffConrad 04:48, 11 June 2007 (UTC)

I should have mentioned that the comparison in the second paragraph with the object field method applies only to distant objects; although the object field method is scene specific, the criteria for near objects often are less restrictive than the criteria of the traditional approach. JeffConrad

I've restored the comment on the ratio of background blur to imaged detail size because this also is objectively true; I've left out the interpretive comment, however. I also removed the interpretive comment from the Background and foreground blur subsection under derivation.

1. Without mention of the ratio, there is a concerted effort to claim that a longer focal length produces greater blur, which doesn't seem NPOV and may or may not be true. No disagreement that absolute blur is proportional to focal length, but to mention only that seems a selective inclusion of facts.
2. Few backgrounds, including those in most of the images in the article, are at infinity, so concentrating on the effect at infinity is of questionable relevance to to most photographic situations.
3. Omitting mentioning the blur to detail ratio while retaining the link to van Walree's article is potentially confusing, because it's exactly what he discusses.

Using "detail" rather than "object" also seems less precise (the behavior applies to any object at that distance), but I've left it for now. JeffConrad 23:08, 11 June 2007 (UTC)

Strictly speaking, the pupil magnification cancels out of the expression for blur spot diameter if the distance is measured from the lens entrance pupil rather than from the object nodal plane. However, we've expressed all other formulae in terms of the distances from the nodal planes, so it would seem reasonable to do so here as well; I used "lens" in attempt to avoid the issue altogether. If people insist on referring to the entrance pupil here, I suppose I won't quibble, but I think by doing so we would confuse more than we would enlighten. JeffConrad 01:43, 12 June 2007 (UTC)

Jeff, you restored part of what I took out, leaving "For a given subject magnification, detail distance, and f-number, the degree of detail blur is proportional to the focal length." It's very hard for me to imagine what could be changing here with focal length if you're keeping subject magnification and background detail distance fixed; you'd have to be moving the background relative to the subject as you change focal length and move the camera to keep subject distance fixed. So I can't really find any truth in it. That's why I reduced it to only the special case of an infinitely distant background. And the next bit "however, the magnification of the detail is also proportional to focal length, so for a given detail, the ratio of the blur disk diameter to imaged size of the detail is independent of focal length," that's also not true, since m is not proportional to f in general, and it's introducing a concept that might make sense to Merklinger, but not to anyone else. I think we should drop it. Dicklyon 04:18, 12 June 2007 (UTC)

Dick, the magnification of the defocused object changes with focal length:
${\displaystyle m_{\mathrm {d} }={\frac {f}{u_{\mathrm {d} }-f}}}$
For ${\displaystyle u_{\mathrm {d} }\gg f}$, the magnification is essentially proportional to focal length. The ratio of blur spot size to imaged object size is constant with distance, for all distances. The proof, which I put in the derivation section, is very simple.
The only constraint that I restored was that of constant subject distance, emphasizing that the relationship between focal length and blur diameter applies at all background distances rather than just at infinity. Most backgrounds aren't at infinity, so I think this is important.
You mean constant subject magnification, yes? That's what it says, anyway. And in this case, the conventional approximation is that the DOF is nearly independent of focal length, meaning the blur diameter is constant, not proportional to f, at those distances at the edge of the DOF. I realize that's not exact, but it's certainly nothing like proportional to f. One of us is confused. Dicklyon 07:08, 12 June 2007 (UTC)
The only reason that background blur spot size is of interest to the average photographer is for isolating the subject from a busy background, and I believe that is what led us to add the section on background blur. The subject is isolated from the background because the background is blurred and the subject isn't; what's not so easy to determine is how blurred the background must be for adequate isolation of the subject. It seems a general rule of thumb that when the blur spot is approximately the same as the imaged object size, the object is difficult to recognize. I'll admit here that I'm relying on John Williams's Image Clarity, and he's really a secondary source—I haven't directly consulted the references in his bibliography. In any event, the concept didn't originate with Merklinger; where he differs from most others is that he applies the concept within the DoF, where most others (including me) consider the blur undetectable, at least under normal conditions of enlargement and viewing. Merklinger's method well may be appropriate for surveillance photography, where the main objective is in identifying objects, employing the maximum usable enlargement.
Certainly, reducing recognizability of the background plays a part in determining isolation of the subject, though I don't think it's as clear cut as Merklinger's example of the "PROWLER" sign on his neighbor's RV, i.e., I don't think it's essential that the background be completely unrecognizable. However, I think it's just as speculative to imply that absolute blur size is the only criterion as it would be to insist that a background object be unrecognizable. Van Walree's examples illustrate this quite well; to me, the image with the long-focus lens appears better separated from the subject, but I'd maintain that it's because of the narrower angle of view than the amount of background blur. This is entirely consistent with my experience in macro photography with long-focus lenses—though I like them primarily for working distance, they're also mighty handy for hiding a busy background simply because they include less of it. I never gave much thought to greater background blur, because I've never been convinced there's much subjective difference compared with a lens of shorter focal length.
In summary, if we're going to have a section on foreground and background blur, I strongly think we should mention the ratio of blur to imaged object size. I don't suggest that it's always the governing factor, but I think it's often as valid as absolute blur size, and to mention one without the other would be very disingenuous and misleading. I originally included the subjective comment just to make clear that neither criterion was necessarily absolute. We could add a comment about differing angles of view; although it's a bit off the topic of DoF, it's probably no more so than many other comments in the article, and in any event, it's an important consideration in isolating a subject from the background. JeffConrad 06:55, 12 June 2007 (UTC)
OK, but let's clear up the objective part that separates us first, and reference Williams on the other.
What is the objective part on which we differ? That should be simple to fix. As for referencing Williams, I'm not sure that's appropriate, because the criteria he cites are quite specific, and relate to legal criteria for identification of suspects and admissibility of evidence. I don't suggest that it's anywhere near that clear cut, but simply that the blur disk size, without consideration of its relationship to the object itself, isn't the entire picture when it comes to isolating a subject. Isolation of subject from background is necessarily subjective; although blur disk size ostensibly is objective, its relationship to background isolation is the only justification for its inclusion in the article. Perhaps a one-sentence comment would adequately cover what I had said in three or four sentences. JeffConrad 07:44, 12 June 2007 (UTC)
I've made a few subtle but important changes to the text; in particular, I've eliminated reference to "proportional". I've also eliminated the "however" in introducing the ratio of blur to object size, so the presentation should be more neutral. Everything in the section is objective, and now, hopefully, strictly correct. Although it might benefit from a sentence or two mentioning why the two measures of background blur were included, I think the material could stand as it is. See what you think.
I've expanded the treatment in the subsection under Derivation to support the claims of how the blur disk changes with focal length. JeffConrad 12:42, 12 June 2007 (UTC)
Thanks. The "proportional" was the main problem, since it didn't account for the variation in s and D. Dicklyon 14:38, 12 June 2007 (UTC)
I am afraid that the present text ("For a given subject magnification, f-number, and distance between the detail and the subject, the degree of detail blur varies with the focal length (varying s and D together as focal length is changed).") is not entirely clear. Somehow the article should say in words that the influence of focal length on the blur disk diameter is small when D is close to s, but sizable when the two quantities are well separated. Odo Benus 17:49, 12 June 2007 (UTC)
Yes, I agree. It's what the equation implies, but it's not yet clear, and it really is the point. For D not too far from s, the D in the denominator nearly cancels the f and there's not much effect, but for D much greater than f, the D in the numerator starts to cancel the one in the denominator, leaving the f to make a difference. Maybe a plot or examples would help. Have a go at it. I'm still not convinced that Jeff's focus on the size of background elements is very relevant to the objective issue here. Dicklyon 18:01, 12 June 2007 (UTC)
The ratio of blur to object size is every bit as objective as the absolute blur; it's just a different criterion. Whether one criterion is better than the other at "isolating the background" is necessarily subjective. I don't think I've ever seen a definitive authoritative statement that quantifies what isolates a subject from a background; van Walree makes as good a case as I've seen. I'd arrived at the same conclusion mathematically, but his images make for a more convincing presentation. One advantage of the ratio is that it's independent of focal length and subject distance, depending only on the defocus of the foreground or background. I don't suggest that it's the "right" criterion, and don't really care whether or not I can read a license plate—I just want the background not to be distracting. There simply is no way to make that an objective call.
I find the statement "varying s and D together as focal length is changed" a bit confusing, because we really aren't actively varying ${\displaystyle D}$. Assuming we're dealing with given scene with fixed positions of subject, foreground, and background, ${\displaystyle D}$ varies with ${\displaystyle s}$ simply because the its distance from ${\displaystyle s}$ is fixed. It may be easier to illustrate this by calling the distance between subject and foreground or background object the defocus, given by
${\displaystyle x_{\mathrm {d} }=\left|D-s\right|}$
We then could speak of fixed ${\displaystyle x_{\mathrm {d} }}$, and
${\displaystyle b={\frac {fm}{N}}{\frac {x_{\mathrm {d} }}{s\pm x_{\mathrm {d} }}}}$
Using the ratio of blur to object size,
${\displaystyle {\frac {b}{m_{\mathrm {d} }y}}={\frac {m}{m+1}}{\frac {x_{\mathrm {d} }}{Ny}},}$
which clearly shows the dependence on defocus and object size. I don't suggest that this is the "right" criterion, but simply that it may be as valid as any other.
It's certainly possible to add a plot, but with all due respect, of all of the many quantities that could be plotted, this would seem far from the top priority. I'm not even sure what a plot would really illustrate. It seems to me the implied question is, for a given scene and subject that I want to photograph at a certain magnification, what lens will give the best background blur? If the absolute blur is the criterion, the longer focal length certainly will give the best blur. But why would I want to blur the background? Presumably, to isolate the subject, and toward that end, I'm not sure the objective criterion is that obvious. Images make the case far better than formulae or plots, as van Walree's treatment shows. The effect of defocus distance could be illustrated with examples somewhat more subtle than van Walree's. I would not be surprised if the long-focus lens gave better isolation, especially with increasing defocus. However, I think the result would be due as much to the narrower angle of view than anything else. There would be one obvious result—it's nearly impossible to isolate a subject from a nearby foreground or background. But isn't this almost self evident? There already is a statement to this effect in the section on Artistic considerations.
Photographing the same subject with different focal lengths will result in differences in blur spot size, differential magnification with distance, and angle of view; all contribute to isolation of subject from background. I think it's a bit arbitrary, and possibly misleading, to concentrate on one to the exclusion of the others.
But in an article on DOF, it would also make sense to ignore things other than how much blur you get due to misfocus. We can't know what size background objects there will be, or whether more or less magnification of them will be a good thing, which is why I didn't take discussing them to be "objective". I do like your new equation that suppresses D in favor of the separation. Dicklyon 23:07, 12 June 2007 (UTC)
Maybe yes, maybe no. By definition, DOF separates what is perceived as sharp from what is perceived as unsharp; it's unavoidably subjective. We make certain assumptions about visual acuity, enlargement, and viewing to estimate what "appears to be in focus"; if we were truly objective, we'd not be able to arrive at an "acceptable" CoC, and we'd be unable to define DOF at all. Ostensibly, blur diameter is completely objective, but again, we'd have no reason to even explore the topic were it not for the unavoidably subjective issue of isolating the subject from the background—if you will, the degree of separation of sharp from unsharp.
It's easy to crucify a subject on the cross of objectivity. Recall 30 years ago when audio equipment manufacturers focused on minimizing total harmonic distortion, an objective and easily measured quantity, and touted THD on the order of a thousandth of a percent, when it was easily demonstrated that hardly anyone could detect THD on the order of several percent. The obsession with minimizing THD led many manufacturers to virtually ignore other issues such as phase shift and limited slew rate, which were easily demonstrated to have very noticeable effects on perceived sound quality. Like THD, both phase shift and slew rate were objective, easily measured quantities—it was largely a matter of what someone considered important and decided to measure. The situation here may be analogous.
In any event, I've given the "relative blur" only one sentence, and have not said anything that isn't strictly correct. I haven't suggested that any particular amount of "relative blur" is good or bad; I've pointed the reader to van Walree's article, and the reader can decide for herself whether it's relevant. JeffConrad 03:10, 13 June 2007 (UTC)
I also wonder if we aren't getting carried away with this topic (I'm certainly as guilty as anyone) and giving it far more emphasis than it merits. This isn't to say that it's unimportant, but so are most of the other sections. The article is already fairly long, and several comments have been made about the surfeit of images. JeffConrad 22:54, 12 June 2007 (UTC)
Sure we are. That what wikiaddiction does to you. Dicklyon 23:07, 12 June 2007 (UTC)
Dick, the "proportionality" holds only for fairly distant background objects; with the expansion to include foreground objects, it totally breaks down, and I neglected to adapt for the change. One way to use "proportional" in the restricted sense and still cover backgrounds short of infinity might be to say that, for a reasonably distant background,
${\displaystyle b\approx {\frac {fm}{N}};}$
we rely on many similar approximations to arrive at the simplified equations. JeffConrad 22:54, 12 June 2007 (UTC)
Yes, that's the thing to do. I figured it was obvious when I wrote the version that only mentioned the infinitely distant background, but you're right that being explicit about the approximation is a good idea. Dicklyon 23:07, 12 June 2007 (UTC)
I'll make that change. Upon further thought, Odo Benus's suggestion to make the comment in the text probably is the simplest approach—one sentence should suffice. I'll also add the defocus distance that I mentioned and see people think. JeffConrad 23:40, 12 June 2007 (UTC)
Well, I took two sentences, but in them I also stated some assumptions that may have been obvious to us but not to the casual reason. I hope the current form addresses Odo Benus's concerns; I don't show the basis for the claims, but I don't know how to do so without substituting for the subject distance, and I think that would be getting pretty complex for the "basic" formulae section. In any event, see what you think. JeffConrad 03:10, 13 June 2007 (UTC)
Jeff, thanks. I think it's much better now. Dicklyon 04:11, 13 June 2007 (UTC)
Yup, it is much better now. However, the sentence "Outside the DOF, the blur increases with the distance from the subject." may confuse people if they interpret "Outside the DOF" as a condition for the blur increase. For the blur also increases with the distance from the subject inside the DOF. Odo Benus 16:33, 14 June 2007 (UTC)
Hopefully, the last change will eliminate the potential confusion. The case could even be made for giving the ratio ${\displaystyle b/c}$, with the implication than when ${\displaystyle b/c<=1}$, ${\displaystyle b/c=1}$. One could describe the blur in terms of CoCs; such a ratio would format independent. I'm not sure that it would add much in this context, though.
On unattached participles: put "${\displaystyle b}$" after "differentiating" if you must, but I don't think it would add much—there is no ambiguity about what is being differentiated. I had originally thought of using "differentiation", but, like many -tion words, it seemed unnecessarily abstract. Use of the participle in this context in mathematical texts is common. The objection to unattached participles usually derives from ambiguity; that certainly isn't the case here. JeffConrad 23:28, 14 June 2007 (UTC)
Ambiguity arises with wrongly attached participles. Your participle is unattached in a "sentence" without a noun. It is true that dangling participles commonly appear in mathematical texts; that is why the author instructions of many scientific journals expressly warn against them. Anyway, there are probably more important things to discuss. Odo Benus 11:31, 16 June 2007 (UTC)
Many expressions like this have long been accepted usage; it could even be argued that "differentiating" is a gerund in this context. In any event, let's not quibble about whether this particular usage is acceptable; I've added the "${\displaystyle b}$", which is also common form for mathematical texts. I've also added a sentence explaining the significance of the sign of the derivative; if it's superfluous, get rid of it. JeffConrad 21:47, 16 June 2007 (UTC)

