# Talk:Circle of confusion/Archive 1

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## Ancient comments

Depth of field range of distances in which the image is in focus. Depth of field depends of an admissible circle of confusion diameter. There is no objective way to define this diameter.

Can you help me to turn this mess in good English.

Seems like a reference to digital-camera sensor pixel size would be useful here — is it true that if you want to make use of your sensor's full resolution, you need to keep the COC below the size of a pixel? For example, a Canon EOS-20D has a pixel size on the sensor of approximately .064 mm by my calculation. Steve 03:14, 7 April 2006 (UTC)

Steve, that issue has been addressed by Doug Kerr here: [1] in which he compared the visual acuity outlook with the camera resolution outlook. This latter outlook has not been widely accepted, but you can write about it here if you like. I think you slipped a digit in your pixel size calculation, and you might want to choose a COC bigger than that anyway, consistent with the anti-aliasing filter spot size more than the pixel size. Dicklyon 04:26, 7 April 2006 (UTC)

You're right, I did slip a digit, the 20D has a .0064mm pixel size. Thanks. And thanks for the info. Steve 16:07, 7 April 2006 (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 04:22, 11 October 2006 (UTC)

I merged it, with a rewrite and new figure. Dicklyon 05:23, 23 October 2006 (UTC)

Dick, I think the dots should be eliminated from the equations (see Wikipedia:Manual of Style (mathematics)#Multiplication_sign). The MoS seems in accord with most other practice. JeffConrad 07:17, 23 October 2006 (UTC)
Jeff, I correctly anticipated that you would say that. I decided to leave it to you to try to make them look good without dots, because I was having trouble. I don't interpret that MoS entry as saying that the middot is not an allowable option. Dicklyon 15:27, 23 October 2006 (UTC)

## Other edits of 23–24 October 2006

I've tried to simplify and clarify the criteria for choosing a circle-of-confusion diameter limit, which I've termed "CoC" in light of the most common meaning among non–optical designers. I've never heard of 50 cm as the assumed viewing distance (was that really what was intended?), so I replaced it with the nearly universal 25 cm. Moreover, I've never seen a reference suggesting that the final-image blur threshold had anything to do with other than the viewing distance, so I eliminated mention of the final-image diagonal in that context (presumably, the intended reference was to enlargement of the original image).

I think it said 30 cm, not 50. That was among the early conventions (12 inches was, anyway, like the "12 to 18 inches" in the T. H. article). But you're right that 25 cm is more conventional.
I disagree about the final image size not being accepted as a relevant parameter for modifying viewing distance. I have researched this history extensively, the it's all over as one of two alternatives on how CoC should be set. Using a fixed viewing distance and a print size that makes the perspective "correct" is one alternative. The other is to assume a viewing distance that's appropriate to the print size, approximately equal to the image diagonal. Neither of these ignores print size, which is a third alternative. See my draft paper section on "Choosing the COC Criterion" for a rambling discussion and references. Dicklyon 15:25, 23 October 2006 (UTC)
My reference of 25 cm admittedly takes no note of historical assumptions about visual acuity (though at 30 cycles/degree, Snellen's criteria of 100 years ago really don't differ that much from current values). I didn't mean to suggest that final-image size isn't a relevant parameter for modifying viewing distance, but simply that image size doesn't directly affect visual acuity. It's a two-step process: 1) the viewing distance may be dictated by the final-image size, and 2) the final-image CoC is determined by the viewing distance. Let's face—hardly anyone views an image at the "perspective-correct" distance, especially when that distance would be less than about 25 cm. There is considerable argument for viewing an image larger than 8×10 at a distance greater than 25 cm, unless the viewer is David Hemmings or simply is looking to find imperfections rather than to appreciate the image (if you're looking for trouble, it's usually not hard to find). There seems to be one school of thought that critical viewing of large prints requires a very small CoC (e.g., 0.010 mm for full-frame 35 mm format). There are at least two problems with this approach, however: 1) motion blur often is a problem, and 2) diffraction defeats the entire purpose at all but the shallowest required DoF. I discuss this in some detail, under "Diffraction," in my DoF paper (PDF). The conclusion, in essence, is that conventional CoC criteria aren't all that far from the mark. JeffConrad 00:31, 24 October 2006 (UTC)
Ah, yes, but which convention? There's the rub. My DoF paper also talks about the diffraction limit, esp. for macro shooting where it is always a first-order effect to trade off with DoF. Dicklyon 00:45, 24 October 2006 (UTC)
Criteria based on detectable blur threshold, and derived from angular visual acuity, and assuming some reasonable viewing conditions; one could quibble about specific values (as many have ...), but the common assumption of an 8×10 final image viewed at 25 cm (and correspondingly greater distances for larger images) seems a reasonable fit to both necessary and practically achievable conditions. There always will be people who insist on viewing very large images at close distances (I'll admit to having done so myself), but it simply may not be possible to ensure that such people always see an acceptably sharp image. For example, Canon's purported CoC of 0.035 mm (for full-frame 35 mm) has sometimes been criticized as a bit loose. In various editions of Lens Work, Canon state that this value derives from the assumption of 5× enlargement, so it really is in accord with common assumptions about visual acuity and viewing. For an 8×10 enlargement, the common assumptions stated above would dictate a CoC of 0.025 mm, which is easily accomplished by closing down one step from the f-number indicated by the lens DoF scale (or the Depth-of-Field AE mode on some cameras). The attendant increase in exposure time my pose a minor problem, but diffraction isn't an issue unless great DoF is required. The process cannot continue forever, however. There always is a loss of sharpness in the plane of focus once a lens is stopped down a step or so beyond f-number at which aberrations are well corrected, but eventually, further stopping down decreases sharpness even at the DoF limits. With an extremely small CoC (e.g., 0.010 mm) sometimes suggested for "critical" viewing, diffraction becomes the limiting factor for almost any DoF that extends beyond the plane of focus. Similar values for CoC have been suggested in order to capture all detail of which the film (or whatever ...) is capable; however, imaging media are pretty much independent of format, so this approach would use a CoC of 0.010 mm for 8×10 as well (1/20th the common value of 0.2 mm), an obviously unworkable situation.
Simply stated, it just is not possible to have an image with DoF acceptably sharp under any arbitrary viewing conditions. DoF/CoC criteria that derive from assuming an 8×10 final image viewed at 25 cm represent minimum necessary, but they also are not far from what often are the maximum practical. It's possible to reduce these values slightly, but diffraction quickly makes the process self-defeating. JeffConrad 02:12, 24 October 2006 (UTC)
One problem with the whole 8x10 idea is what to do about the 2:3 aspect ratio of 35mm cameras. Use 8x12? or 6.67x10? It's a 20% effect on your choice of CoC. Using diagonals helps, and I think that's why they've been popular. 0.2 mm on 8x12 is d/1830, but on 6.67x10 it's 1/1530, more in line with typical usage I think.

It would seem clear that in most photographic contexts, terms such as "film," "negative," and "print" are now unreasonably restrictive (and there soon may be readers who never have heard of film). I've used "original image" in place of negative, and "final image" in place of print. I don't have especially strong feelings about either term, but it would seem sensible to adopt consistent terminology for which the meanings are reasonably self-evident. JeffConrad 07:32, 23 October 2006 (UTC)

I made a few more edits about that; putting film and print parenthetically to make sure the new terms are understood in terms of the old, in case they're not self-evident to everybody; and changing another film reference to original image. And I reversed the old point that was there about CoC needing to be smaller if the reproduction is blurry, and explained why the opposite is more true. Dicklyon 15:25, 23 October 2006 (UTC)
Doug Pardee's references to "capture" under Limitations of DOF formulae in the Depth of field article suggest "captured image" as an alternative to "original image"; I've used the term myself in a few papers. The role of Wikipedia editors isn't really to create new terms, but some alternative to "film" and similar clearly is needed, and absent consensus terminology in one or more "verifiable" sources, some initiative may be needed here. At the very least, consistency among related articles would seem helpful to the reader. Any thoughts? JeffConrad 01:04, 24 October 2006 (UTC)
I never much cared for the "capture" concept; too vague. But I haven't checked the literature to see if there's a good precedent here. Dicklyon 02:47, 24 October 2006 (UTC)

I still have a bit of a problem with 'The CoC of d/1500 is intended to represent "average" reproduction and viewing conditions.' I don't dispute that it's in common use, but I don't know what "average" means here. There have been more criteria for CoC than I can count, including f/1000 (deprecated for some time), diagonal/1500, diagonal/1730, and many others. I don't have any great ideas for rewording, though, so I've left it alone. JeffConrad 00:31, 24 October 2006 (UTC)

Yes, I agree. I hope I'm not the one who wrote "average", but it's possible. I'll think about it. By the way, the d/1730 never was used by anybody, as far as I can tell, with the exception of an online calculator and a community of people who were misled by web nonsense. Dicklyon 00:45, 24 October 2006 (UTC)
You are preaching to the converted ... Knowledge for the people; give them a light and they will follow it anywhere. It's particularly true for net lemmings (witness "light value"). The only safe bet is to treat anything that doesn't cite a verifiable source as urban legend. JeffConrad 02:23, 24 October 2006 (UTC)
I found this diff in which the quoted "average" came in, way back in '04. Its sentence has evolved over time, and I should have flushed it when I had a chance. My usual way of saying these things is that it's a "conventional" choice based a "typical" condition or something like that. You had backed out one of my "conventional" lines, so now I wonder if that term seems too vague for you. That diff is also where the quotationed "Zeiss formula" came in, though it was a red link for a long time until I wrote the article on it. Dicklyon 02:47, 24 October 2006 (UTC)
There were quite a few "conventionals" in the same sentence ... I just tried to make it more concise; I didn't think my edit really changed the meaning. Strictly speaking, of course, it's one thing to note that a practice is common, but another to determine the basis without a solid history of its usage. Perhaps it suffices to note the practice without attempting to infer the basis (which might be the same for d/1500 as for d/1730 ...). Again, I like criteria that derive from considerations of visual acuity and viewing, recognizing that they don't give the entire picture. JeffConrad 03:05, 24 October 2006 (UTC)

Yet another attempt. A bit general, perhaps, but it avoids assumptions about "average" or "typical." What really matters is the difference between actual reproduction and viewing conditions and those assumed in determining the CoC, which aren't always d/1500 (for example, Canon claim an a 0.035 mm CoC for full-rame 35 mm cameras). I think the "common" assumptions have been stated more than adequately in the preceding paragraphs.