Not all limited-DOF photographs involve separating flowers or cats from distracting backgrounds. Upon further thought, it seems to me that some mention needs to be made of the recognizability of objects, as much for situations in which an object must be recognizable (e.g., evidence and surveillance photography) as for situations in which they should be unrecognizable—I've made many photographs of the former type myself. It would be nice to look at one of Siljander's books, but absent that, Williams probably would suffice as a reference. I'm not sure the discussion belongs with the formulae, however.

On a related note: would the section "Artistic considerations", which initiated the fascination with foreground and background blur, be better titled "Selective focus"? This isn't to suggest that artistry isn't involved, but that "selective focus" is the common term (at least in the U.S.A.), and its use makes content of the section more obvious to a reader scanning the article. Also, is "differential focus" sufficiently common in British English that it should be mentioned as a synonym? JeffConrad 00:17, 15 June 2007 (UTC)

Good idea on the new section title. I hadn't heard of "differential focus", but looks like it is pretty common. Thanks again for all your concientious work on this article. Dicklyon 03:52, 15 June 2007 (UTC)

## Chabacano's new figure

This figure is interesting. Mighty large, and not particularly helpful at illustrating where the size of the blur circle comes from, since the crossing of rays in front of and behind the focal plane is a tiny hidden detail. For now, I'll just shrink it a bit and copyedit the caption. Dicklyon 17:29, 15 June 2007 (UTC)

I tend to agree; the diagram is certainly more attractive than mine, but I'm not sure that it really illustrates what's happening. When the request for additional diagrams was made, I had thought of adding a couple of diagrams similar to the one in the Derivations section, but less cluttered. This could be added if people think it it would help.
The captioning illustrates once again the rather casual alternation between DOF and background blur. It's hardly unique to here; a quick review of every photographic text that I have confirms that for good or ill, it is almost universal practice to speak of employing shallow DOF (limited DOF/selective focus/differential focus) to isolate a subject from the background. Consequently, I think that's the terminology we should use. Though DOF and blur are different quantities, shallow DOF and background blur are really two ways of looking at the same thing. What usually isn't stressed is that the amount of background blur also depends on the distance between the subject and background. I'm working on a way to say this succinctly; perhaps a diagram also would help, though getting a reasonable scale might be tough because of the horizontal space required to illustrate the distant background. I'm also mindful of the comments about the clutter of too many images; I assume that, at some point, this would apply to diagrams as well. JeffConrad 19:48, 15 June 2007 (UTC)

Whatever the figure's merits, I find it rather confusing in the subsection "Focus and f-number". Logically, it should be close to the section "Effect of f-number", but without some further shrinking, I can't find a graceful way of putting it there. JeffConrad 22:07, 16 June 2007 (UTC)

Hi, I drew this figure because I tried to understand the relation between aperture and DOF and after browsing the internet some time I did not find good simple figures and explanations for it, so finally I did this draw for es.wikipedia, and eventualy placed it here too. I thought that an isometric diagram would be better, because I have noticed that most of people just skip standard optical diagrams and formulae, as they find them obfuscate, or hard and then they just memorize recipes like "big aperture->small DOF" as if it was product of magic :) (that is the only explanation I can came up to explain why so many photographers do not understand what is going on with this things apart from "reducing aperture will increase depht of field" when the try to explain it in their blogs or home pages). If you have improvements, please tell me and I will modify the diagram. Maybe the crossing lines in front of and behind the image plane should be emphasized in the caption, or maybe a mark (a small black circle) could be placed to emphasize them. I also dislike it in the focus and f-number section, but I couldn't find any better place. Finally, if you think that would be better to remove it, do it without hesitation.
Also, if you have more ideas for diagrams I would be happy to draw them. Thanks for the copyedit. Chabacano 03:40, 17 June 2007 (UTC)
If you could work on clarifying where the rays intersect the focal plane, and make the fuzzy spots more disk-like, it might help clarify where the circle of confusion comes from. Thanks for offering. Dicklyon 03:56, 17 June 2007 (UTC)
I've made yet another copy edit in attempt to say what the figure really shows; if we're not there, I think we're certainly closing in. I'm assuming that we really don't care whether how aperture size is decreased. I agree with Dick's comment, but I think perhaps the greatest value of the figure is in showing that the spade, heart, and club all appear sharp with the smaller aperture. JeffConrad 07:45, 17 June 2007 (UTC)

I was thinking in adding this closeup of the details, although maybe it just adds complexity. I tried to make the disc thing by increasing the size of the blurred spots. It is less real (now the blurred spots are "bigger", not only blurred), but maybe is more comprehensive and no noticeable. What do you think, better or worse? Thanks for your comments. Chabacano 10:13, 17 June 2007 (UTC)

The closeups certainly are illustrative, but they do add complexity, as you noted. The depiction in the main figure now is much better, though—I think if you simply extended the red rays to meet, the illustration of blur would be more than adequate, especially when viewing the full-size figure. JeffConrad 19:25, 17 June 2007 (UTC)

### Accuracy

The diagram discussed above appears to be slightly inaccurate. The circles of confusion are, in the SVG, drawn as blurred ellipses. I'm not sure what convolution kernel the SVG standard calls for for "blur", but it looks like it's probably Gaussian, not a circle. The circle of confusion should be drawn as a lighter circle not as an amorphous blob. —Ben FrantzDale (talk) 17:20, 26 January 2008 (UTC)

## Circles?

I'm not well versed in optics and am reluctant to tinker with this excellent article. But something strikes me as an oversimplification. We read: Precise focus is possible at only one distance; at that distance, a point object will produce a point image. At any other distance, a point object is defocused, and will produce a circular image (my emphasis). I believe that this is only true if the limiting aperture (in photographic applications, normally the iris diaphragm) is circular. In Image:Diaphragm-detail.png the diaphragm consists of a number of arcs that approximate a circle fairly well; however, in plenty of cameras that I have encountered -- notably early examples of "shutter-priority" automatic exposure (the photographer sets the speed, the camera sets the aperture) -- this is not so, and out-of-focus point sources of light are rendered as blurry octagons or even pentagons.

The crudest diaphragm would be triangular, and somewhere on the web there's an article that shows what happens to out-of-focus light sources via a triangular diaphragm.

And with mirror lenses you'll have what approximate to annuli (rings), though of course these are indeed circular. -- Hoary 00:53, 12 September 2007 (UTC)

Good point. The assumption of circular aperture is the conventional simplifying assumption, and we should just say so. Dicklyon 00:57, 12 September 2007 (UTC)
<homer>Mmmmm... Donuts of Confusion...</homer> -- Coneslayer 17:52, 12 September 2007 (UTC)

In a sense, I guess the link is from olympuszuiko.com, though it's actually to a personal blog by the registrant of that domain. I think we already have plenty of these links—we're starting to approach link spam. If someone disagrees and thinks the link should be restored, though, I won't quarrel over it. JeffConrad (talk) 23:30, 11 December 2007 (UTC)

I made a diagram to replace the fence and flower examples. I don't want to just replace it since it seems like a large change to the page, and I don't know if this is better. The fences don't really help a lot, and here it is easy to see the difference, and I have f/32 as well. I have 2 versions, the rolled-out and the animation, I don't know which people like more. They are of the same images, but the gif had to be indexed. Only one of these should go on the article, of course.

DOF at various apertures, from f/2.8 to f/32 using a macro lens at the minimum focus distance.

Hustvedt (talk) 02:39, 19 December 2007 (UTC)

I can't make much sense of the pictures. Without a familiar subject, it's hard to get a good sense of the depth. Dicklyon (talk) 07:14, 19 December 2007 (UTC)
Hmm, that is quite true. It is more apparent that it is a series of the miniature Christmas tree lights when the aperture is at f/32, so would it be better if I reversed the order of the images, or should I look for something else that would be better? Hustvedt (talk) 17:34, 19 December 2007 (UTC)
I don't think reversing the order would make a great deal of difference. I think the flower images are fine; the biggest objection to the fence images is that the DoF differences aren't quite as obvious as we might like. I agree with Dick that a reasonably familiar subject is essential. JeffConrad (talk) 23:18, 19 December 2007 (UTC)
Ok, how about this? I went for as simple as possible, and here I have a ton of contrast to make it easy to see what is going on. I hope you guys like this version. I only made an animation because the tall version is just huge. Hustvedt (talk) 02:56, 20 December 2007 (UTC)
This diagram illustrates some interesting behavior, such as the light and dark inversion at small f-numbers, but this is pretty esoteric for the average reader. Again, a more familiar subject (preferably, non-macro) would be much easier to comprehend. The two flower images sufficiently illustrate what happens with macro images. JeffConrad (talk) 20:44, 20 December 2007 (UTC)

## New section Obtaining maximum DOF

Although the purpose of using the hyperfocal distance or the object field method is probably obvious to most of the major contributors, it may not be so to the average reader. Hopefully, the new subsection clarifies the purpose. I eliminated the reference to bokeh because it really doesn't make sense in the context.

I think this section should also have a subsection on Zone focusing. Although zone focusing often is used to describe the “zone” of sharp focus that obtains from a particular focus and f-number, it is also possible to determine the focus and f-number from the required zone, as is discussed in §7.4, Focus and f-number. I'll see what I can put together if no one has a strong objection.

On an unrelated minor issue: I propose that we replace “formulae” with “formulas” throughout to make the article less pretentiously academic. JeffConrad (talk) 02:20, 12 January 2008 (UTC)

## New lead section 11 February 2008

I've made yet another attempt at a lead section; until we get this cleaned up, I don't think the article is a candidate for much of anything. I think there's still plenty of room for improvement, but hopefully this latest attempt will help get the process off dead center JeffConrad (talk) 01:06, 12 February 2008 (UTC)

## DOF and Lens Aberrations

I'm not an expert on optics, but I do wonder what is the cause of DOF. My current understanding is that spherical lenses have a type of aberration that causes limited DOF. Perhaps someone who is more knowledgable than I can comment and make appropriate links to the page on lenses, which has illustrations of various types of aberrations. 129.176.151.7 (talk) 14:54, 21 March 2008 (UTC)

The usual approach to DOF ignores both diffraction and aberrations, and just assumes a perfectly converging cone of rays. Put another way, the only aberration considered is the defocus aberration. It's a simple geometry problem then to find out how much the rays are spread for objects at different distances, and to compute the range of distances that keeps that spread within a selected bound. That's all there is to it. Dicklyon (talk) 01:49, 27 March 2008 (UTC)
As Dicklyon says, it's not caused by any "aberrations". It's just a result of geometric optics. If you have a pinhole camera with a big pinhole, it'll make blurry pictures (blurred by the shape of the pinhole). If you add a lens, you'll get a sharp image if it's in focus but you'll go back to the same blur shape if it's out of focus. —Ben FrantzDale (talk) 02:05, 27 March 2008 (UTC)

## Betacommand edit of 26 March 2008

I don't consider the Cambridge in Colour tutorial link spam. It's been in this article for quite some, and none of the substantive contributors seems to have had an issue with it. Unless someone has an objection, I think we should restore the link. JeffConrad (talk) 21:48, 26 March 2008 (UTC)

that site in question has been repeatedly mass added by the webmaster and others working for that company since 2006. Recently the spammer has been active again. due to the aggressive and forceful method of the spammer their links have been removed countless times. βcommand 21:52, 26 March 2008 (UTC)
I agree. I have removed their links from numerous articles myself; it seems too spammy. Dicklyon (talk) 22:24, 26 March 2008 (UTC)

## 35mm MP area

For a 35 mm motion picture, the image area on the negative is roughly 22 mm by 16 mm (0.87 in by 0.63 in).


That's the camera aperture for Academy (1.37:1). While that may indeed by the image area on the negative, almost no one shoots with that as their intended viewing aperture (or aspect ratio). Is this really what DOF calculations are based on? [Also, it seems weird to give apertures to only two decimals, since normally they are given to three]. Thanks. jhawkinson (talk) 21:44, 3 May 2008 (UTC)

For DOF calculations, you don't need much accuracy in the format size or CoC. If the standard frame is cropped a bit, it doesn't change the format size or CoC criterion or DOF enough to be concerned about. Dicklyon (talk) 23:03, 3 May 2008 (UTC)
The format may have some marginal effect on the DoF mainly because of the method of projection and the fact that most motion picture theaters use a constant screen height and adjust the width of the sides. This means that an Academy ratio film uses the least screen area but almost all of the frame area, while a 1.85 film will crop a significant portion of the frame in the projector, but require a much larger screen area. Therefore, the magnification of a frame will vary within an identical venue depending on which format is being projected. The magnification effect will also be determined by the absolute size of the screen and the distance of the viewer, though, so I would hazard to guess that the CoC number for motion pictures is determined to tolerances able to accommodate many of these parameters where probable. Girolamo Savonarola (talk) 06:09, 4 May 2008 (UTC)

## Effect of lens aperture: entrance and exit pupils

I'm all for being strictly correct, but I think we'll simply confuse most readers if we discuss pupils at this point. Except for extreme closeups with highly asymmetrical lenses, the difference in pupil sizes/locations has almost no effect, and I think we quite reasonably confined discussion of pupillary magnification to a separate subsection. JeffConrad (talk) 00:47, 8 June 2008 (UTC)

I agree. I also left you a comment on your talk page before I noticed that you commented here. Dicklyon (talk) 01:05, 8 June 2008 (UTC)

## Exposure compensation

I take issue with the text

"For example, if a 35 mm camera required f/11, a 4×5 camera would require f/45 to give the same DOF. For the same ISO speed, the exposure time on the 4×5 would be sixteen times as long;".

I understand that the f-ratio needs to be converted between formats. However, the conversion leads to the same aperture diameter, i.e., assuming the same exposure time, the same total amount of light on the sensitive area. While the intensity (light/square mm) is lower on the larger format, the larger format also has a larger light collecting area. The latter cancels out the loss in intensity. Therefore, I don't see why an increase in exposure time (or, alternatively, ISO sensitivity) is necessary.

Either the text is erroneous or it should be amended by an explanation as to why a compensation is needed. Note that obviously a compensation would be needed if the format stayed the same, i.e., to maintain the same EV from f/11 to f/45, obviously the exposure time needs to be ~16.73 times as long, but the above text refers to a change in formats. ClassA42 (talk) 22:29, 10 November 2008 (UTC)

Exposure depends on light intensity, not total flux. At infinity focus, a given combination of f-number, exposure time, and ISO speed leads to the same exposure, regardless of lens focal length or image format. As focus is decreased from infinity, exposure increase is needed precisely because the same light flux is spread over a larger area, decreasing the intensity. JeffConrad (talk) 04:16, 7 November 2008 (UTC)
Isn't the loss of intensity due to the focus decrease the same for both formats? Are you saying the loss is greater for a larger format? ClassA42 (talk) 22:29, 10 November 2008 (UTC)
The format is irrelevant to the required exposure time increase for lens extension; I mentioned lens extension simply to illustrate that when intensity decreases, exposure time must be increased to maintain the same exposure, whatever the format. Again, it's intensity, not total flux. JeffConrad (talk) 01:09, 11 November 2008 (UTC)
Putting it another way, ISO speed is defined in terms of the required photons per area, not total photons. That's why the text includes the qualifier "for the same ISO speed". If instead you used an ideal photon-counting detector of unlimited resolution, no exposure increase would be needed to get the same image quality from a given total number of photons; but photographers never think that way, because film speed is based on intensity at the film; as a result, a given exposure on a larger format leads to a higher image quality (much better resolution relative to photon shot noise). Dicklyon (talk) 06:40, 11 November 2008 (UTC)

## New Equations 17 Nov 2008

I am proposing some changes to the Derivations of the DOF Formulas. I find the derivations can be simplified by first deriving (simply) a set of exact equations and then showing how the one approximation affects all the equations. I have used "exact" equations without an explicit caveat about the assumptions that are mentioned as Limitations. I also added a derivation for the "One third rule" that goes directly at the fraction rather than at the related ratio of the distance in front and in back of the focusing distance. I replaced the arguments that allow the approximation of the DOF for macro with ones that are more apt. I also provided a derivation and procedure for the calculation of the DOF limits from the aperture and focusing distance. Using reciprocal distances makes derivation and calculation much simpler. The changes are based on derivations and explanations in Appendix H of Photographic Exposure Calculations and Camera Operation by Prais. Jeff, I like the variables that you used in your paper. (Nice work.) I think they are much clearer in the relationship between variables. They are also very similar what is used in Prais. The presentation of the Depth of Field Formulas in the first part of the article would be helped with some closer connections with the derivations. --Calculist (talk) 22:41, 17 November 2008 (UTC)

I haven't studied the changes in detail yet, but it looks mostly OK. Can you please take care of fixing the heading case to conform with normal wp style (sentence case)? And there's what appears to be an error where you say focusing beyond hyperfocal decreases the near limit. In fact, the near limit increases to the hyperfocal distance as the focus distance recedes to infinity. Dicklyon (talk) 03:43, 18 November 2008 (UTC)
This bit: "The fraction of the depth of field in front of the focusing distance is often and erroneously claimed to be one third of the depth of field" should be done better, and in a different place. This "rule of thumb" is not a claim about exact DOF, and doesn't belong in the exact section; in the approximations sections, it would be better to discuss in a positive way when it is a useful approximation, rather than call it "erroneous", which is what I'd called WP:OR; if you want to cite someone that calls it erroneous, that would be OK, too (this one calls it "certainly incorrect" while honoring it as a useful rule of thumb). But it's sometimes correct, and often useful, to think of DOF as being about twice as much behind as in front, even though it's almost never exactly so; this treatment is typical. Even more useful if you temper with the extreme cases: about equal in front and behind for macro shots, and infinitely more behind when at hyperfocal for further. The notion of a sequence of fractions fits well with Piper's "consecutive depths of field" idea, but doesn't really suit the continuous analysis you provided. Some more sources here will help you find a more positive and typical way to present it; amusingly, a couple of them state it backwards. Dicklyon (talk) 04:15, 18 November 2008 (UTC)

I think some of the additions are helpful, but for the most part, I thought it was more clear as it was. Most of the changes seem to simply reflect personal taste. If they remain nonetheless, they should be cleaned up. A few specific comments:
I question the statement that begins “Since photographers more commonly measure distances in front of the lens”; some photographers undoubtedly do, but many measure it from the image plane because that's how most hand-camera lens distance scales are marked.
The distance H was clearly intended to represent the approximate hyperfocal distance; defining it as special unnamed parameter adds unnecessary confusion. Introducing uh adds a yet another nomenclature for object distance (we now have D, H, s, and u). Preferably, these distances would all use the same symbol (such as s or, preferably, u, as was done in the material added to Focus and f-number from DOF limits) with appropriate subscripts.
Units don't usually belong in derivations (e.g., under Approximate Depth of Field Equations). With the units mentioned, the equations are incorrect without additional constants.
It's probably OK to put all the approximations in one place.
It's certainly OK to examine the near:total DoF ratio, but it's confusing to look at it that way and later examine near:far (e.g., under Near:far DOF ratio). I agree with Dick that it probably doesn't belong on the new “exact” section.
It seems pretty strange to use H in the context of closeups (which is usually the only context in which DoF is expressed in terms of magnification.
Use of the obscure aperture number in place of the far more common f-number seems pretty offbeat; what's wrong with a WL to f-number as we have done elsewhere?
I see absolutely no purpose to the material added at the beginning of Focus and f-number from DOF limits, and take issue with the accuracy of several statements:
“The depth of field equations are a pair of equations that allows photographers to calculate the limits of the depth of field”
This seems a pretty capricious designation; the term was previously used to refer to all equations relating to DoF.
“It is possible to use these equations to precisely calculate an aperture and a focusing distance from the preferred limits of a field of focus found in the field--even when focusing beyond the hyperfocal distance.”
These equations won't ever give a focus distance beyond hyperfocal.
There also are several spelling errors, numerous typographical and formatting errors, and at least one reference (prais) that is cited but not listed at the end. JeffConrad (talk) 09:08, 18 November 2008 (UTC)
Jeff, thanks for the careful review. I think for now it will be best to revert this major change and then when he has time to work it over, try it again, taking our comments into account. Dicklyon (talk) 15:35, 18 November 2008 (UTC)