I deleted the reference to apparent DoF because all DoF is apparent by definition. JeffConrad 02:00, 25 October 2006 (UTC)

## Conversion to English units

There would seem no basis for converting the distances to English measure, especially with other values still metric. If there is a valid reason for the change, it should be stated. Moreover, the "normal" viewing distance is usually given as 10 inches in English measure—for the purposes of DoF and CoC, it's equivalent to 25 cm. JeffConrad 20:30, 15 May 2007 (UTC)

## Definition comment

Could someone put in a proper definition at the beginning please rather than just saying that it is something that arises during a situation --82.36.185.145 18:14, 5 June 2007 (UTC)

What are you referring to? The lead already says what it is and what it's caused by, and the next section talks about two situations in which the term is used. Dicklyon 22:13, 5 June 2007 (UTC)

I also think the circle of confusion should change back to what it used to be: circle of diffusion.

"When a lens is focused at (say) 3 ft and the aperture is wide open (say 1.4) only a small section of the scene will be sharp. (at 3 ft) . As other elements in the frame are closer and further away (from 3 ft) their image gets softer. If we were to shoot X-mass lights, their contour will be softer and the image will get larger, dimmer and diffused creating a circle of diffusion. Stepping down the aperture, only the smaller section of the lens gets used (providing a sharper image) the aberrations get corrected and "diffused" image gets "sharper". The circle of diffusion gets smaller up to the point where it may be only a small percentage larger than the image created at 3ft and thus we will accept it as sharp. (close enough to be undistinguished from the sharp one)." http://www.cinematography.com/forum2004/index.php?showtopic=32534&hl=

The circle of diffusion is the increased size of a defocused image relative to a properly focused one.

When were the “good ol days” in was it called “circle of diffusion”? The answer actually is almost irrelevant, because “circle of confusion” is the commonly used term; a Google search for “circle of confusion” gave about 105,000 hits, while a search for “circle of diffusion” gave 73. As has been discussed extensively on several other photography/optics talk pages, it is not the prerogative of WP editors to arbitrarily change terminology.
The proposed definition addresses only one of the two common meanings; the current definition covers both, as Dick mentioned last year. Although “diffusion” might work for the first definition, it doesn't work at all for the second. JeffConrad (talk) 01:18, 9 December 2008 (UTC)

It must have been 1973 or '74 when I got a photography book and this is why I remember it as "circle of diffusion" (but that is irrelevant as you say). Just because is the commonly used term is not a very strong argument (imo of course). There are lots of of other examples in every single domain one could think of. I will not turn this matter into an argument, just offered my 2c hoping to correct something that makes me laugh each and every time I come across,... and here is my explanation:

Light and circles do not get confused. Only people do. Light only gets diffused. Think about it! (and thank you for your contributions) Dan Diaconu —Preceding unsigned comment added by 79.118.233.79 (talk) 22:17, 10 December 2008 (UTC)

## Convolution?

It seems like this article should mention convolution. Also, shouldn't deconvolution be possible? 155.212.242.34 21:07, 25 October 2007 (UTC)

## Table of d/1500 for different image formats

This table strikes me as odd and in one sense misleading. An important reason for using medium and large formats in photography, probably the main reason, is to increase the resolution of the image. The 1/1500 rule gives 5 lpm on a 30 cm diagonal print, which is easily achieved with small format. Medium and large format are used when higher resolution is needed. For example, with large format a wide angle landscape image can be printed at poster size and viewed close up. Another example, professional medium format digital cameras today aim for higher resolution that 1/1500.

So I think including a table that computes c=d/1500 over a the full range of d as it relates to photography is confusing and misleading. I would suggest deleting this section.

Much more interesting and informative would be a table comparing the max coc values required for the image systems in different branches of photography, for example, 4x6 holiday and party snapshots, 20x24 gallery prints, posters, high-end fashion print advertising, 35mm, 70mm and IMAX movies, HDTV, etc. —Preceding unsigned comment added by Nono1234 (talkcontribs) 14:42, 13 December 2008 (UTC)

For good or for ill, all formats give the same resolution at the DoF limits using standard values for CoC; this follows directly from the criteria discussed in the article. Thus 0.1 mm is the standard CoC for 4×5, 0.2 mm is the standard value for 8×10, and so on. Nothing says that one must use the standard criteria, of course. One reason the standard criteria are discussed is so that a person with different objectives can determine a CoC suited to those objectives.
A table such as that proposed might be interesting, but it would be entirely subjective, and almost impossible to support with verifiable sources. JeffConrad (talk) 21:27, 13 December 2008 (UTC)
You're both right. It hardly makes sense to use a large-format or high-megapixel camera and settle for a blur of d/1500. But the d/1500, while maybe not exactly standard, at least has some reliable sources. I've written a bit about this myself, but my "draft" "Depth of Field Outside the Box" remains unpublished, or self-published online, at: http://www.dickyon.com/tech/Photography/DepthOfField-Lyon.pdf. I didn't really get to an answer I'm happy with. While you don't want the COC diameter to scale with format, you also don't want it to remain fixed; somewhere in between might be OK. Similarly, you don't want the scaling d/1500 for high-megapixel digitals, but you probably also don't want a fixed number of pixels as your COC limit either. Something like 1 pixel at 1 MP, 2 pixels at 6 MP, 3 pixels at 20 MP might be sensible. But then you'll always get pushback from people who are not willing to accept that with more megapixels they get less DOF. We should be able to explain this stuff without resorting to an unsourced table of values. Dicklyon (talk) 06:14, 15 December 2008 (UTC)
But as we've often discussed, it all depends on one's criteria. The standard criteria derive from supposedly undetectable blur (about 0.2 mm) for full-image viewing (about 60°) at the near distance for distinct vision (about 250 mm). If any of these criteria change, the permissible CoC changes as well. If, however, they remain largely as stated, then the standard value of d/1500 remains reasonable. Another school, comprising mainly small-format photographers, argue that the CoC should be based on what the film is capable of capturing rather than on undetectable blur. This argument isn't often made by large-format photographers because it would often lead to impractically long exposure times and in some cases impossibly small apertures. The situation may be somewhat different with small-format high-resolution digital capture, because the magnification (which is the main reason for longer exposures with large-format) doesn't change as resolution is increased. Moreover, with greatly reduced noise on some of the most recent digital SLRs, increasing ISO speed (at least up to a point) is an alternative to longer exposures.
One other issue—diffraction—still cannot be avoided. I discuss this in my paper (linked in the article) in the section Diffraction, and particularly under Optimum f-Number from MTF. Although it's usually OK to reduce the CoC by closing down an extra stop or so, one soon gets into trouble going much further, because the increased diffraction actually results in less sharpness. In the plots of MTF vs f-number, I show three different criteria for sharpness, and it can be seen that as the sharpness criterion increases, the maximum usable f-number as well as the maximum achievable MTF decrease. Although their approaches are slightly different, both Paul Hansma (discussed in the paper) and Bob Wheeler (Notes on View Camera Geometry, www.bobwheeler.com) reach similar conclusions, at least qualitatively. As anti-progressive as it may appear, these conclusions seem to suggest that what we've done for years isn't really that far from the mark.
The analyses I've cited are only the opening chapter, and I'm not sure when the next will appear—especially the one examining the situation for high-resolution digital capture (if indeed it is different). The heavy lifting was done by Harold Hopkins in 1955, but I've yet to see it practically applied to photography by a “verifiable” source (whatever that really means in this context). JeffConrad (talk) 08:49, 15 December 2008 (UTC)
I agree with all that. There's still a viable role for tighter CoC, e.g. when shooting landscapes for close viewing, with an aperture size that's big enough to avoid diffraction being a problem. That's what the large-format guys largely do, and so do the high-megapixel guys when they want to show off the resolution that their cameras are capable of. So I argue that there is something important about the notion that "high-end" cameras should choose a smaller COC than d/1500. But using d/1500 is a great reference point to work from. For an example of close viewing, see the description of my friend's photo exhibit The End of Viewing Distance. Dicklyon (talk) 16:46, 15 December 2008 (UTC)
It's not just a matter of using a tighter CoC, though. There is a “minimum” f-number that derives from the CoC, and a “maximum” f-number that derives from consideration of combined defocus and diffraction. As long as the minimum f-number is less than the maximum, the photographer can choose any value within the range. But if the minimum is greater than the maximum, the sharpness dictated by the CoC cannot be achieved. The allowable range is determined by the focus spread; when the focus spread is small, the photographer has considerable leeway; when the focus spread is large (roughly corresponding to large DoF), it may not be possible to achieve the desired sharpness. The CoC also affects the allowable range of f-numbers; a smaller CoC gives a narrower range. I show the tradeoff in my Fig. 14, comparing CoCs of 0.1  and 0.05 mm for a resolution of 12 lp/mm in a 4×5 captured image. Wheeler gave a similar argument with slightly different values; Hansma gave a similar argument with values similar to mine.
Hansma treated my “maximum” f-number as an optimal value, technically ignoring CoC, but in effect choosing a CoC to give the greatest possible sharpness at the DoF limits. Another way of looking at this is that, in effect, the focus spread determines the CoC.
Ultimately, the focus spread determines the extent to which the CoC can be decreased. When the focus spread is small (and this is the case with a fair number of outdoor scenes), the CoC can be decreased significantly, but when the focus spread is large, even the standard CoC may be too small. So I don't think it's a matter of just adding a table of d/2000 (or whatever) for “critical viewing”. JeffConrad (talk) 03:43, 16 December 2008 (UTC)

BTW, I notice that the "APS-C" entry in the table doesn't actually use APS-C dimensions (25.1mm x 16.7mm), but rather those of Canon's 1.6-crop format (22.5mm x 15mm), about a 10% difference. Why not just say "1.6 crop" or something? Snogglethorpe (talk) 08:09, 13 August 2009 (UTC)