After further examination, I don't think it's such a good idea to introduce the approximate equations without including the exact equations in the same place—it's not obvious just how the equations simplify, forcing the reader to go back and forth. Including the exact equations with the simplifications, e.g.,
quantity = exact ≈ approximate
would address this, but seems unnecessarily repetitive. I also don't see the need for a section on “exact” equations; isn't a derivation presumed exact unless a simplifying approximation is introduced? JeffConrad (talk) 06:20, 19 November 2008 (UTC)

Okay, here are some things to think about as I make some of the changes:
One-third rule:
I evidently did not word it strong enough if Dick still thinks that the rule should be used. I don't have a problem substituting wording (for instance, "certainly incorrect" for "erroneous"), but the point is that when you look at the mathematics, the "rule" should be "dishonored". The mathematics, that is, an critical examination of exact formula for the fraction, says, "There is no rule." Another way of putting that is: A "one-half rule", a "one quarter rule", a "one-twenty-fifth rule", and a "40% rule" are all just as useful as a"one-third rule".
The formula says simply that it is not generally true that one third of the DOF lies in front of the focusing distance. It is specifically true that in one specific instance (s = H/3), but by and large it is false. Rules by definition are not true in one of many instances. (That is the definition of an exception.)
The rule is not even an approximation. Is one-third an good approximation to one half? to one twentieth? In what situations does the approximation hold? The claim seems to be "in all situations". That does not sound like an approximation.
(Proof by contradiction) Suppose that the "rule" is valid. Then what DOF are you going to use? The only place that the "rule" is valid is at s = H/3. The DOF at this point is H/4. Are you suggesting using this one value for the DOF at all focusing distances? No? Are you suggesting calculating and using the DOF for each focusing distance? If you are, then you can calculate the limits for each focusing distance, and you find that "rule" is inaccurate. For instance (Prais p296), a 50 mm lens set to f/11 has a 9 m hyperfocal distance. Focused at 8 m, the near limit is 4 m, and the far limit is 75 m. The fraction in front is only 5%. Focused at 1 m, the near limit is 9/10 m, and the far limit is 9/8 m. The fraction in front is 44%. I would not call either of these close to 33% (especially considering the values only run between o% and 50%). The bottom line: There is no "rule" because the "rule" as stated is generally invalid. This is what the readers need to be told.
(If anything can be said, the fraction in front is one half less the fraction of the focusing distance to the hyperfocal distance.)

No, I think you totally missed the point; it's not that you "did not word it strong enough"; I totally understand the extent to which it is not literally true except at a unique distance of about one-third the hyperfocal distance. But we're here to report, not to analyze and criticize. We can report the "rule of thumb" without implying that it's more than a useful approximation, and we can report criticisms of it; but we can't pretend it's a "rule" and insert an original debunking of it. As to whether it's useful or not, that depends on how you look at it; in general, it's correct that the DOF has more behind than in front; the "twice as much behind as in front" rule of thumb is useful as it reminds photographers to focus somewhat closer to the front than to the back of the region of interest. Of course, if you try to apply it literally when the "behind" stretches to infinity, you'll focus at infinity, which is not the right thing to do, but photographers will usually apply it less literally than that. A more accurate rule would be to set the focus at exactly the center of the range on your focus distance scale (assuming that scale is linear in lens extension and hence nearly linear in reciprocal distance); maybe you can find a source for such a rule and report that, too. Dicklyon (talk) 23:28, 22 November 2008 (UTC)

What's wrong with the way the “1/3” rule is currently handled? We state that despite what's often claimed, the rule is only true at one distance, without dwelling on it. I'm not sure deprecation is needed or even appropriate. I personally think the “1/3” rule is nonsense, and never make use of it. But the article is arguably better without my editorial comments.
Setting focus to the point on the distance scale midway between the near and far points to be within the DoF is well established; it's simply the hand-camera implementation of the image-side relationships that are already covered in the article. Unfortunately, this is usually almost impossible with the scales on autofocus lenses.
There's yet another technique for setting focus. For a planar subject at an angle to the image plane, setting focus to the middle of the image area actually sets the harmonic mean of the near and far distances. In other words, exactly what photographers learn not to do is sometimes actually the right approach. To my knowledge, this was first reported by Martin Tai in a post Hyperfocusing the Tulips to photo.net on 25 May 1996. The technique can even be further generalized; see Christopher Jones's article. JeffConrad (talk) 03:12, 23 November 2008 (UTC)
Thinking about the equation for near:total, it can be described in words as the fraction of the DoF in front of the point of focus is exactly half the fraction of the (true) hyperfocal distance behind the point of focus. The way to visualize this is from the point of view of the hyperfocal point to the camera. Picture the point of focus relative to the hyperfocal distance, and move it to half that distance. The relationship between that new point and the hyperfocal distance is the relationship between the point of focus and the DoF. Note well that the new point can move/be anywhere between the hyperfocal point and the camera, so the focusing point can be placed anywhere within (relative to) the DoF. There is not one special value. Making this useful requires values for and visualization of the hyperfocal distance and the depth of field. I think that I would rather work from an immediate, exact calculation or a table of near and far limits. But then, ignorance and the one-third rule is bliss.
${\displaystyle {\frac {u_{s}-u_{n}}{u_{f}-u_{n}}}={\frac {(h+f)-u_{s}}{2h}}}$ exactly --Calculist (talk) 14:20, 23 November 2008 (UTC)
If you can find a source for that relationship, we can discuss it in the article. Dicklyon (talk) 18:53, 23 November 2008 (UTC)
The relationship is easy enough to derive. But how is it an improvement over what we have, especially the approximate relationship for near:far:
${\displaystyle {\frac {s-D_{\mathrm {N} }}{D_{\mathrm {F} }-s}}\approx {\frac {H-s}{H+s}}\,.}$
I agree that the “1/3” rule isn't much use, but as I have said, I think we cover it adequately as it stands, debunking it without getting carried away. I honestly can't see either the proposed equation or the one that we have being much use in the field. Because the current equation is simpler, I'd stick with it.
Ostensibly, it's probably easier to think of focusing 1/3 of the way into the scene than to split the foreground and background in a 1:2 ratio. But it's not really that simple. The “1/3” setting (or the proper one) apply to the distance between the near and far limits of DoF; unless something else has been done, these points aren't known. If one simply choses an f-number, the hyperfocal distance can be calculated, and focus is simply set to that distance, and the “1/3” (or whatever) rule is irrelevant. If, alternatively, the near and far limits are chosen, the ensuing calculations (tedious on the object side, simpler on the image side) determine the f-number and focus, so again, the “1/3” rule is irrelevant.
Again, I think the article as it stands covers this more than adequately. JeffConrad (talk) 22:42, 23 November 2008 (UTC)
Ah! You're starting to see how the near:total ratio is easier to visualize than the near:far ratio. To my knowledge, Prais is the first place I have seen the near:total ratio expressed precisely. (It looks like the book came out this year.) He's pretty definite about the invalidity of the "rule" in the book and on a web page. We're pretty much in agreement that the "rule" has limitations. My point is that, given that we now have an precise expression for the ratio (as a function of focusing distance), straight algebra (allowed for making conclusions under Wiki rules) allows us to offer that the "rule" is wrong most of the time. If we, as editors, saw something that failed to use the rules of algebra, we would be within our purview to reject it. Right?
It might be nicer if there was only Dick's more-behind-than-in-front rule because that is always correct. We need to have the near:total ratio in the article because it is precisely an equation for the quantity to which one-third refers. --Calculist (talk) 01:42, 26 November 2008 (UTC)

Notation:
Jeff's paragraph "It seems pretty strange to use H in closeups..." and his statement "The distance H was clearly intended ..." together are a great example of the problems with the current notation. It really needs to be improved. There are a lot of connections that can be illustrated with notation that can help the reader--especially the novice. Here are some things that have worked:

• Use d or dc for the diameter of the circle of confusion.
• Use Da or da for the diameter of the aperture. It would be hard to get away from Da because N = f/D or N = f/Da is so frequently seen. Asymmetric lenses create a problem. Du ad Dv might as the front and back diameters might make a recognizable connection for the reader in this context.
• Use u and v as distances connected by the focusing equation. They look alike, and they are close in the alphabet.
• Use subscripts on all pairs of u and v. Without a subscript someone could interpret simply u to represent the set of three distances, but get confused when focusing distance does not have a subscript.
• Use lowercase letters as much as possible. Uppercase creates emphasis like D for DOF or DOF itself. Just Like Not Capitalizing Each Letter In A Sentence Is Hard To Read, and using all caps in an e-mail is effectively SHOUTING, using UPPERCASE letters is harder to read. We are no longer in eighth grade using a single formula with all caps. The viewer sees lots of formula here.
• Use n, s, and f as the subscripts for near, subject, and far. Assigning a subscript to the focusing (subject) distance is a problem because there is no better word than far for far and f is focal length.
• Use uh for the hyperfocal distance, and h for the super-parameter f2/Nd that simplifies many of the equations (without approximation). Equate them as needed.
• Use p for the ratio of diameters of an asymmetric lens.
• Think twice about using y as a horizontal distance or a "characteristic" distance. It carries some weight as an arbitrary coordinate (not necessarily simply a distance) in the vertical direction.

The idea is to make it easy to read, to make it consistent, to make connections in context, and to avoid double or imprecise assignments.

I would be more inclined to consider a change of notation is you cited a source that does it that way. Dicklyon (talk) 23:28, 22 November 2008 (UTC)

I could go along with some of the changes, but I agree with Dick that there should be reasonable conformance to common usage—in other words, I would be unpersuaded by citation of one esoteric source. The role of an encyclopedia is to report rather than to proselytize. A few specifics:
• The use of c (or sometimes C) for acceptable circle of confusion is so common that I think d or dc, no matter how logical you consider them, is a nonstarter.
• I'd be fine with using primarily lower-case subscripts because they're easier to read, especially with HTML-rendered TeX. I'd be careful of using too many upper-case quantity symbols because the math then becomes harder to read, much like putting a sentence in full caps (which is why I prefer c for circle of confusion).
• Most sources with which I'm familiar don't subscript the focused (or subject distance), but simply give it as u. It's one less thing to decode, and the “subject” may not be in exact focus when considerable DoF is required.
• For object and image distances, I prefer u and v, with appropriate subscripts, but as I recall, Dick and some others felt this might be a bit intimidating to many readers. I agree that DN may introduce unnecessary confusion, but H and s, whether or not the most systematic, are well established in the photographic literature. Consequently, my concern with using H in the manner proposed remains; because of the common usage, the association with hyperfocal distance, exact or approximate, remains. JeffConrad (talk) 03:12, 23 November 2008 (UTC)
Jacobson, Ray, and Attridge in TMoP use u, v, and h. I believe that it is the most technical text in photography. They tend to mimic standards and other research efforts (lots of the time without any additional processing). Even though I find Ray's DoF derivation full of unnecessary complexity and assumptions, it's an appropriate model (except for the capital letters that have no association with the geometry and that make the derivation even more confusing).
I strongly advise against doubling up on the definition of a variable like h. It causes confusion for the reader. --Calculist (talk) 01:42, 26 November 2008 (UTC)

Aperture Number:
I prefer aperture number to f-number for at least these four these reasons:

• "f-number" is not the standard notation. ANSI Z38.4.7.1950 Standard Lens Markings allows "f/", "f", "f:", or "f-stop" followed by a number for the "relative aperture".
• "f/number" is precisely the aperture diameter Da = f/N. Using f/number as a label doubles up on its meaning potentially causing confusion. (See notation.)
• "f/number" tells the viewer that focal length is the concept on which they should focus, while I want them to think aperture.
• Those who know do the extra work to make the association. I like to be a writer who makes it easy on my readers where possible. (See customer service. :->)
I don't understand; does someone refer to the f-number as an "aperture number"? Who does so? I don't think it's a common practice. Dicklyon (talk) 23:28, 22 November 2008 (UTC)
With all due respect for ANSI Z38.4.7.1950, I take issue with the statement that f-number isn't the standard notation; it's commonly used in more recent standards and elsewhere in the photographic literature. And f-number refers to N rather than f/N. I'm not sure I've ever seen “aperture number”. As Dick and I repeatedly said in similar discussion about “shutter speed”, it is not our prerogative to invent new terminology, even if we thought it would help. In this case, I don't even think it would help. JeffConrad (talk) 03:12, 23 November 2008 (UTC)

Finally, The Big Stuff (Organization of the Whole):
I attempted to recast the organization of this whole section as an exact followed by an approximate section , but I did not have enough time and input about the significance of some parts to integrate everything. Jeff's suggestion of quantity = exact ~ approximate make sense to me for the approximate section. The real benefit is in using the approximate section in this format as the reference from the front sections.
I put the "fraction in front" derivation with the exact stuff because it can be done exactly.
I left the "Near:far DOF ratio" and "... from DOF Limits" separate at the end because I need a sense of how important the near:far ratio is to large format photographer or if it can be replaced with the exact front:dof ratio. Jeff, are you making the point about the s ~ H/3 limitation of the "rule" or do you have another purpose?
I sense that LF photogs use the formulas "from DOF limits" for the image side, so I left part of that section in place. I'm also thinking that it is possible to derive the equations in this part of the section simply from the similar triangle equations at the top of the derivation section to make the connection easier to see. I didn't get a chance to look into the "FG and BG blur" section.
Since proposing my changes, I looked at the asymmetric stuff in vanwalree and in Jeff's pdf and see that the equations for the sym and asym cases from similar triangles are the same type (proportional and linear relations between vn or vf and vs), so the derivation from there is the same. It should be simple to present the similar triangle equations and the final equations for asym lenses in the section for exact results for asymmetric lenses, and put that section after the sym section and before the approximate section. BTW, Prais offers diagrams that show the similar triangle tactic works for points off the lens axis. That makes me wonder whether this analysis based solely on the focusing equation is restricted by paraxial optics as an assumption. Only if the focusing equation assumes paraxial optics, is it the case.

I think it's a tossup between near:total and near:far; the former is probably more common for general photography, and the latter probably more common for closeup work. I don't think format comes into play. If it's a tossup, I'd leave things as they are.
Replace s in near:total with (1+m)f/m for close up work. --Calculist (talk) 01:42, 26 November 2008 (UTC)
Focus and f-number from DoF limits are usually done on the image side in all formats. In LF, the measurement is often direct; in medium format and small format (i.e., helicoid-focused lenses), it's done with the lens DoF scales. Or at least it was before the advent of AF lenses. Until early 2004, some Canon EOS cameras included “Depth-of-field AE” mode, which did much the same thing (the purported “7/17” rule to the contrary not withstanding). Again, these techniques are simply various implementations of the image-side formulas given in the article. And these techniques actually have been put to practical use (perhaps without photographers' being directly aware of it), in contrast to most object-side formulas, which seem to get used primarily in endless academic discussions.
There was some hesitance to include any derivations, because even they probably aren't of interest to most readers (we've had occasional vandalism by folks who apparently aren't math fans). I decided to include a basic derivation because it's quite simple and illustrates that there's little magic involved, in contrast to a lot of nonsense on the web. But we nonetheless had to stop somewhere.
We moved the derivations to the end to make it easier for the average reader to skip them. I had considered including full derivations of the formulas for asymmetrical lenses, but left it out because it didn't seem that relevant to the general audience; the article can't include everything, and this seemed a reasonable cutoff. This article isn't primarily a mathematical treatise; we included numerous external links for the few readers who actually want all the details.
The similar triangle technique indeed works off axis, and the proof would arguably be more elegant if done that way. But we still rely on paraxial optics, because the thin-lens equation itself depends on the small-angle approximations for sine and tangent. JeffConrad (talk) 03:12, 23 November 2008 (UTC)

I Lied. Some small stuff:
Neither the equations I presented in the "... from DOF limits" nor the ones Jeff presented there can "give a focusing distance beyond the hyperfocal". The value of the far limit is not defined in mathematical parlance because infinity is name for a limiting situation and not precisely a value. The two sets of equations are the same equations expressed in different ways, so they should give the same results. However, most anyone will have a difficult time substituting infinity for the far limit in Jeff's version. The reciprocal version that I offer has the added benefit of making the step to the equations for the image side simple by substituting 1/u = 1/f - 1/v.
BTW, my quick derivation of the approximation for N in that subsection suggests that an additional approximation was used. I'm expecting something like N ~ (f2/c)(vn - vf)/(vn vf).
The new sequence of steps is not driven simply by capricious taste. I can offer value and logic for the order usually based on "need to know" (what do you need to know at this point?).
I could not figure out how to put Prais into the references and how to get the formatting to be consistent in the time that I had. --Calculist (talk) 17:12, 22 November 2008 (UTC)

I'm not familiar with your source, but I know these derivations are done many different ways. I had a different approach a year or two ago and Jeff reorganizaed it current way, which has been stable for a long time. I think that if you want to change it, you need to convince the rest of us that it's for a good reason. I agree with Jeff that so far it sounds like just a personal taste difference. Dicklyon (talk) 23:28, 22 November 2008 (UTC)
If it's felt necessary, we could mention the special case of infinity; on the image side, this is simply vF = f. The “exact” version of the expression for N is exact; no additional approximations were used.
A “need-to-know” order is probably more defensible in the first section that in a derivation, where the smooth flow of concepts that derive from those that precede them is usually more important.
I stand by my comment that most of the changes simply reflect personal taste, and a taste that's a bit outside the mainstream. I'm amenable to some changes in nomenclature if others go along with them, but for the most part, I'd leave things as they are. JeffConrad (talk) 03:12, 23 November 2008 (UTC)
If there is a derivation section, it should at least be structured so that the reader can see the starting equations, the resulting equation, and any equations or approximations used in along the way. The algebra is left to the reader because algebra is logical argument. Several results in the current article are simply stated. They do not belong in the derivation section unless the above pieces can be added. The start of my alternate offering uses this structure: Similar triangle equations ... focusing equation ... resulting equation ... grouping of terms using N and h (definitions not substantive equations) ... resulting equations ... approximations ... resulting equations I'll revise the whole section incorporating the parts that I left out after the holiday so that you can see what I have in mind. --Calculist (talk) 01:42, 26 November 2008 (UTC)
The derivation section already starts with the proportion relationships "from similar triangles". If there's a probem in the section, please point it out more specifically, or simply fix it. Dicklyon (talk) 05:12, 26 November 2008 (UTC)

I've reread the derivation section once again, and for the most part, I don't see may places where the procedures used to reach the final equations haven't been clearly described, especially in the first section. It seems to me that we currently include all that you propose to add. If you have some specifics in mind, it would help if you could mention them. Again, I'd really like to see how what you have in mind fills a gap or improves the article rather than just reflects a personal preference. I think we'd be wise to avoid offbeat stuff such as “focusing equation” when nearly everyone else refers to it as the thin-lens equation.
It does appear that the introduction of the image-side equations under Focus and f-number is a bit abrupt, so I've expanded the treatment a bit to show how we got there. See if this works.
The basic equations for asymmetrical lenses are introduced without proof because the reader is referred to other sources for complete derivations. It wouldn't be that difficult to include a complete derivation (I could just about copy it from my paper), but we could easily end up duplicating almost every section in the derivation. Given the relatively small impact of lens asymmetry in most situations, I think we sensibly chose the cutoff that we did. JeffConrad (talk) 08:05, 26 November 2008 (UTC)

## Digitally enhanced DOF: real or just simulated?

I reverted an edit indicating that digital techniques can simulate rather than actually produce increased DOF. Some of the terminology (e.g., “apparent DOF”, “graphically altered”) was a bit off, but the basic question may be valid. Do techniques such as wavefront coding, plenoptic cameras, and focus stacking actually increase DOF? Using the classical optical definition they may not, but should we treat an increased zone of apparent sharpness the same as increased DOF? If we do not, I thing we should apply the same criteria to anything that can't be done with a single focus setting with a conventional camera. I'd consider this question analogous to asking whether techniques such as HDR really increase exposure scale. JeffConrad (talk) 05:47, 22 July 2009 (UTC)

I was the guy who made that edit. I admit it was a bit clumsy, as I am a photographer, not a writer. I take issue with the paragraph as it stands on two points, and hopefully I can express them without bogging the expression down with semantics. The first is that depth of field is an optical property, not a property of an end result, and the article is about, or at least should be about DoF, not imaging, and not cameras or post production effects. The second point is that the ability to simulate such an effect is not dependent on digital technology, as a proficient darkroom technician has a number of methods available to an create increased zone of apparent sharpness as well. Perhaps not as elegantly, certainly not as easily, and with a limited tool set in comparison, but possible nonetheless. The creation or utilization of methods to alter the appearance of an image doesn't somehow alter the laws of optics, which to my mind is the impression that the paragraph conveys. I feel this creates a disservice to readers who may be at a point where they struggling to understand the concept in the first place. (JasBrunner (talk) 03:57, 23 July 2009 (UTC))

In a sense, I agree on both points, which is why I raised the question here. Like you, I tend to view DoF as s a simple optical characteristic, and I also think there is an unwarranted tendency to ascribe magical properties to anything digital (it's only one technique). You'll notice that I avoided mention of “dynamic range” in connection with HDR, because strictly, it's a misnomer in this context (unlike in application to sound recording, there's nothing dynamic at all). I also generally avoid vogue terms such as “tilt-shift photography” (can you imagine Adams ever having used it?) that are most often uttered by people who have no clue about what they are saying. But the train has left the station on both latter counts; as authoritative works such as The Chicago Manual of Style, as well as most dictionaries, remind us, usage is the ultimate determinant of what is “correct”, and I think that is what must guide Wikipedia editors.
My second point is that even if we agree that techniques other than a single exposure only simulate increased DoF, the impact is more far reaching than just the lead section of this article. The concept should be applied consistently throughout this article, and among related articles as well. We do a grave disservice to the reader when one article says one thing and a related article says something completely different; faced with such, the sensible reader concludes that at least one of them may be wrong, or perhaps that Wikipedia is simply a tale told by an idiot, signifying nothing. But I think to insist (or at least strongly urge) that this concept of DoF be applied across a range of articles needs consensus of more than two or three editors; absent such consensus, I think that, at least for now, this article should be left as it stands. Again, I'd like to see what others think. JeffConrad (talk) 07:26, 23 July 2009 (UTC)

I would like to hear from others as well. Consistency is important, and while Wikipedia shouldn't be a tale told by an idiot, facts by consensus don't serve very well either. I agree with your assessment and comparison to HDR, however point out that the HDR effect isn't the best analogy, because not withstanding the endless subjective discussion on acceptable sharpness, one can choose a CoC as an objective measurement and follow the law from there to a conclusion. HDR can't be reasoned out the same way, as it is an arbitrary effect applied subjectively. HDR is a distortion of reality, or perhaps another view of reality, but in no case did the luminance range of the subject change, merely the interpretation. In regard the the question at hand I have some difficulty with the idea that fiddling with the interpretation changes the facts. Photoshopping my blue shirt to red doesn't change the color of my shirt, would be my pedestrian way to express the position.JasBrunner (talk) 14:46, 23 July 2009 (UTC)