## CoC calculation

Hello, There's something that confuses me. When it's mentioned that: "At this distance , a person with good vision can usually distinguish an image resolution of 5 line pairs per millimeter (lp/mm), equivalent to a CoC of 0.2 mm in the final image.". Won't the CoC really be 0.1, as there are 5 line pairs in one millimeter? That's 10 lines in one millimeter, so each line would need a CoC of 1/10mm at most to resolve in optimum conditions. Am i wrong? Norfindel (talk) 23:57, 19 April 2009 (UTC)

It's a crude approximation. But using 0.1 instead of 0.2 doesn't necessarily make it much better. You'd have to plot the MTF and decide what threshold you want to corrrespond to the human resolution limit (which actually also depends on contrast, lighting, and SNR). It's just a handwave... Dicklyon (talk) 01:57, 20 April 2009 (UTC)
Ok, i understand. Thanks for the explanation. Norfindel (talk) 01:47, 22 April 2009 (UTC)

## Preview Changes 7/29/2009

I have spent several hours reading and re-reading the information on this page and on this talk page, as well as the other wikipedia entries on depth of field, depth of focus, hyperfocal distance, etc. to try to understand what is going on here. I think simple explanations in the first paragraph or two would greatly decrease the amount of time people need to spend reading this literature to understand the concepts and to be able to extract the information they need. I tried to accomplish some of this with my small edit to the introduction paragraphs. I think more wikipedia editors need to pretend they are writing for http://simple.wikipedia.org to make the information more easily understood. It doesn't have to be taken to the extreeme that that part of wikipedia is, but simplification and mass reorganization of some wikipedia articles is starting to become necessary. I think for the most part, articles like this are written and edited by the people that know a lot about the technical side of the topic, and when that happens, people that know nothing on the topic can get lost quite easily. I have the same problem in writing and instructing others, but I am making a conscious effort to fix that in myself and bring the concept to the attention of others. Nathan (talk) 15:07, 29 July 2009 (UTC)

Though the edit is obviously a good-faith effort, I don't think it improves the article. It's unencyclopedic, reading like a how-to guide, which Wikipedia is not (see WP:NOTHOWTO). I agree that the previous lead section was a bit terse, and some of the ideas covered may be worthwhile additions. But if the material remains, it needs a significant rework. JeffConrad (talk) 00:22, 30 July 2009 (UTC)
Indeed, it's not ideal, either as it was or with this addition. Perhaps the "two uses" section should be pulled into the lead, and then that added material put back in a more suitable form with respect to the one use that it applies to. For now, I reverted it. Dicklyon (talk) 03:53, 30 July 2009 (UTC)
I think pulling the entire section would be a bit much (and possibly intimidating for the casual reader). I think a sentence or two about each use would suffice. With regard to photography, I'd probably mention only DoF and leave the other topics linked in the reverted edit for elsewhere. JeffConrad (talk) 05:48, 30 July 2009 (UTC)
I've made a first attempt; see how it works. I've avoided mention of hyperfocal distance and depth of focus because I think they're somewhat secondary at this level of detail. I'd have cited Ray (2000, 52) on both the long and short forms of maximum permissible circle of confusion, but alas, there seems to be a typo; it reads “(minimum permissible) circle of confusion”. JeffConrad (talk) 00:32, 31 July 2009 (UTC)

## Blur Spot or Blur Circle?

These terms come up several times, but only one should be used throughout the article after the first mention of both. Should it be spot or circle? And what are these "four tildes" I'm supposed to put at the end? Guyburns (talk) 23:55, 17 April 2010 (UTC)

Blur spot would probably be better. The “four tildes” (~~~~) expand to your name and the date—see Wikipedia:Talk page guidelines#Good practices. JeffConrad (talk) 02:00, 18 April 2010 (UTC)
Looking at how blur circle is used in the section Calculating a circle of confusion diameter, I'm not sure blur spot would be appropriate, because blur circle is used there to describe the projection of the idealized image-side blur circle into object space. I agree that it may be confusing, and at least to me, it seems that the concept of projection into object space needs some additional explanation. I've made a couple of quick changes where blur spot is appropriate. I agree that we need to look at optical spot, blur spot, blur circle, disk, and perhaps a few others. JeffConrad (talk) 02:49, 18 April 2010 (UTC)

## Hockey Pucks

I removed hockey pucks because it was confusing, and was only being used to explain a circle. Unfortunately, it gave the impression that there was something special about hockey pucks that mimicked a tightly-focusses spot of light, so I had to look up hockey pucks. Turned out they are a three-dimensional object and I spent several minutes scratching my head trying to work out how the blur spot on the focus plane became three dimensional. Finally I realised that a hockey fan probably included the reference, but they may have just as well included a reference to anything circular (CD, communion wafer and so on). I think it is unnecessary to explain a circle. Guyburns (talk) 00:23, 18 April 2010 (UTC)

I agree with you on the “hocky pucks”, and the final sentence in that section should probably have a reference.
I reworked your edit to the beginning of the section. The lens focal plane is not the same as the plane of focus; the former is is a plane one focal length from the nodal plane (there's one for each side of the lens). Distances can be measured from any reference, but they're commonly measured from the nodal planes (in the case of the object side, from the front nodal plane), and that's the way we've specified them in this article. Please, please, please be careful about making edits unless you really understand what you're editing. A comment that something is confusing or misleading may well be indicated, but making a change based on what you're guessing may be right does not improve the article. JeffConrad (talk) 02:31, 18 April 2010 (UTC)

## Largest blur circle

I'd like a copy of pages 50-53 from the Sidney Ray book (The Manual of Photography: Photographic and Digital Imaging), the part that covers this "largest blur" topic. The local library hasn't got a copy. If anyone can photograph and gmail to gdburns I would appreciate it. —Preceding unsigned comment added by Guyburns (talkcontribs) 01:40, 18 April 2010 (UTC)

Try a Google search "manual of photography" "circle of confusion" and scroll back to p 50. JeffConrad (talk) 03:15, 18 April 2010 (UTC)

## Revert of edits of 13 April 2010

I've reverted the edits by Guyburns. The edits appear to be good faith, but have several problems:

• They inject considerable unsupported personal opinion.
• The one source, cambridgeincolour, is not citable under WP:V; the claimed value for human visual acuity is markedly at odds with several reliable sources.
• Removal of the nonbreaking spaces between quantity values and unit symbols is gratuitous and at odds with ISO, NIST, and WP guidelines.

Please discuss these changes before making them again. JeffConrad (talk) 08:50, 13 April 2010 (UTC)

### Visual acuity

The claim that visual acuity is actually much greater than suggested by common values for the acceptable diameter of the circle of confusion is a common one in webland, so perhaps it merits some additional comment.

The material with which I had the main objection was the claim of visual acuity of 0.07 mm (presumably, per line pair) at a distance of 250 mm:

“At this distance, a person with good vision can distinguish a line pair if they are spaced further apart than about 0.07 mm (http://www.cambridgeincolour.com/tutorials/depth-of-field.htm). However, in the days of SLR cameras, manufactures assumed a circle of confusion of 0.01 inch (0.25 mm), three times that of human visual acuity at a viewing distance of 250 mm, and used the 0.01 inch standard when providing depth-of-field markers on camera lenses. But the circle of confusion should be chosen smaller than this to achieve acceptable sharpness throughout an image.”

which closely paraphrases the Cambridge in Colour web page, except that it's not clear whence the value of 0.07 mm obtains (the page does not specifically state that value, and it's not clear how it relates to the value of 0.01 inch that is stated).

Similar claims are common on the web, but they're almost never supported by reliable sources. A Snellen chart is based on visual acuity of 30 cycles/degree on a high-contrast, brightly illuminated chart. More recent studies have shown slightly greater acuity; I am told by a local research ophthalmologist that a more realistic value for a high-contrast sinusoidal pattern is in the mid to high thirties. In a normal pictorial photograph, the contrast, and consequently the visual acuity limit, is less. Most sources I've seen (e.g., Ray 2000; Ray 2002) accordingly adjust the value; for example, the oft-cited value of 0.2 mm for a final-image CoC viewed at 250 mm is equivalent to 5 lp/mm at that distance, or about 22 cycles/degree. I haven't consulted the original sources Ray cites, so I can't comment on how much the adjusted values are supported by actual testing. I suspect some guesswork was involved.

Not all presumptively reliable sources agree on the practical value. A white paper Depth of Field and Bokeh in the Carl Zeiss Camera Lens News #35, April 2010 (under The diameter of the circle of confusion, p. 19) claims visual acuity of 8 lp/mm at 250 mm, equivalent to about 35 cycles/degree, close to the value I mentioned for a high-contrast sinusoidal pattern. The paper refers to “the ability of the eye to recognize resolution with periodic black & white patterns”; if indeed the reference is to a high-contrast pattern, the value may be a bit optimistic for normal pictorial photographs. But without additional information, it's tough to tell. And that's precisely the problem with so many sources, reliable and otherwise—they often don't indicate exactly how the values are derived.

The claimed value of 0.07 mm is equivalent to 14.2 lp/mm, or about 62 cycles/degree, almost double the value for 20/20 (6/6) vision, so it's simply not credible without solid explanation and support. Perhaps it derives from using a single line (e.g., the lower stroke on the letter E) rather than a line pair, and failure to account for lower perception at contrast typical in pictorial photographs. Perhaps it relies on Campbell and Green (1965) cited on the University of Utah web page on Visual Acuity but overlooks the fact that purpose of that study was to determine the degradation caused by optics of the eye, and takes the value of 60 cycles/degree as the actual acuity.

This article may imply that the common value of 0.02 mm for the final-image CoC is more hard and fast than is actually the case; if we can find reliable sources for other values, perhaps we should mention them. Ray's value probably includes some arbitrary adjustment, but at least he gives a reasonable description of how it was obtained. Without similar support for something else, I think that's the primary value on which this and related articles should rely. JeffConrad (talk) 03:18, 14 April 2010 (UTC)

### Problems with the article

Response by Guy Burns —Preceding unsigned comment added by Guyburns (talkcontribs) 11:10, 16 April 2010 (UTC)

There are a number of problems with this article, apart from being unclear and overly complicated even before the maths start. I may be mistaken, but other writers appear to be using this article as definitive and they should not be doing so (see Smart Cameras By Ahmed Nabil Belbachir, p6).

I'm quite familiar with the topic, and think I understand the math pretty well, yet I, too, find the article more complex and less accessible than it should be. Unfortunately, people grab all sorts of things from the web that are pretty shaky; this article is far from the worst of those dealing with photography that have gone viral with apparently little more scrutiny than ensuring that all material was copied and pasted. Many people copy uncritically from other sites when they should not do so. A good example is Cambridge in Colour; though the presentations are generally accurate and nicely done, there is some material that isn't correct (like that which I reverted here). And that site almost never cites reliable sources in support, even with fairly controversial material. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

1. CoC is defined differently in two different places: the circle of confusion (“CoC”), and the circle of confusion diameter limit (“CoC”). It should be made clear early in the article that one term -- and one alone -- will be used thereafter.

This unfortunately reflects common usage. In most contexts, circle of confusion is used to mean acceptable (or permissible, or whatever) circle of confusion, or circle of confusion diameter limit, namely, the “the largest blur circle that will still be perceived by the human eye as a point under specified viewing conditions”, which is essentially how it's defined in the article. I agree that sometimes using the more formal term and at others using the the simpler (and more common) term is confusing. I'd opt for using the formal term at the introduction (and perhaps the formal definition), and the simpler term (or just CoC) thereafter, but this might meet with objection from other editors ... always a problem in a multi-author work. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

2. As a definition, what does "the largest blur circle that will still be perceived by the human eye as a point when viewed at a distance of 25 cm" actually mean? Where did that statement originally come from. If no original reference can be found, it should be altered. This statement is being repeated on many websites and it is nothing but confusing when you try to understand it. I suspect it is defining CoC as the smallest point which can be perceived by the human eye. If so why not just say that, instead of bringing in "largest" but then using "largest" to define "smallest".

The statement is essentially correct, and is covered quite well (if not as succinctly) in Ray (2000, 50–53). CoC is not the smallest point that can be perceived by human vision; the detection threshold (for lines or points) is smaller than the resolution threshold. An example: it's far easier to detect a distant power line than it is to recognize that the “line” is actually two or more that are close together. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

3. The article accepts the definition in (2) when it uses the words: "With this definition...", but then does not use this definition, but introduces line pairs as the definition.

It's common (if perhaps confusing) to alternate between a blur spot size and a spatial frequency (usually in line pairs/mm), so we speak of either a blur spot (more casually, CoC) of 0.2 mm or a spatial frequency of 5 lp/mm at a specified viewing distance (commonly taken as 250 mm, the near distance of distinct vision). Equivalently, an angular spatial frequency could be used, as is more common in research ophthalmology. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

4. In the section Circle of confusion diameter limit in photography where it says "And variations thereon". What does that mean? Is it trying to say: "the size of the blur circle depends on the viewing distance. The larger the distance, the larger the blur circle"?

Not all sources use the same conditions as “standard”; distances vary from about 250 mm to 300 mm, and final-image CoCs seem to vary between 0.2 mm and 0.25 mm. Normally, the greater the viewing distance, the greater the CoC. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

5. The caption for the first diagram states: "The depth of field is the region where the size of the circle of confusion is less than the resolution of the human eye (or of the display medium). Circles with a diameter less than the circle of confusion will appear to be in focus." That's just gibberish. First it says that the CoC is less than the resolution of the human eye (so I assume can't be seen), and then it says such circles will be in focus.

I agree this is essentially gibberish. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

6. In the section where the CoC formula is first mentioned, "desired print resolution" defined as line pairs per mm, and a typical value of 5 lp/mm is used in the example. Previously, this figure was called "image resolution". Print resolution is too common a term to be used here. A person reading this might think: "I thought print resolution was supposed to be 300 dpi for a good print." Nothing confuses a beginner trying to understand somethign more than having multiple names for the same item. It just confuses.

I agree that needlessly using different terms, especially technical ones, for the same concept is confusing. I'd go for using final image rather than print, because the former includes display on a monitor or projection onto a screen. In doing so, we're somewhat coining a new term, something best avoided if possible. But I'm not sure we have much of a choice here; at least we've used the term fairly consistently in Wikipedia articles. There's a similar issue with the “initial image”; it's no longer reasonable to refer to the negative (and for users of transparency film, it never was reasonable). In the WP photography articles, we seem to alternate between initial image and captured image (and I'm probably the guilty party). I think we should use the former for conceptual parallelism with final image. Because all of these terms are neologisms that aren't even in widespread use, they're probably properly in scope only from first mention to the end of a particular article, and probably require definition in each article in which they appear. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

7. The first formula for a CoC is unclear, both in its concept and the way it is presented. It might work, but it needs improving and simplifying.

The one that begins, “CoC Diameter Limit (mm) = anticipated viewing distance ...”? If so, I tend to agree. The use of words in formulas is generally deprecated, but for very simple formulas, it may be less intimidating for the reader who is not mathematically inclined. In this case, I think the formula is sufficiently complicated that it would be much better to follow standard practice and use quantity symbols. Some may object to that being too “mathy”, though. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

8. The whole article seems heavily weighted towards 8 x 10 prints and it shouldn't be. I came to this article (as I suspect most other people would in today's digital age), wanting to know about CoC and how I could use it with my digital camera for images projected on a screen. Not a silver halide molecule in sight. The article should mention the historical aspect (8 x 10 prints and so on), but it really should be targeted to a general discussion of what CoC is, and not tie it to one particular technology.

The frequent mention of 8×10 prints may imply that this criterion is to be taken more literally than is intended. Most treatments of DoF base the CoC on a final image viewed at the near distance for distinct vision, usually about 250 mm. They also tend to assume full-image viewing at that distance; comfortable viewing angle is about 55°–60°, which at 250 mm is close to the diagonal of a bordered 8×10 print (obviously, there's some convenient rounding). So the common 8×10 print is a reasonable reference point. Obviously, not every image ends up as an 8×10 print; however, if we assume full-image viewing of larger final images (in whatever medium), the viewing distance will increase accordingly, and the criteria that derive from the traditional 8×10 image viewed at 250 mm still work quite well. If the final-image size and viewing conditions are known at the time a picture is taken, the CoC criteria can be adjusted to suit. But often the viewing conditions aren't known in advance, and even if they are, images are sometimes repurposed in different sizes in different media and ultimately viewed under different conditions than originally envisioned. Hence the fallback to the traditional values. The concept of full-image viewing certainly lends itself to angular criteria; for some reason, though most sources prefer the traditional reference. The two approaches are actually equivalent for full-image viewing. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

9. Angular criteria is disparaged and it should not be. The article states: "Angular criteria evidently assumed that a final image would be viewed at “perspective-correct” distance (i.e., the angle of view would be the same as that of the original image)... However, images seldom are viewed at the “correct” distance." I find that statement bewildering, because the 5lp/mm also has a correct distance -- 250 mm and images are not often viewed at that distance.

I essentially agree with your comment; it's not clear to me how angular criteria assume perspective-correct viewing distances; it seems to me that they rather assume full-image viewing, as discussed above. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

10. If my understanding is correct, CoC is simply a very confusing name for a very simple concept: human visual acuity. We can distinguish so many lines per mm at a certain distance (or it can equally be defined as an angular measurement). That concept ties in very nicely with the todays digital cameras and displays. There is an exact analogy between lp/mm and the way images are recorded in a digital camera and then displayed -- using a certain number of lines horizontally and vertically. There should be less emphasis on the 8 x 10 format and more on the digital formats. Guyburns (talk) 11:08, 16 April 2010 (UTC)

Again, unfortunately, CoC has two meanings, as noted in the article, and we really need to cover both:
1. The actual size of the blur spot
2. The largest defocus blur spot that is indistinguishable from a point (or at least is perceived as acceptably sharp), in the context of DoF
Although CoC as it relates to DoF relies on human visual acuity, the two concepts aren't synonymous. Your restatement of the definition is essentially correct. The name may be confusing, but it's the term used, and we can't simply make up something because we think it might be less confusing. The spatial frequency criterion (either angular or at a fixed distance) is useful because it lends itself to other analyses, such as the modulation transfer function (MTF), and also because it more directly relates to actual research that normally used sinusoidal line patterns. Though we speak of equivalence to a defocus blur spot with the same diameter of the size of a line pair, I'm not sure how much this is backed by actual testing. But we really can't dispense with the blur spot size, because the blur spot, rather than spatial frequency, is the basis for all geometrically based derivations of DoF relationships.
I don't think the article is really as focused on 8×10 prints as you take it to be, but perhaps this merits a closer look.
As should be obvious, I think many of your objections are quite valid. This article has had many authors, some of whom have long departed. And the knowledge of the authors has varied considerably. As with so many of the photography-related articles, editors have ranged from those who really know what they're talking about to casual hobbyists hampered less by what they don't know than what they know for sure that just ain't so. And even authors who generally know of what they speak sometimes disagree on how material should be presented. The result, unfortunately, is sometimes an article that's barely accessible to many readers, especially those new to a subject. JeffConrad (talk) 03:58, 17 April 2010 (UTC)

### Edits of 19 April 2010

I've cleaned up the article a bit to address some of the issues above, though at first glance, it may not seem that much has changed.

• I revised the section Two uses so that the titles for the paragraphs describing both uses are more parallel in thought: in the first case, it's the largest defocus blur spot that looks like point; in the second, it's the smallest blur spot a lens can make with no defocus.
• Where practical, I've used blur spot rather than the several variants, though there still are a couple of places where I don't think it's the right term, so I've left what was in place. In the section now titled Determining a circle of confusion diameter from the object field, I've used blur circle consistently.
• In the section Circle of confusion diameter limit in photography, I removed a few words from the definition at the beginning of the section to make the definition more manageable. We already state the specifics in what immediately follows (and we essentially stated them in the preceding section), so I don't see a problem.
• In the section Circle of confusion diameter limit in photography, I removed a few words from the formulas (we already define CoC to stand for the long term, so we don't need anything else to describe it.
• I removed reference to angular criteria and their having fallen out of favor. All CoC criteria are angular; the real distinction is whether they're tied to the lens focal length or a fixed characteristic dimension of the format.
• I replaced most instances of print with final image to allow for other display media.
• I retitled the section Calculating a circle of confusion diameter to indicate that it's a different approach than used in the section that precedes it.
• I fixed a couple of instances of focal plane where image plane was meant.
• I did some minor cleanup of the equations in the section now titled Determining a circle of confusion diameter from the object field.
• The equations in that section still measure the distance from the lens entrance pupil rather than from the front nodal plane as is done in most of the Depth of field article, but unless a lens's pupillary magnification is considered (and this is seldom necessary), there is no difference.