How are these concepts represented in sources? If they're consistent, we should be, too. If not, we should try to clearly represent the points of view in sources. Dicklyon (talk) 15:26, 23 July 2009 (UTC)
Sources? ... We don't got no sources ... I don't have to show you any stinking sources! Sources for a Wikipedia photography article? Ya gotta be kiddin' ...
It's hard to say what the sources for Focus stacking say, because ... well ... there really aren't any sources. The sources for Plenoptic camera and Wavefront coding all seem to speak of extended depth of field, but are those sources reliable? Most are written by the developers of the techniques. Many of the authors are trying to commercialize the techniques, so they have a vested interest in the claim.
I think the issue is mainly semantical—is DoF restricted to its classical optical meaning, even in the face of some “sources” who maintain otherwise? And if so, can we cite a source in support? It seems to me that, at present, we don't really have sufficient sources to make a definitive call. JeffConrad (talk) 04:44, 24 July 2009 (UTC)
I've never been a fan of design by committee; things have always worked out better when everything has been done my way. But not everyone has always agreed, so consensus has sometimes been necessary, perhaps even with a few concessions to dimwits. We face the same situation in Wikipedia; if we simply go making changes to a bunch of articles, we're going to end up in nasty edit wars, which won't do anyone any good. I somewhat cringed at the addition of focus stacking to this article, but didn't think I really had solid grounds for removing it. I suppose I could have insisted on a few reliable sources, but if we strictly applied that requirement to all the articles on photography, we wouldn't have any articles on photography. And I think consistency is as important in the application of rules as it is in describing the facts—one either applies rules consistently or there are no rules, however much we may try to deceive ourselves. But this is really a larger issue, beyond the immediate scope.
I agree that with a choice of CoC, we can readily arrive at a DoF—provided we insist that the classic optical definition is immutable. I don't know that we can do that. A definition that seems equally common (and perhaps more common in the popular literature) is the part of an image that appears sharp.
The question here is analogous to that of HDR, though as always, different is never the same. As with many things, whether HDR is a distortion of reality depends on how far it is taken. It can simply be a representation that more closely matches what was perceived in the original. If we are strict, almost any photographic image is a distortion of reality—the colors don't usually match, the brightness usually doesn't match, and the image is usually two-dimensional. So I think the distortion argument may be a bit peripheral.
As somewhat of a purist, I'm not thrilled about taking claims of extended DoF at face value. But I'm not sure we really have a basis for claiming otherwise, and revising articles to suit. We could say that some sources claim that various techniques can increase DoF, but I'm not sure this would go over well, either. It does seem reasonable to make slight revision to this article so that methods for increasing the region of apparent sharpness aren't exclusively digital, but I would think at least one specific example of a viable alternative would be indicated—I'm not sure I've ever actually seen one, aside from a composite that's obviously not a single image. JeffConrad (talk) 05:20, 24 July 2009 (UTC)
Right, and there are no rules in a knife fight (you know that movie?). Here's a source that refers to "the equivalent of infinite depth of field" and a "Miracle cure for depth of field", as if DOF is a disease. It doesn't say focus stacking increases depth of field, but that it's a workaround, basically. So we could go that way, citing that, until someone comes up with something better. (Better than a book? How can that happen?) Dicklyon (talk) 06:15, 24 July 2009 (UTC)
Better than a book? Depends on the book ... if you look hard enough, you can find one to support almost anything. We could probably safely start with retitling “Digital techniques for increasing DOF” to something like “Techniques for increasing the extent of sharpness” (or something less ponderous, with suitable expansion in the text), and a commensurate change in the lead section. We could cite Johnson, but he's arguably a fairly obscure source, at least in comparison with many of the others cited in the photography articles. But this probably is beside the point—I doubt than many would disagree that any of the techniques can increase the zone of apparent sharpness—the disagreement, if any, will arise from the implication that the techniques don't increase DoF. And I don't know if Johnson is much help in that regard.
We could make the changes to just this article, and ignore the disparity with the related articles, but it would seem to me that many readers would think, "Why does this article say one thing and that article another?" And the chickens may come home to roost (much as with California finance). I'd have a bit of a problem with treating focus stacking differently than plenoptic cameras or wavefront coding. As I've indicated, I'm far from sold on the arguments of a few decidedly self-interested papers. But I don't know that we have solid grounds for refuting them, either.

One possible approach, at least with techniques that combine optics and signal processing (e.g., wavefront coding, plenoptic imaging) is to use the term that the sources for those articles use: extended depth of field. The term has been around for a while, and a web search shows usage in many areas, including scholarly journals and governmental agencies. A book search gives a fair number of hits as well, including the venerable Sidney Ray, who talks of ... gasp ... increased DOF (2002, 232). So my question about whether these folks properly equate their techniques with increased DoF is moot, because it's apparently already been answered. And in any event, the sources don't generally use “increased DOF”, so I stand corrected.
We then go back to focus stacking, to which Extended depth of field redirects. I have a problem with the redirect, because it ignores other equally valid means of achieving the result. Short of writing an article, I don't know of a good quick fix other than creating a disambiguation page that lists the various related articles (and this seems stretching disambiguation a bit).
Going back to this article, I suggest we leave things much as they are, perhaps replacing “increased DOF” with “extended DOF” for consistency with most of the sources. The one remaining issue is “digital”; although there are and have been other techniques (those that Ray describes don't involve signal processing or digital postprocessing), I don't think they were frequently used outside of microscopy (correct me if I'm wrong). So aside from a historical perspective, a strong argument could be made for leaving the mention of digital as it is. If nothing else, digital processing, whether of a single exposure or of multiple exposures, has made the technique available to vastly more people. It's possible that alternatives have been reduced to fringe applications, and WP:DUE might well lead us not to even worry about them. This isn't to suggest that they aren't important; it's simply a matter of the appropriate weighting when the entire topic is covered in one sentence in the lead section. If more coverage is felt necessary, the best approach might be to add another subsection (and perhaps eventually, an article).
Again, after further consideration, I'm for leaving things largely as they stand. We could add a citation of Johnson, but I think the citation would be more appropriate in the main article on Focus stacking. JeffConrad (talk) 21:45, 24 July 2009 (UTC)

So what do we do? I added citation of Johnson to the main article on focus stacking but made no other changes. JeffConrad (talk) 03:08, 27 July 2009 (UTC)

## Gibson ref

Jeff, I see you just added the 1975 Lou Gibson ref. Unfortunately, his calculations and conclusions on macro DOF include a bad error, where he got the wrong magnification into his equation at one step, which led him to conclude that you need to do contact prints to get the best DOF, if I'm recalling it correctly. Anyway, it's a great book, but beware relying on it for his DOF derivation. Dicklyon (talk) 01:30, 22 August 2009 (UTC)

Dick, I'm roughly familiar with Ted Clarke's criticism of Gibson's findings, but haven't investigated in detail. I did notice Gibson's Eq (6), p. 97, which essentially says the total DoF (or “depth of detail”, as he calls it) T is given by
${\displaystyle T={\frac {2NC\left(M+1\right)}{M}}}$
when I think it should be
${\displaystyle T={\frac {2NC\left(M+1\right)}{M^{2}}}\,,}$
which he gives on p. 90. I say “think” because he refers to the total (subject–to–final image) magnification M and projects the CoC C to the subject plane, which is a bit different from what I am accustomed to. Nonetheless, this error (or whatever) has no effect on the optimal f-number (i.e., that which maximizes DoF), though it obviously affects the total DoF. To be honest, I find Gibson's writeup (at least as it appeared in the version I cited) a bit aggravating to follow, simply because one must consult many other pages to find definitions of some parameters, and no support is given for some premises (like Eq. [6]). For that reason, I never really attempted to verify his findings until last night. And I still ignored everything but diffraction and defocus from the camera lens, attempting only to compare his results with Hansma's—so I did not even look at his claim that the magnification must be achieved in camera rather than by enlarging. The results compare quite well for “optimal” f-number, though interestingly, the f-number that maximizes DoF (Gibson's objective) isn't quite the same as the f-number that minimizes the total (defocus + diffraction) blur spot (Hansma's objective).
In any event, my purpose in finally mentioning Gibson was to show that using a root-square combination of defocus and diffraction blur spots isn't exactly a new idea. I'm still not sure it has a solid theoretical basis; I prefer Hopkins's 1955 method using MTFs, on which David Jacobson and I relied in our analyses.
Eventually, I think this article should say a bit more about diffraction, if only to mention that one cannot improve DoF by simply stopping down forever. This has at least two applications:
1. Situations in which extreme DoF is wanted; one simply may not be able to get there from here. Or one may need to employ movements to reduce the focus spread.
2. Smaller CoCs chosen for critical viewing of images captured with high-resolution media. A step or two may work, but diffraction quickly dominates when any significant DoF is required.
JeffConrad (talk) 04:30, 22 August 2009 (UTC)
I agree, the Hopkins 1955 analysis is more correct, and doesn't quite back up the idea of adding the squares of spot diameters from defocus and diffraction; that idea has a solid theoretical basis in convolution, which unfortunately is not applicable to combining a diffraction blur and a geometric blur. The Gibson derivation is aggravating to follow, as you note; I did manage to find the step where he plugged in the wrong M, after corresponding with Ted Clarke about it. Id didn't check to see if he got the same optimal f-number. As long as we're both aware that it's not all quite right, it should be fine. I'd have to get it out and study it again to see what you're saying about the equation above. Dicklyon (talk) 05:50, 22 August 2009 (UTC)
(indent--;) After a further quick look, it appears that Gibson's equation for total DoF is error, though not quite as I had originally guessed. On p. 95, he indicates that total DoF T is given by
${\displaystyle T={\frac {uc}{D-c}}+{\frac {uc}{D+c}}\,,}$
where u is the object distance, D is the diameter of the aperture stop, and c is the CoC, referred to the object plane. This formula is correct, if a bit different from the form in which it is usually given today. Combining terms on the right-hand side gives
${\displaystyle T={\frac {2Duc}{D^{2}-c^{2}}}\,.}$
Because c2 << D2, T is well approximated by
${\displaystyle T\approx {\frac {2uc}{D}}\,.}$
Noting that
${\displaystyle D=f/N}$
and
${\displaystyle u={\frac {m+1}{m}}f\,,}$
one arrives at
${\displaystyle T\approx 2Nc{\frac {m+1}{m}}\,.}$
So I think Gibson should have used the camera magnification m rather than the overall magnification M (= Em, where E is the enlargement). But shouldn't the denominator be m2? The reference of the CoC to the object plane incorporates a factor of 1/m, so that if the DoF is given in terms of the normal (i.e., referred to the image plane) CoC c′, the DoF is given by the familiar
${\displaystyle T\approx 2Nc'{\frac {m+1}{m^{2}}}\,.}$
This error has no effect on the quantity b under the radical on p. 97, so it wouldn't affect the optimal f-number. The error does affect the quantity a, so the value for the DoF would be wrong.
So we can't reasonably use some of Gibson's conclusions. But for the most part, he was conceptually on target, and remains a good reference if care is taken when citing it. Even the root-square convolution of defocus and diffraction blur spots, though weak in theoretical justification, isn't all that bad. Using Hopkins's 1955 method, I get almost the same “optimal” f-numbers as Hansma does using the root-square convolution. And Gibson's approach is essentially the same as Hansma's with a slightly different objective; even if theoretically imperfect, it's apparently much better than ignoring diffraction altogether. And it's infinitely better than much of the nonsense one finds on the web. JeffConrad (talk) 07:15, 23 August 2009 (UTC)
Agreed. And now we have it all on record here. Dicklyon (talk) 15:21, 23 August 2009 (UTC)

## Photolithography

Because the wafer surface is the image plane, don't we really mean depth of focus rather than depth of field? JeffConrad (talk) 03:37, 27 August 2009 (UTC)

## Tag for inline citations.

Every reference has at least one inline citation, so I don't understand this tag. Perhaps the editor could indicate statements that he thinks require additional support. Absent some explanation, however, I'm going to remove the tag. JeffConrad (talk) 05:12, 10 October 2009 (UTC)