I hope I've addressed some of the major inconsistencies, though I'm sure I've missed a few things. And like most articles, it still could be improved considerably. I've proposed a replacement for the first CoC formular; if there are no objections, I'll incorporate it, along with a derivation in a section at the end of the article. JeffConrad (talk) 02:37, 19 April 2010 (UTC)

## Formula for CoC; Defocus Blur Spot

Thanks for the link. I searched for the book by Ray but no scanned version came up.

CoC Equation I think the best way to present that formula is to define the variables as single letters, and use those single letters in the formula, the usual way in enginering text books:

X = Y/H

where X is...

Y is...

H is ...

Clear and easy to understand. CoC involves maths. It has to. This first part of this article should not be subject to what someone told Stephen Hawking: "that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation..." Anyone coming to CoC would expect some equations. Let's make them clear and use a clear example.

That's certainly my approach; I find the current presentation almost incomprehensible. Using too much math has drawn objection in the past; some readers have apparently become so angry as to delete entire sections containing equations. If no such objections are raised in the near future, I'll add the material much as presented here. But I'd like to give other folks, especially other contributors to this article, at least a few days to comment. JeffConrad (talk) 07:59, 18 April 2010 (UTC)

I'll go through your equations over the next day or two in detail so that I understand them, but for the moment I can't really comment on their suitability except -- they still look more complicated that necessary. —Preceding unsigned comment added by Guyburns (talkcontribs) 07:12, 18 April 2010 (UTC)

I honestly don't see how they could be any simpler, especially the final one. JeffConrad (talk) 07:59, 18 April 2010 (UTC)

Defocus Blur Spot? Why is the word "defocus" needed? A blur spot has already been defined as: "Point objects at other distances are imaged as blur spots", so it is obvious that it is not focussed. Defocus is simply another word to add confusion. Aren't these three statements clear (removing the word defocus)?

1. ...A blur spot has the same shape as the lens aperture, but for simplicity...

2. ... is that the blur spot be indistinguishable from a point...

3. ...the shape of a blur spot from a lens with a circular aperture is a hard-edged circle of light..

"Defocus blur spot" implies a difference from a "blur spot". What is the difference? If there isn't any, the qualifying term "defocus" should be removed. Guyburns (talk) 06:28, 18 April 2010 (UTC)

I seldom add things like this without reason ... defocus isn't the only thing the that contributes to blurring, as is briefly mentioned in the section Two uses. Because of diffraction, even a perfect lens doesn't image a point as a point, but rather as a series of concentric light and dark rings known as an Airy pattern, which is essentially, a diffraction blur spot. Diffraction is an unavoidable consequence of the wave nature of light, and it's a characteristic all lenses, regardless of design or pedigree. Almost every practical treatment of DoF is based on geometrical optics; although this is often adequate for solving the problem at hand, it's an approximation of the real world. It's (almost) possible to have diffraction without defocus, but it's impossible to have defocus without diffraction. For most practical photography, diffraction isn't a significant factor except when people adopt ridiculously small CoCs for “critical viewing”, but it does become an issue in closeup work. There's really no such thing as a “defocus blur spot” and a “diffraction blur spot”; the two effects combine to produce a blur spot that has characteristics that each would have if it could exist separately; this is very briefly discussed in the section Two uses. Additionally, real lenses suffer from aberrations, especially at small f-numbers.
We typically ignore diffraction when discussing DoF because the treatment would otherwise be so complex as to be of little practical value. But it's at least worth examining to see when it can reasonably be neglected. If you're interested, see my paper and the articles by Paul Hansma and David Jacobson in the External links section of the Depth of field article. For a good idea of what defocus and diffraction blur spots look like, see the Stokseth paper in the References section of that article; it's available through the Harvard Abstract Service: [2]. We ignore aberrations because they're different for every lens. When considerable DoF is wanted, larger f-numbers are typically used, and many aberrations decrease significantly, so ignoring them is reasonable. The same isn't true at small f-numbers; my results and Hansma's are probably meaningless when using a lens wide open, but are much more usable at greater f-numbers, which was the main interest for both of us. The short answer? You can't keep stopping down forever and improve sharpness.
Properly, we probably should say “blur spot due to defocus” because it doesn't exist independently from other blurring. But at least for me, it's just too unwieldy. Perhaps we don't need the qualifier for every mention. JeffConrad (talk) 07:59, 18 April 2010 (UTC)

## Error in Jacobson? And C instead of CoC?

Is this an error? In the last paragraph on p52 he states:

This leads to a practical definition of resolution. A limit is set to the diameter of the image blur circle that is not distinguishable from a true point ... and this is called the (minimum permissible) circle of confusion, C.

Talk about confusing. Doesn't he mean "maximum" not minimum?

I think I know why he choose to use "minimum" -- because of the way he constructed his sentence using the word "not". He is approaching the limit from above. He starts at a point where the blur circle is distinguishable (large), and makes the blur circle smaller and smaller until it becomes a point, and therefore not distinguishable -- thus his use of the word "minimum". Whereas the definition in Wikipedia approaches the limit from below. This should be stated in the article, and I'm going to reword the intro to the definition and run it by anyone visiting this page to make it clear that the limit is being approached by a blur circle that starts small and increases until it becomes distinguishable from a point. But maybe I've misunderstood.

I agree that he's inverted the normal sense, but the way he's stated it is still correct, if confusing. I ask you to please avoid getting too creative with a topic you're just learning—I think it's quite clear as worded, and the treatment you propose is pretty off the wall compared with most others I've seen. So please be careful unless you have a solid source to back it up. JeffConrad (talk) 08:06, 18 April 2010 (UTC)
A suggestion that I should have made with the last comment: propose the rewording here, much as I did with the suggested changes to the formula. It's certainly not a requirement of Wikipedia, but it's a common practice when testing ideas that may not reflect consensus and may be at odds with convention in other sources. JeffConrad (talk) 09:06, 18 April 2010 (UTC)
One other point: we've used the current description fairly consistently in this and several other articles, especially Depth of field, and I think to the extent practicable, we should keep them consistent. It really matters little how the limit is “approached”, as long as it's clearly stated, which I think it currently is. And a double negative is usually not the best way to express something. With DoF, we're concerned with what appears sharp rather than what is unsharp, and accordingly, most sources think of the maximum permissible circle of confusion rather than the minimum. The way Ray states it is correct, but he takes several pages to say what we need to cover in a few paragraphs, so keeping it succinct is usually helpful. JeffConrad (talk) 08:28, 18 April 2010 (UTC)

No wonder this "Circle of Confusion" is so confusing -- because it hasn't been clearly defined for the lay person. Wikipedia refers to it as the maximum permissible C, while Jacobson (who appears to be an authority) uses "minimum", both sources not explaining how the definition is derived.

One other thing: Jacobson uses "C" for circle of confusion. CoC seems very clumsy by comparison. Should this be changed? I strongly suggest that whatever previous authors have used as terminology, that Wikipedia should strive for clarity. We shouldn't be beholden to history. Acknowledge historical terms, but feel free to use clearer terms in certain cases. In this case, C, because the maths section uses C, as does Jacobson. —Preceding unsigned comment added by Guyburns (talkcontribs) 07:05, 18 April 2010 (UTC)

Actually, Ray is the author of this chapter ...
There's a difference between a quantity symbol like c and an acronym like CoC. In mathematical material, acronyms are deprecated; we've used “DoF” in some mathematical material because there simply has never been a widely recognized symbol for it. In We've used CoC, DoF, PoF, and other acronyms in the text because they're far less cumbersome that the spelled-out terms, yet generally are quickly recognizable—which can't always be said for the quantity symbols. JeffConrad (talk) 08:15, 18 April 2010 (UTC)

## CoC definition; equations

I'll have to disagree with you saying that: "the largest blur spot that will still be perceived by the human eye as a point when viewed at a distance of 25 cm" is clear. It may be clear to someone who already knows what it means, but this article should be written so that a typical new visitor to the page can understand it. It needs more explanation. What's wrong with providing it in a sentence or two?

There's nothing necessarily wrong with doing it that way; the most logical approach would be to repeat some of the material in the first case under Two uses. But given that we've just said it does it really make sense to repeat it, especially since the next section is really just an expansion of that first case? One option is simply to more or less eliminate the definition at the beginning of circle of confusion limit in photography. I suggest indicating here what you propose. JeffConrad (talk) 12:03, 18 April 2010 (UTC)

The new equations you provided should not be in the introduction. They are just too intimidating the way they are presented. Put them in the maths section by all means and refer to them. The following equation is more like what is needed in the "non maths" section:

I certainly wouldn't use anything but the final equation under Calculating a circle of confusion diameter, as I suggested. I think it's easier to follow than the current presentation, though perhaps not by much. Perhaps the option to, in effect, specify a visual acuity criterion isn't needed, because most people won't (and probably shouldn't) deviate from the standard value. The problem with any formula with embedded “magic numbers”, though, is that, especially without citation of a reliable source, many people are led to ask, “Where did this come from?” I'll concede that this was my reaction to the current presentation (but at least the “magic number” there is fairly obvious). But perhaps support from a later derivation would suffice. JeffConrad (talk) 12:03, 18 April 2010 (UTC)

"The CoC required of an original image, given an enlarged image for final viewing, can be calculated from the formula (assuming a typical value of CoC for the final image of 0.2 mm):

CoC = 0.0008D/E

where

• Coc is the circle of confusion for the original image measured in mm;

• D is the viewing distance of the final image in mm; and

• E is the enlargement factor.

An example should make the equation clear. Assume a 35 mm slide enlarged to 350 mm (an enlargement of 10 times); a viewing distance of 500 mm. The equation becomes:

CoC = 0.0008 x 500/10 = 0.04 mm for the original slide."

Simple equation, simple maths, and easy to understand.

Except that it isn't quite correct. The angular visual acuity criterion is the same as 0.2 mm CoC at 250 mm, but the actual final-image CoC is 0.4 mm. This would somehow need to be stated more clearly. I agree that the current way it's stated takes a bit of thought to understand, but at least if presented as a normal equation, the reader has some idea what's happening, even if it takes a couple of reads. I also agree with not mixing mm and cm. JeffConrad (talk) 12:03, 18 April 2010 (UTC)

CoC in the Digital World Since photography is now largely digital based, I suggest the section after Two Uses be renamed "Circle of confusion diameter limit in film photography" and another short section introduced, called "CoC in Digital Photography", which would briefly examine CoC in regards to final presentation on a digital screen, with the image from a digital camera.

There's been an ongoing discussion on this at Talk:Depth of field. The bottom line: digital vs. film is irrelevant, unless you have so few pixels that defocus blur spots aren't distinguishable from points, which is hardly ever the case. There is no more reason to consider pixel density (or count) than film resolution. This isn't to say that the imaging medium doesn't affect final-image sharpness (that's why many people still shoot LF); it's simply not covered as part of DoF.

You end up with a simple equation to work out the number of horizontal pixels, "P", required of a digital camera to satisfy the typical CoC requirement. Given a screen "S" mm wide, and a viewer sitting "D" mm from it, P = 1250S/D. Unless my calculations are incorrect, it turns out to be a surprisingly small figure. It appears to me that digital cameras have far surpassed the requirements of CoC when the final image is viewed on a screen in a movie theatre. i.e. For a 15 metre viewing distance on a screen 12 metres wide (figures for the local cinema) you only need 1000 pixels, yet HD screens offer 1920, and upmarket digital cameras offer 5000.

For all DoF treatments of which I am aware, the characteristics of the imaging medium aren't considered. And I don't think we should (or can) break new ground here.
It's hard to tell if your calculations are correct, because it's not clear how you arrived at this equation; it looks to me as though you've taken 5 lp/mm as equivalent to 5 p/mm. But it seems to me that you're mixing two different things; the optical resolution and the resolution of the imaging medium combine, roughly as
${\displaystyle {\frac {1}{R}}_{\text{total}}={\frac {1}{R}}_{\text{optical}}+{\frac {1}{R}}_{\text{medium}}}$
according to a common rule of thumb (some prefer a root-square rather than a linear combination). So that pixel density will contribute significantly to the overall sharpness degradation: with 5 lp/mm, you'd have 2.5 lp/mm overall resolution. We probably can arrive at a similar conclusion from sampling theory, but I'll confess that this isn't my area of expertise, so I can't really comment on what the pixel density needs to be to not significantly degrade the optical resolution.
Looking at this again, you'd need at least 10 p/mm to image 5 lp/mm, and from sampling theory, you'd need at least twice that many to do it reliably (some insist even that isn't always enough). But we don't need to answer that here, because it has nothing to do with CoC, so it's far outside the topic of the article. JeffConrad (talk) 23:31, 18 April 2010 (UTC)
But the key issue is that this is conflating two different issues. Moreover, without a good source (or a very good explanation), this is original research and we can't do it. JeffConrad (talk) 12:03, 18 April 2010 (UTC)

I think a lot of visitors to this page would be very interested in such a topic. —Preceding unsigned comment added by Guyburns (talkcontribs) 09:14, 18 April 2010 (UTC)

This well might be true, but without a good supporting source, it's a nonstarter. We simply can't do original research. So I'd suggest proposing what you have in mind here before adding it to the article. JeffConrad (talk) 12:03, 18 April 2010 (UTC)

## Why is the proposed formula for CoC not correct?

Jeff, please explain why this formula is not correct:

CoC = 0.0008D/E

or a simpler restatement: CoC = D/1250E

The example given in the Wikipedia article results in a CoC of 0.05 mm. Using the formula above gives CoC = 500/(1250 x 8) = 0.05 mm.

It's the same formula as far as I can see, making the same assumptions.

Also, when you reply to my discussions, I think it would be clearer if you posted in a new discussion. Re-reading my own discussions now, it's tricky to tell who is talking. —Preceding unsigned comment added by Guyburns (talkcontribs) 01:53, 19 April 2010 (UTC)

It's not that the equation isn't correct, but simply that it's unsupported by a reliable source and has nothing for the user to go on but embedded “magic numbers” for which it's not obvious how they were obtained. The threshold for inclusion in Wikipedia is verifiability, not truth. Moreover, your formula lacks the option to specify a different criterion for visual acuity; you may not personally wish to change it (and probably most others won't, either), but recognize that not everyone may have the same preference. The current formula (which I think Dick added) covers all the factors just discussed, as I think is reasonable. Finally, I think that unless something is wrong, or a proposed change is a consensus improvement, stare decisis has to mean something. Were it otherwise, any article could fluctuate daily strictly because of personal preferences. What I've suggested is simply the current equation in symbol form, and it includes your suggested simplification. What's the problem?
As for replies under separate sections, that's just not the way it's usually done here. I agree that sometimes threads of discussions can be tough to follow, but putting every reply in a new section has problems as well—it's often tough to seen that a new section is a reply to something in another section. Finally, the number of sections would quickly proliferate to the point that a Talk page would be impossible to navigate.
One more point: please sign your comments with four tildes. JeffConrad (talk) 06:06, 19 April 2010 (UTC)

## Equation for CoC?

Jeff, can you post the equation you intend including? I haven't seen it yet in final form. Can I suggest keeping it simple-looking, which means superscripts and subscripts are an unnecessary complication. Leave those for the maths section.

I've already given it above. But since it doesn't seem to find consensus, I'm suggesting we leave things as they are for now. JeffConrad (talk) 16:06, 20 April 2010 (UTC)

Also, I had to ask what was wrong with my equation because I said: "Simple equation, simple maths, and easy to understand." and you replied: "Except that it isn't quite correct." Yet it is correct, with assumptions clearly stated.

The equation gives the right answer, but the way you describe it isn't correct. See my comments above. JeffConrad (talk) 16:06, 20 April 2010 (UTC)

And let me be playful, Jeff. You said, re me making changes: "But please don't make changes unless you're sure they're correct." But, to use your own words, they do not have to be correct (your words again: "Wikipedia is verifiability, not truth."), so does that mean as long as I can verify an untruth, I can put it in?

I should think it obvious that material must be both accurate and verifiable. Stated otherwise: truth is necessary but not sufficient. You know this as well as I do. JeffConrad (talk) 16:06, 20 April 2010 (UTC)

Let's be realistic about this. Just because I can't find another source to verify CoC = D/1250E, doesn't mean I can't put it in if I include all the assumptions; given that that equation gives the same result as the equation already there. It's just got a simplified look. Guyburns (talk) 14:04, 20 April 2010 (UTC)

Actually, it does mean that ... Challenged but unsourced material can be removed at any time. And be assured that it will be. That it gives the same answer as the current equation is irrelevant. The current formula isn't given in common sources, but at least it includes enough information that a reasonably competent person can figure out where it came from. Even so, I've suggested that it needs support, which is why I proposed the derivation section above.
You seem to be missing a key point: I haven't suggested that we can't use your formula; rather, I have suggested that we also need to include the more general equation so that it's more obvious that we didn't just make it up. And why should we include your equation but not the one that I had proposed first? Yours is simpler and you like it? I'm afraid I'm unpersuaded.
Finally, your equation doesn't allow for adjustment for visual acuity. It may address your objective, but it ignores the objectives of some others, even if I think they're nuts. Why do you think your objectives are more important than anyone else's?
Bottom line: absent support from a reliable source, it ain't gonna happen. Though I think my symbolic form is better than the current textual form, the current form is manageable. So unless we can reach a reasonable consensus for changing it, stare decisis rules. JeffConrad (talk) 16:06, 20 April 2010 (UTC)

## Edits to clarify CoC

I have made some minor edits to improve clarity and unnecessary qualifying words ("defocus").

The Two Uses section has three definitions in the space of a few paragraphs:

1. For describing the smallest blur spot that is indistinguishable from a point;

2. The diameter of the largest blur spot for which an object is acceptably sharp;

3. The diameter of the smallest circle that can contain 90% of the optical energy is a suitable definition.


And in the next section there is a fourth definition:

4. largest blur spot that will still be perceived by the human eye as a point.

Uhhh ... I blew it on the first one in a recent edit, and I fixed it accordingly as soon as I read your comment.
The concept of DoF is described in various ways, and perhaps they're not always perfectly consistent. The general idea is that the DoF is the region that “looks sharp”, or “appears to be in focus”. Authors sometimes disagree on whether the unsharpness is undetectable or simply “acceptable”; the material based on visual acuity and cited from Ray leans toward the former. The fourth definition is really about the same as the first two (with the first one corrected ...); I have no problem with deleting “the human eye”. I disagree that the third definition is too mathematical; that's just the nature of a real blur spot that results from combined defocus, diffraction, and aberrations. It's briefly pointed out that we're dealing with a very simplified model of what's really happening, and we then move on using that simplified model. As I've said, though, it should have a source. I'll add a tag. JeffConrad (talk) 05:44, 19 April 2010 (UTC)
After discussion with Dick Lyon, I've revised the third definition: the WL'd article includes a source, so I don't think we need to repeat it here. There may be one remaining issue: every source I've seen (including a different work by Smith that I have) applies the criterion to a “best focus” condition (which varies with criteria used to determine it) rather than a defocused system covered under the first use; I don't think the concept changes much, but it might be tough to say what the “right” value is, so I've avoided giving a specific value. The key idea is that the uniform hard-edged blur spot discussed in this article and most similar treatment never exists in the real world.
The WL'd article for defocus refers to defocus aberration, which is often how it's handled in more sophisticated treatments than this article. But it's largely a notational convenience, so I've retained the common practice in photography of treating defocus, diffraction, and lens aberrations as three separate effects. JeffConrad (talk) 08:01, 21 April 2010 (UTC)

I intend making changes to remove the inconsistencies listed above, both in the Two Uses section and in the Introduction. It is confusing to have the one concept defined in terms of "largest" and "smallest".