Please use ref tags.--Kozuch (talk) 10:02, 11 October 2009 (UTC)
Also, looking at this talk page, seems like you need to read Wikipedia:Ownership of articles. Thanks for listening.--Kozuch (talk) 10:07, 11 October 2009 (UTC)
The author-date reference system is common in the social sciences, physical sciences, and natural sciences, and the University of Chicago Press recommend it for works on those topics. They also additionally recommend it when a work includes both inline citations and substantive footnotes, to avoid the awkwardness of two different tagging systems for notes. Such a dual system is awkward even in paginated material, but is simply a mess in unpaginated material such as Wikipedia; that’s the main reason I've used author-date here. I don't suggest that Chicago are the only word on the subject (as they readily acknowledge), but they're unquestionably authoritative. More to the point, the Wikipedia guidelines clearly indicate that author-date system is acceptable for Wikipedia articles, and the guidelines also clearly indicate that new sources should follow the existing style. This is simply common courtesy as well as common sense.
It would appear that the tag was added in protest to the author-date system used in this article, which is hardly an appropriate use. In any event, every source has at least one inline citation, including page numbers, so the tag makes no sense, whatever the reason for adding it. Accordingly, I've removed the tag.
I've once again removed the link to Bob Atkins’s page on optimal f-number. There’s nothing wrong with Atkins or the article; the article is unrelated to depth of field. The sources cited in this article do address the tradeoff between defocus and diffraction, and are appropriately included. JeffConrad (talk) 01:03, 12 October 2009 (UTC)
I agree with you both. I understand how to use ref tags, but I can't understand how to maintain an article in this other style. Nonetheless, since Jeff introduced this style back when the article was sourceless, and has maintained and expanded it, we should respect and stick with the style he chose. And while Jeff does exhibit a bit of ownership of some photography articles, it's not excessive or autocratic, and he has earned the right watch over the content that he has done so much to improve over the last three years. I have never known him to reject good contributions from others. Dicklyon (talk) 07:20, 12 October 2009 (UTC)
I've once again removed the tag, because it simply makes no sense, as I've already mentioned. It still appears that the tag was added because Kozuch doesn't like the author-date system of references, which isn't a valid basis. I'll concede that this perception has added considerably to my annoyance. In no way do I suggest that this article is perfect, or a good article, or even that it has all the inline citations that it could. But it's much like the New Englander's response to “How's your wife?”: “Compared to what?”. In comparison with most of the other photography articles, I'd say this one is pretty well sourced. This isn't to say that I find “We're not as bad as our competitors” especially persuasive, but I do think things should be kept in perspective.
This article has been dinged before for lack of inline citations; although many have since been added, the documentation still may not be what it should be. But comments like “article needs further sourcing” or “Many paragrapshs and even sections without a footnote at all” aren't very helpful. Again, if there are statements or even general ideas for which someone thinks support is indicated, please give some idea of what they are. I don't necessarily buy the idea that citations/sentence is a valid criterion for documentation, but rather think it should depend on context. Moreover, many of the statements are quite well supported by derivations of almost every important mathematical relationship, and those that are should not require external support. At one time, I was inclined to get rid of the derivations entirely, but upon further thought, think they are probably better retained simply because there is so much extant nonsense on this topic that the only solid approach is to show the origin so that the user can make his or her own assessment rather than rely on my authority vs. your authority. A good example was Dick's comment that some of H. Lou Gibson's formulas were in error; short of showing exactly what the error was, we have no justifiable basis for making such a statement.
I'll readily concede that I have little patience with tweakipeidans who make edits seemingly solely for the amusement of manipulating the words, and really take issue with edits that are at odds with nearly all published sources. It's possible that sometimes, like Van Jones, I may be aptly described by a technical political term. But at other times, especially when it comes to sourcing, I think I'm pretty easy compared to the merciless Dicklyon, who seems to have a pathological aversion to patent nonsense. Especially when unsupported even by published patent nonsense.
Maintaining author-date citations? How hard can it be? One simply gives the author's last name, the date of the work, and preferably, also the page number. I'll concede that manually coding the links is a bit of a pain; at the time I began doing this, the templates for author-date had a number of shortcomings that have since been largely fixed. One interim approach would be to change the link IDs so that they match those generated by the harvard citation templates; I originally used different names to avoid collisions, but in retrospect, I don't think this was the best choice. I'll work to change this so that future inline citations can simply use the harvard templates.
Now it seems to have been suggested that I've created an unmanageable reference system; if so, I'll volunteer to add the needed citations myself—it's really not that difficult. But it would really help to know where those citations are needed.
It's obvious that in some instances, such as this article, I prefer the author-date system, for reasons I've already discussed at length. Again, it's the predominant system in technical journals, so it's hardly as if I've extracted it from the effluvia of the lodestone, and it shouldn't be all that mysterious. Quite honestly, it's never been my instinctive system, but I've so often found the need for substantive footnotes that I've had to revise quite a number of papers, and have grown quite weary of doing so; mindful of this, I now usually use author-date from the beginning. As the University of Chicago realized long ago. But if it's really the wrong choice here, perhaps we should discuss it. I'm not fond of commingling notes and references, and commercial publishers almost never do it, but it's not without precedent in Wikipedia (see, for example, Contempt of cop).
In any event, I'm quite averse to playing games with inserting tags intended for another purpose. If there are really strong feelings about statements that require additional support, let's offer some specific suggestions. We'll go a lot further in improving this article with a lot less effort and aggravation. JeffConrad (talk) 12:15, 12 October 2009 (UTC)
I am not going to place the template all over unreferenced sections... though it is very sad you dont get this. Look at an FA for how to do referencing right.--Kozuch (talk) 14:42, 12 October 2009 (UTC)
Sounds like Jeff gets it just fine. I even like his characterization of me. The problem I've had with this style is that it requires edits to multiple sections to add a ref, and the structure of those things like span tags and ids is unfamiliar to me, and it's sometimes hard to find what to remove when reorganizing material across articles, etc. Plus I find it harder on the reader to go through an extra level of indirection to find what the source is. My preference is to avoid putting substance in footnotes, and just use refs, but Jeff is right that the MOS says both methods are fine. If there are sections missing sources, just add unreferencedsection tags as needed. Dicklyon (talk) 21:25, 12 October 2009 (UTC)

I think sourcing can become an end in itself. Some editors think that almost every sentence needs a citation, and there are some articles that approach this. But I don't think the MOS even remotely suggests that sourcing need go that far. From WP:CITE:
“Sources should be cited when adding material that is challenged or likely to be challenged, when quoting someone, when adding material to the biography of a living person, and when uploading an image.”
I'm not sure this article falls all that short of compliance. This isn't to say that the article couldn't use some additional citations, but I question whether lack of a citation for every statement or even every section merits the tag that was added; were that the case, 90% of articles would get tagged, and at that point, the tag would cease to have any meaning. If a reasonable case can be made for restoring the tag, I don't have a problem with it. But it's very difficult to address only a general comment, and quite honestly, neither “Please use <ref> tags” nor “though it is very sad you dont get this” is very helpful. It would be far more constructive to indicate even general areas where material needs support, as Dick suggested. But again, the MOS doesn't require a citation for every statement, every paragraph, or even every section—it's substance, not numbers.
There are pros and cons to any citation style, some of which are discussed here.
The notes here address issues that sticklers might reasonably raise, but that are probably of little interest to most readers. The notes could be merged into the text, but after looking again at most of them, I think the text would be cluttered and more difficult to read. Perhaps an even better example is the article Scheimpflug principle; if the material in the notes were incorporated into the text, the article would be a mess. Yet without the qualifications in the notes, some of the statements would be incorrect. But I suppose it's open to discussion, just as is the citation style. JeffConrad (talk) 03:32, 13 October 2009 (UTC)

I've changed the format of the id attributes in the citations and references to match those generated by the {{harv}} templates. And I've replaced the <span> tags for the references with <cite> to get the cute highlighting. Unfortunately, the format of the citations generated is slightly different from the Chicago style used in this article, so every instance would need to be replaced. It would be simple enough (and arguably justifiable) to create Chicago-style templates, which I'd probably call {{harvcomma}} or {{harvCMOS}}. “Harvard” referencing is largely a Britishism not commonly used in the U.S., but since the templates would be only slight variations on those extant, I think the naming scheme should be consistent. But if input in the form of
{{harvCMOS|Ray|2000|pp=52–53}}
isn't seen as an improvement over
([[#CITEREFRay2000|Ray 2000]], 52–53),
perhaps it's not worth pursuing.
For what it's worth, I counted 27 inline citations. Admittedly, they're far from equally distributed. JeffConrad (talk) 05:43, 13 October 2009 (UTC)

I've gradually been adding citations over the last year or so, concentrating on statements that someone might reasonably claim aren't common knowledge in photography. Though perhaps it's not quite up to FA standards, I this article is reasonably sourced. I'm not even sure a technical article like this needs as many citations as one on historical or current events; in any event, I don't think it's strictly a numbers game. (for those counting, there are 21 references with 36 inline citations). Again, if there are particular statements that seem to need support, it would be much easier to address them with some specifics.

Girolamo—you were one of the first to suggest that this article was shaky on sourcing; any more recent thoughts? JeffConrad (talk) 05:12, 15 October 2009 (UTC)

## External link to Atkins Digital Depth of Field article

On another issue, I noted that the formula for DoF in Atkins's article Digital Depth of Field is off by a factor of two; compare with Ray (2002, 218). I had mentioned this to him six years ago, but never got a reply, and had forgotten about it. Because the factor cancels out when computing DoF ratios, its omission doesn't affect his conclusions (which are correct), but I nonetheless have a problem with a link that contains an obvious and significant error. I've sent another message pointing out the error; if I don't hear back in the next week or so, I think we should remove the link. We can restore it if the error eventually does get fixed. JeffConrad (talk) 03:32, 13 October 2009 (UTC)

## Effect of cropping on DoF

I reverted the edit 29 October 2009 by 68.33.206.177. I assume the edit was good faith, but it was half thought out, both technically and grammatically incorrect, as well as uncommented and unsourced.

Though it's seldom discussed, cropping does affect DoF if the the final image size does not change: the captured image requires greater enlargement, so the CoC decreases. If it's thought to be of sufficient importance, we could add a treatment of this, though offhand, I don't know what to do about sourcing. At the cost of yet more math, we might be able support it with an analysis similar to that used in DOF vs. format size under Derivation of the DOF formulas. JeffConrad (talk) 04:27, 29 October 2009 (UTC)

I think Leslie Stroebel is a reliable enough source, and quite explicit. Or you could cite my draft paper... Dicklyon (talk) 04:52, 29 October 2009 (UTC)
But I think the edit you reverted was agreeing with us. Dicklyon (talk) 05:08, 29 October 2009 (UTC)
I was about to mention the same link. I don't have the 7th ed. (and I've exceeded my Google previews), but it's also covered on p. 134 of the 3rd. ed., which I do have. As for citing any of the current external links, I think we've been pretty selective about what's included; most explain how they arrive at what they get, so they're amenable to self verification by any reader with a mastery of high school math. Though I don't see a problem mentioning them, I'm not sure WP:SOURCES allows citing them. I realize that a great percentage of articles violate this egregiously, but I'm not sure that justifies doing it here. But perhaps I'm being overly strict.
In concept, the edit was saying what we've said here, but it wasn't stated correctly, and I also think that because lead section ideally summarizes the key points in the body of the article, anything in the lead section needs some treatment in the article text, which the editor did not provide. To be fair, I think you've summarily whacked some similar edits (e.g., the Leica M9 in Full-frame digital SLR) that were less questionable than this one. Had the edit been amenable to a simple correction, I'd have just made it—doing so would have taken less effort than a revert. At the risk of ownership, the issue then would seem to be the extent to which an uncommented, unsourced, and technically incorrect edit that requires significant additional material to justify inclusion creates an obligation on the part of others. I'm not sure that it always does.
But it seems as if you think the material merits inclusion, so I'll see what I can come up with. I don't see a current section where this would fit comfortably, so a new section, perhaps just after DOF vs. format size, may be needed. Consistency would seem to indicate a treatment in the derivation similar to that for format size, again with another section. We could, of course, get by with far less if article quality were of no concern. JeffConrad (talk) 05:46, 29 October 2009 (UTC)
Stroebel also says essentially the same thing in Basic Photographic Materials and Processes, p. 153. JeffConrad (talk) 05:56, 29 October 2009 (UTC)
I agree, it was malformed, and I probably would have "summarily whacked" it myself if you hadn't. And I was kidding about citing me, since we have a good source. Since this point comes up a lot, we should say something -- but I sort of thought we did already. Maybe not. It could be a last paragraph in the format-size section, to just indicate that cropping is the same as choosing a smaller format size. So people who argue that a "crop factor" has no effect get another chance to get the point. Dicklyon (talk) 06:37, 29 October 2009 (UTC)
And as I recall, I protested some of the summary whackings ... the attack of the devil's advocates. I suppose in adding this section, I conceded that we probably should cover this, and I think we subsequently convinced ourselves. We may have already covered this, but only indirectly—we didn't explicitly mention “cropped” formats. I've now added explicit mention of cropping to the lead section, DOF vs. format size in the article body, and DOF vs. format size, so hopefully, the bases are covered. I've seen many silly and seemingly endless discussions on this, so the added treatment probably works to good effect. Since I covered this in at most two sentences, I couldn't see adding two new sections. Hopefully, it's not so buried that a reader can't find it.
Stroebel additionally discusses the effect of viewing distance, but I think we already give that sufficient coverage. The lead section is a bit choppy, but I think it may end up unnecessarily longer if it's given much smoothing. Perhaps someone else has some ideas.
As to your paper, I too was half kidding ... the limitations of written language. Though we'd probably strictly be on shaky ground citing most of the linked articles, many of them, including yours, are more useful than some “official” reliable sources because they explain what was done, including simplifying assumptions, in arriving at conclusions. For example, Stroebel (at least in the 3rd ed.), does not make it clear that some of the DoF comparisons apply only over a limited range of subject distances. And these comparisons fail badly near the macro range for the larger format and near the hyperfocal distance of the smaller format. But we're probably better off strictly following the rules. JeffConrad (talk) 08:18, 29 October 2009 (UTC)

The article now has several instances of enlarging an “image” to a “final image”, which I find a bit awkward and potentially confusing. And if it confuses the editor ... For Adams, it was easy enough to speak of the “negative” and the “print”, but that terminology no longer is really appropriate. I have no better alternatives than “captured image” and “final image”. I think the meaning of the latter is fairly clear, and we've used it for some time. The former finds some support in the sources (e.g., Evening, Langford, Langford et. al.), but it's new enough that it probably should be defined at first mention if we use it here. I think “when the captured image is enlarged to the same size final image” quickly gets to be a bit much, so perhaps the former could be used sparingly. In a few places, I think replacing “if an image is taken” with “a picture is taken” might also help preclude confusion. Any thoughts? JeffConrad (talk) 04:12, 30 October 2009 (UTC)
Certainly something needs to be done. I like to think that I've already grasped the practical basics of DoF, but when I read the following (after markup stripping) --
When an image is taken in two different format sizes from the same distance at the same f-number with lenses that give the same angle of view, the smaller format has greater DOF. When an image is taken in two different formats from the same distance at the same f-number using lenses of the same focal length, the smaller format has less DOF.
-- I'm mystified. The first sentence of that is fine. I believe that I understand the second sentence of that, and it's plain wrong. Let's suppose that I have two cameras: one taking 24x36mm images and the other taking what are commonly called 6x9 images (though they're slightly smaller), both with an 80mm lens. For the former camera, the 80mm lens might be marketed as a portrait lens: for the latter, the (very different) 80mm lens as rather wide angle. I believe that (putting aside internal reflections, spherical aberration, etc etc) the negative I'll get from the former camera will be like the central section of the negative I'll get from the latter camera, and with the same DoF.
Now, I'm willing to believe that I'm wrong, but my guess is that I'm mostly right on the issue but have managed to misunderstand or fail to notice some part of the explanation here.
Both sentences are correct as written. Let's not get sidetracked by aberrations, internal reflections, or how a lens is marketed. When a picture is taken from the same distance with lenses of the same focal length set to the same f-number, the magnification is the same, so there's only one variable left—the circle of confusion. Because the 24×36 captured image must be enlarged more than twice as much as the 6×9 captured image, the CoC for the 24×36 image is less than half that for the 6×9 image; accordingly, it has less than half the DoF. I think this is explained pretty well under DOF vs. format size. You are correct that the 24×36 image will be equivalent to the central part of the 6×9 image; when an image is cropped, the DoF decreases, as also noted here. Stroebel said the same thing over 30 years ago (and perhaps earlier), so it's nothing new to the digital era. JeffConrad (talk) 06:32, 30 October 2009 (UTC)
Because the 24×36 captured image must be enlarged more than twice as much as the 6×9 captured image -- It does? Well yes of course it normally does. (See below.) But let's say you and I are in front of the Taj Mahal and I have these two cameras, each with an 80mm lens. We stand still. (We're an odd couple indeed.) With the 35mm camera, I do a head-and-shoulders of you. I also aim my Mamiya Universal Press or whatever straight at your head. The latter photo is compositionally awful in its entirety, so I just use it for head and shoulders..... Hoary (talk) 10:10, 30 October 2009 (UTC)
I'm afraid I don't follow. Aren't we saying the same thing? Assuming we have the same field of view in each final image, the 24×36 and cropped 6×9 images would have the same DoF, which would be less than the DoF for the uncropped 6×9 image. JeffConrad (talk) 20:03, 30 October 2009 (UTC)
Clearly digital image capture is now commoner than image capture on film, and the balance will continue to swing toward digital. However, medium/large-format digital will continue to be esoteric for some time, and the differences in image size among the digital cameras with which readers are likely to be familiar are not so dramatic. For that reason, I think that even for the second decade of this century it might be more helpful to introduce a discussion of the effect of captured-image size via a comparison between (a) APS or Four-Thirds and (b) a medium-format film size that's of the same or similar aspect ratio.
I agree that the most common comparison is between full-frame 35 mm and various “cropped” formats that use the same lenses. But I think the intent of this article is to be generic and essentially format-neutral, so I think the comparison with 4×5 is apt, especially since DoF ratios of various 35 mm formats are already covered in at least two other articles, including Full-frame digital SLR. There actually are quite a few people who still use 4×5, 8×10, and even larger. JeffConrad (talk) 06:32, 30 October 2009 (UTC)
Yes, 4×5 (or above) would be fine, as you say. -- Hoary (talk) 10:10, 30 October 2009 (UTC)
Where you said "the negative I'll get from the former camera will be like the central section of the negative I'll get from the latter camera, and with the same DoF," you would have been correct if instead you had said "the negative I'll get from the former camera will be like the central section of the negative I'll get from the latter camera, and with the same amount of blur at every corresponding point." But this will not correspond to the same DOF unless you use the same sharpness criterion (same Circle of confusion criterion) for both formats.
But it is more consistent, and more conventional, to take a CoC criterion as some fraction of the image size (for a print), or format size (for a negative or sensor). The smaller format, having a more stringent sharpness criterion (smaller CoC diameter), has a smaller DOF. Your reasoning on this is what we were referring to as a common misconception, which we ought to try to clarify, by citing sources that explain it. Yes, cropping really does reduce DOF if you use the conventional criterion; see for example Alan Horder, The Ilford Manual of Photography, fifth edition, Essex: Ilford Ltd, 1958, which gives the CoC criterion as explicitly affected by cropping, "1/1000 of diagonal of that portion of negative used to make print." For more related history, see my paper on DOF. Dicklyon (talk) 05:37, 30 October 2009 (UTC)
Yes, I follow the logic there. Of course in reality people don't use 6x9 or larger negatives merely for central portions that could just as well have been taken with a 35mm camera. (To do so would be perverse to put it charitably.) But the convention isn't an obvious one either. -- Hoary (talk) 10:10, 30 October 2009 (UTC)
I'd say it's uncommon, but hardly perverse. The most obvious reason for doing so would be a grab shot for which there wasn't time to change lenses, which I think is what you were saying above in the example using the Taj Mahal. JeffConrad (talk) 20:03, 30 October 2009 (UTC)
Right; and my paper discusses that issue quite a bit, esp. in the context of digital multi-megapixel cameras. Dicklyon (talk) 16:54, 30 October 2009 (UTC)
It seems to me that we have a source; if Stroebel isn't good enough, no one is. We additionally explain it in far more detail than any source I've seen, in the derivation but also in the main text. From Acceptable sharpness:
“The acceptable circle of confusion is influenced by visual acuity, viewing conditions, and the amount by which the image is enlarged (Ray 2000, 52–53).”
With regard to cropping, it seems pretty simple to start with assuming visual acuity and viewing conditions of the final image are constant, and work backward; the captured-image CoC is the then final-image CoC divided by enlargement. If the image is cropped, it requires greater enlargement. Again, it's really the enlargement, not the format size. I thought this was covered pretty well, but perhaps not. I hate to create a section with only a sentence or two, but if cropping is getting lost in the discussion on format, perhaps that's what we need to do. JeffConrad (talk) 20:03, 30 October 2009 (UTC)
Incidentally, I'm troubled by the way the introduction now allies deep focus with landscape and shallow focus with portraits. There's a lot of truth to this, of course, but I can think of plenty of shallow-focus landscape photos and deep-focus portraits. How about a change to "conventional landscapes" versus "publicity head shots" or similar? -- Hoary (talk) 05:15, 30 October 2009 (UTC)
I agree that not all landscapes have a large DoF, and not all portraits have a small DoF. But I think they're reasonable examples with which the reader can readily identify. And we qualify them with “may be”, which seems sufficient to me. If we say something like “conventional landscapes”, we really need to explain what that means; I think “publicity head shots” is a bit limiting, and there are probably a fair number of people who don't know what that means, either. And of course it means something else entirely to G. Gordon Liddy. If others also see this as a problem, we could remove the examples entirely, but I think at that point we might be better off removing the sentence entirely. I'm not sure that's a good idea. JeffConrad (talk) 06:32, 30 October 2009 (UTC)
Right. The (stereo)typical postcard is deep focus; I wonder if there are any PD postcards, especially the kitschy Alpine ones with Edelweiss or whatever in the foreground, snowy peaks in the back. And I do realize that attempts to be more informative can easily just add to confusion. -- Hoary (talk) 10:10, 30 October 2009 (UTC)
I can't think of any type of photography that always employs either deep or shallow DoF, especially the latter. I wouldn't necessarily assume that head shots always have shallow DoF. So I think almost any illustrative example would be open to criticism. We could try to add some qualifying words, but I'm not sure they'd be much more than weasel words. Another approach would be to borrow from the section Selective focus, and use something like
“In some cases, it may be desirable to have the entire image sharp, and a large DOF is appropriate. In other cases, a shallow DOF may be more effective, emphasizing the subject while de-emphasizing the foreground and background, perhaps giving only a suggestion of the environment.”
It's a bit more abstract, so I'm not sure it's as informative, but it assumes no stereotypes. JeffConrad (talk) 20:03, 30 October 2009 (UTC)

## Assessment comment

The comment(s) below were originally left at Talk:Depth of field/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

 As a new student to photography, I appreciate the examples that were given, instead of just text. It was helpful. Perhaps it is too simplistic, but I'd like another example such as: (This close up photo with a blurred background and clear subject, which was taken with the following settings on a Canon XXX: xxxxx) 67.169.221.47 (talk) 15:47, 30 March 2008 (UTC)

Last edited at 15:47, 30 March 2008 (UTC). Substituted at 14:39, 1 May 2016 (UTC)