But please don't make changes unless you're sure they're correct. JeffConrad (talk) 05:44, 19 April 2010 (UTC)

It is even more confusing to say: "indistinguisable from a point". A point is defined (http://en.wikipedia.org/wiki/Point_(geometry) as having no dimensions. It cannot be seen. It is a mathematical construct. Jacobson is wrong (p52) when he says of CoC (after defining it in point terms): "This is arrived at by empirical means." It is not possible by observation to arrive at a value for CoC based on a point. Definitions 1 and 4 are nonsense. Definition 2 is vague; definition 3 is too mathematical.

Once again, the author to whom you refer is Ray, not Jacobson. I agree that he's not always perfect, and in some cases, is even confusing. But he's nonetheless one of the more highly-regarded authors in the field. Is it really reasonable to say that Ray (and most of the previous contributors to this article) have everything wrong?
The real intent is probably more at “the defocus is undetectable” or “the resulting unsharpness is acceptable”. We talk of “points” in the context of DoF because that's what we deal with in geometrical optics, and that's the only way we have of quantifying DoF. And we're pretty much bound to follow the published sources. Perhaps it's not the perfect term, but we can't just go making stuff up because we don't like the accepted terminology. Photography is full of nonsense terminology, e.g., “shutter speed”, “fast” lens, “dragging the shutter”, but we can't discard them just because we don't like them.

I would like to see evidence that other authors, pre internet, have defined CoC in terms of a point; and if they have, their justification for doing so. The description of CoC at this site (http://toothwalker.org/optics/dof.html) is the clearest I have come across.

I now have a fair understanding of CoC; others more so -- but that understanding involves visual acuity, not the ability to see a non-dimensional point and compare that to a blur circle.

Again, the essence of the concept is that the unsharpness within the DoF is either “undetectable” or “acceptable” (and I don't think its possible to resolve this slight difference). Van Walree is indeed a good source, but not really citable under WP policy.

Jeff, you must have resources in book form that define CoC. If you have, please transcribe the appropriate sentences and post here. Also, before you revert my changes in future please discuss here first under a new Topic. I don't mind small edits, but a complete revision is unacceptable unless there are factual errors in my changes. —Preceding unsigned comment added by Guyburns (talkcontribs) 03:17, 19 April 2010 (UTC)

In the Ilford Manual of Photography, second through fourth editions, you'll find "It is generally assumed that prints will be examined at about 10 ins. from the eye, and that at this distance image disks not more than 1/100th of an inch in diameter are not distinguishable from points." I'm sure there are more. If you think of a "point" as an "impulse" it makes more mathematical sense. Dicklyon (talk) 04:44, 19 April 2010 (UTC)
I have quite a few books on the subject, but transcribing every definition takes quite a bit of effort. And as Dick mentioned, I think you'll find that most of the definitions are similar, and also decrease in precision from Ray and his associates. JeffConrad (talk) 05:44, 19 April 2010 (UTC)
From a few sources that I have handy:
• “For a photograph viewed at Dv, any subject detail resolved and recorded optically within an image circle of 0.2 mm diameter may not be perceived....” (Ray 2002, 216). This and the discussion that continues is, unsurprisingly, the same as Ray (2000, 52).
• “The largest that appears as a point to the eye is referred to as the acceptable circle of confusion. A diameter of 1/100 inch is often considered to be the largest circle that will appear as a point on a print viewed at a distance of 10 inches.” (Stroebel 1976, 134)
• Depth of field is the range of acceptably sharp focus in front of and behind the distance the camera is focused on.... Any point in a scene that is closer or further way than the distance focused upon will register on the film as a small blurred circle rather than a point. This blurred circle is called the circle of confusion. When these circles are small enough to appear as points, the subject looks sharp.” (Kodak 1972, 2–3)
So yes, the sources have spoken in terms of points since long before the Internet. And they've been somewhat inconsistent and sometimes even sloppy in the use of terminology. I honestly think our definitions are OK as they stand. JeffConrad (talk) 06:49, 19 April 2010 (UTC)

Guy, I don't like reverting someone's good-faith edits. I reverted some of your first edits because you added some unsupported material that was utter nonsense (the acuity claims from Cambridge in Colour) and that were in direct conflict with material still in the article that was supported by reliable sources. Should fixing it be my problem or yours? I suppose reasonable minds might differ. Again, be bold but also be careful, especially when new to a subject. I think a well-intentioned but misguided edit is just as inconsiderate as a revert, especially when it's not the first time. If you take a bit more time to make sure what you're looking to add, there won't be a reason to revert. JeffConrad (talk) 05:44, 19 April 2010 (UTC)

## Medium-neutral terminology

Guyburns suggested that despite the significant transition from film to digital photography, much of the terminology in this article had yet to catch up. Several years ago, I tried to address this, and I've recently tried to catch some of the instances I missed, but I wonder if I've chosen the best terms. In particular, I've generally used original image to refer to that recorded on film or an electronic sensor, and final image to refer to the image that is viewed in a print, a projection screen, or an electronic display. It seems that most published sources have the same problem, so I don't think there's currently a “right” answer for most of the terms. I would think that whatever we use be as descriptive as possible, and where possible, consistent with common usage. A few categories that initially come to mind:

For film plane/sensor plane:

• image plane

To me, this would seem an obvious choice that's compatible with well-established use in optics.

For film format, when format alone isn't enough:

• image format

For general film/electronic sensor:

• imaging medium
• recording medium

For specific negative/transparency/image recorded on electronic sensor:

• captured image
• initial image
• original image
• recorded image

I think recorded image is the most descriptive, and fits well with recording medium, but captured image gets about 10 times as many hits from a Google search (if we really think that's meaningful), and also fits well with usage such as digital capture and post-capture processing.

For general print/projected image/image on electronic display:

• display medium

For specific print/projected image/image on electronic display:

• displayed image
• final image
• viewed image

This one also seems an obvious choice. For specific examples, we may still need to mention the specific medium because of the considerable differences in resolution. For example, in determining a CoC for images displayed on a computer monitor at 500 mm, typical characteristics, such as ~0.25 mm dot pitch, put the resolution of the device at about the same resolution (or less) as the calculated CoC, so the effect on the displayed image is considerable.

I'm sure there are many that I've overlooked, but these seem to be the ones of chief concern in this article and the one on Depth of field.

As I suggested earlier, we might need to define some (or all) of these on first use in each article so there's no need to guess at what they mean. Because the words we're using now are largely my doing, I'll take it as an assignment to change them if we decide there are better choices.

Thoughts? JeffConrad (talk) 09:06, 22 April 2010 (UTC)

I've added one obvious oversight to the list: image format. JeffConrad (talk) 00:27, 23 April 2010 (UTC)

## CoC formula

RE formulas: Why are they so big in Wikipedia? Do they have to be that large? That's one reason people may be put off -- apart from the equation aspect, they look so intimidatingly big. Can they be made smaller? I have rarely seen equations in a text book that use fonts 2-3 times the size of the rest of the text.

Consensus? There's only two of us talking about this equation and I don't have any problems with your proposal, as long as it is user friendly. Also, my original equation was just a starting point. It would have ended up with a more general equation along these lines:

The CoC required of an original image, given an enlarged image for final viewing, can be calculated from the formula (assuming a typical value of CoC for the final image of 0.2 mm):

CoC = D/1250E

where • Coc is the circle of confusion for the original image measured in mm; • D is the viewing distance of the final image in mm; and • E is the enlargement factor.

An example should make the equation clear. Assume a 35 mm slide enlarged to 350 mm (an enlargement of 10 times); a viewing distance of 500 mm. The equation becomes: CoC = 0.0008 x 500/10 = 0.04 mm for the original slide.

A more general equation that includes a user defined value for the final image CoC can be shown to be (see below):

CoC = D/(6250E*R)

where R is the final image CoC. —Preceding unsigned comment added by Guyburns (talkcontribs) 12:45, 22 April 2010 (UTC)

## Optical Energy?

A search of Google Books for the terms "circle of confusion" and "optical energy" came up with only one automotive reference. CoC coupled with "encircled energy" came up with none. "Coc" by itself came up with 899.

Reference to "Optical Energy" and the 90% bit should be removed, shouldn't it? I can't see that it adds anything to the understanding of CoC... but I do actually like it in there. It makes clear the difference between a "blur spot" and a "blur circle". The problem is, both those terms seem to be used interchangeably in the few books I have read.

Also, "defocus blur spot" is still in there. The term appears in no "CoC" books in Google books. —Preceding unsigned comment added by Guyburns (talkcontribs) 13:21, 22 April 2010 (UTC) Guyburns (talk) 12:54, 22 April 2010 (UTC)

Some books ([3]) say things like "defocus blur disc" and "threshold diameter", but on balance I think the terminology variant that we've got is more clear. Dicklyon (talk) 15:13, 22 April 2010 (UTC)

A book search for "encircled energy" will give you more hits.
Yes, authors are inconsistent, in many cases even more that we were a week ago. I don't necessarily say it's right, and I've tried pretty hard to address it here. But despite the time I've spent on it, the differences are really pretty minor. The article was (and still is) far from perfect, but I don't think it was broke.
Blur spot is very common in some of the references we cite for this article. Defocus blur spot is used in some spots here for two reasons:
• To distinguish it from other blurring, especially diffraction. This really is a big deal; see Stokseth (1969) in the Depth of field article to see just how different our idealized defocus blur spot is from what really happens, even at large defocus. Incidentally, Stokseth uses patch rather than spot, for defocus blur ... so there's yet another choice.
• To acknowledge that the spot may not be circular.
I could add Stokseth as a reference, but I think it's a bit much for the average reader who's unfamiliar with the OTF. I also could add Merklinger (1992, 46), which has several very simple illustrations of what a composite blur spot actually looks like. Perhaps I should just add them both.
One more point, at the risk of harping: would you please sign your posts with four tildes, as shown just below the save button? The poor SineBot is getting tired ... JeffConrad (talk) 00:08, 23 April 2010 (UTC)

## Formula for CoC

The use of words rather than symbols is generally deprecated. Moreover, a general rule in a formula using the solidus rather than built-up fractions is that there be only one solidus; addressing the latter, the current formula

CoC Diameter Limit (mm) = anticipated viewing distance (cm) / desired print resolution (lp/mm) for a 25 cm viewing distance / anticipated enlargement factor / 25

becomes

${\displaystyle {\text{CoC Diameter Limit (mm)}}={\frac {\text{anticipated viewing distance (cm)}}{{\text{desired print resolution (lp/mm) for a 25 cm viewing distance}}\times {\text{anticipated enlargement factor}}\times 25}}\,.}$

I think it's a bit easier to follow, but still find the plethora of words distracting. The words could be trimmed a bit; one possibility might be

${\displaystyle {\text{CoC Diameter Limit (mm)}}={\frac {\text{viewing distance (cm)}}{{\text{desired resolution (lp/mm) for a 25 cm viewing distance}}\times {\text{ enlargement}}\times 25}}\,.}$

But I think it's much like rearranging deck chairs ...

However the formula is presented, it needs either a source or a derivation. The latter is fairly simple, and possibly explanatory in itself. Given that

• c is the initial-image CoC (the one used in most DoF formulas)
• cf is the final-image CoC
• E is the enlargement from the initial image to the final image
• cstd is the desired final-image CoC at the standard viewing distance
• Rstd is the desired final-image resolution (probably more properly, resolving power) at the standard viewing distance
• dv is the actual final-image viewing distance
• dstd is the standard final-image viewing distance

The initial-image CoC is just the final-image CoC divided by the enlargement:

${\displaystyle c={\frac {c_{\mathrm {f} }}{E}}\,.}$

At the standard viewing distance,

${\displaystyle c_{\mathrm {f} }=c_{\text{std}}\,.}$

For a different actual viewing distance,

${\displaystyle c_{\mathrm {f} }={\frac {d_{\mathrm {v} }}{d_{\text{std}}}}c_{\text{std}}\,.}$

The initial-image viewing distance is then

${\displaystyle c={\frac {d_{\mathrm {v} }}{d_{\text{std}}}}{\frac {c_{\text{std}}}{E}}\,.}$

Expressed in terms of the desired resolving power, this becomes

${\displaystyle c={\frac {d_{\mathrm {v} }}{d_{\text{std}}\,R_{\text{std}}\,E}}\,.}$

If we take the standard viewing distance to be 25 cm,

${\displaystyle c={\frac {d_{\mathrm {v} }}{d_{25}\,R_{25}\,E}}={\frac {d_{\mathrm {v} }}{25\,R_{25}\,E}}\,,}$

and we need to specify that the distance is in cm (and if c is to be in mm, we need to specify that R25 is in lp/mm). This is the formula given in the the article. I think it's much easier to read than the text presentation, but others may disagree. The derivation, though simple, adds yet more math, though either a derivation or a source is probably needed to justify using the formula. A derivation could possibly go at the end of the article so that only those who want to know how the formula was obtained need read it. Incidentally, it's essentially an angular criterion, much like the Snellen criterion except that with the standard photographic resolution, it's adjusted for the assumption of other than a high-contrast line chart. JeffConrad (talk) 04:48, 18 April 2010 (UTC)

### Proposed revision of first CoC equation

I suggest something to the effect of

“All three factors are accommodated with this formula:

${\displaystyle c={\frac {d_{\mathrm {v} }}{d_{\text{std}}\,R_{\text{std}}\,E}}={\frac {d_{\mathrm {v} }}{250\,R_{\text{std}}\,E}}\,,}$

where

• c is the original-image CoC in mm
• dv is the actual final-image viewing distance in mm
• dstd is the standard final-image viewing distance of 250 mm
• E is the enlargement from the original image to the final image
• Rstd is the desired final-image resolution at the standard viewing distance of 250 mm

With the common final-image resolution of 5 lp/mm (equivalent to a CoC of 0.2 mm), this simplifies to

${\displaystyle c={\frac {d_{\mathrm {v} }}{1250\,E}}\,.}$

For example, if the long dimension of a 35 mm slide is enlarged 10× to 360 mm and viewed at a distance of 500 mm, the CoC for the slide is

${\displaystyle c={\frac {500}{1250\times 10}}=0.04{\text{ mm}}\,.}$

I think the formula is manageable, yet shows enough to suggest that it wasn't simply extracted from a region in which the “Sunny 16” rule is inapplicable. Though it's essentially the same as what we currently have, I don't think it can reasonably stand without including a derivation elsewhere in the article. A large integer in the denominator is usually less likely to get wrong than a small decimal in the numerator (and additionally shows that it wasn't just rounded), so that's why I've shown it that way. JeffConrad (talk) 01:34, 19 April 2010 (UTC)

After trimming a few words from the existing formula, I think it's fine, and suggest we leave it as is. JeffConrad (talk) 02:50, 23 April 2010 (UTC)

### Proposed section Adjustment of CoC for enlargement, viewing conditions, and required resolution

I don't sense that we have consensus for changing the first CoC formula, so I suggest we leave it as is for now. I still think it needs support from a source or a derivation; absent the former, I propose that we add a section at the end of the article that shows how this formula was obtained:

“The common values for the original-image CoC may not be applicable if reproduction or viewing conditions differ significantly from those assumed in determining those values. If the original image is to be given greater enlargement, or the final image viewed at a closer distance, then a smaller CoC will be required. If the final image will be viewed at a greater distance, a smaller CoC may be acceptable. If the original image is given greater enlargement, but the final image is viewed at a correspondingly greater difference, the common value for the original-image CoC may be appropriate.

Conventional assumptions for CoC do not account for the resolution of the display medium. If the final image is displayed on a low-resolution medium such as a computer monitor, the detectability of blurring may be limited by the display medium rather than the optical blurring, so a larger CoC may have little effect on the sharpness of the final image. But if the image may also be displayed in a high-resolution medium such as a print, the normal assumptions for determining CoC should apply.

If

• c is the original-image CoC
• cf is the final-image CoC
• cstd is the standard final-image CoC
• d is the actual final-image viewing distance
• dstd is the standard final-image viewing distance
• E is the enlargement from the original image to the final image
• Rstd is the desired final-image resolution at the standard viewing distance

At the standard viewing distance,

${\displaystyle c_{\mathrm {f} }=c_{\text{std}}\,.}$

For a different actual viewing distance,

${\displaystyle c_{\mathrm {f} }={\frac {d}{d_{\text{std}}}}c_{\text{std}}\,.}$

Expressed in terms of the desired resolving power, this becomes

${\displaystyle c_{\mathrm {f} }={\frac {d}{d_{\text{std}}\,R_{\text{std}}}}\,.}$

The original-image CoC is the final-image CoC divided by the enlargement:

${\displaystyle c={\frac {d}{d_{\text{std}}\,R_{\text{std}}\,{E}}}\,.}$

If the standard viewing distance is taken to be 25 cm,

${\displaystyle c={\frac {d}{25\,R_{\text{std}}\,E}}\,.}$

Examples:

An 8″×10″ print is made at 2× enlargement from a 4×5 original image, and the print requires the standard resolution when viewed at the standard distance of 25 cm:

${\displaystyle c={\frac {25}{25\times 5\times 2}}={\text{0.1 mm}}\,.}$

The same original image is given 4× enlargement, and the resulting 16″×20″ print requires the standard resolution when viewed at 50 cm:

${\displaystyle c={\frac {50}{25\times 5\times 4}}={\text{0.1 mm}}\,,}$

the same as for standard viewing conditions. This criterion might be typical if comfortable whole-image is assumed. If, however, the larger print is viewed at the standard viewing distance of 25 cm,

${\displaystyle c={\frac {25}{25\times 5\times 4}}={\text{0.05 mm}}\,.}$

A 36 mm × 48 mm original image is given 5× enlargement, and the print is viewed at the standard distance by a person with better-than-average visual acuity who requires a final-image resolution of 8 lp/mm:

${\displaystyle c={\frac {25}{25\times 8\times 5}}={\text{0.025 mm}}\,.}$

An APS-C original image is enlarged 12× and viewed on a computer monitor at 50 cm, and the standard resolution is required:

${\displaystyle c={\frac {50}{25\times 5\times 12}}={\text{0.033 mm}}\,.}$

The resolution of a typical monitor is comparable to the criterion for the optical blur, so the actual sharpness will be less than predicted by this calculation. If the image may also be printed and viewed under similar conditions, the value calculated here may still be the best choice.

A 35 mm slide is projected onto a screen at 5 m (500 cm) at which it is enlarged 50x, and the viewers require the standard resolution:

${\displaystyle c={\frac {500}{25\times 5\times 50}}={\text{0.08 mm}}\,.}$

The final formula is the same as the current CoC formula except that it's symbolic instead of in words, so I think the average reader should be able to connect the two. The distances are in cm for consistency with the current formula; I have no problem changing to mm (and would prefer that we do so), but I think both sections should be changed simultaneously if we decide to do that. Some of the examples could be moved to the first section, but if they are, the format should follow that of the current example.

For the example of the 16″×20″ image viewed at 25 cm by the high-VA viewer, the resulting 0.006 mm CoC would likely prove unworkable for most practical situations because the required f-number would be so large that diffraction would more than offset the reduction in defocus, but I'm not sure we have anything that would support such a statement.

Offhand, I don't see how we could get by with much less math. Putting the symbol definitions in paragraph form (as the MOS prefers) might make the beginning a bit less imposing, but at least to me, given the number of symbols and the lengths of some of the definitions, doing so would make the definitions much harder to follow.

We probably could get by with fewer examples. SuperVision would be the first casualty on my list, but the folks in cyberland who think they can see through walls might disagree. JeffConrad (talk) 07:26, 20 April 2010 (UTC)

I've made a couple of tongue-in-cheek allusions to web sites that claim normal visual acuity is far greater than that claimed by most reliable sources, but properly, there are many people whose vision is considerably better than average, and it's probably reasonable to include a more realistic example. Keeping the resulting CoC larger also makes diffraction less of an issue.

A few other thoughts:

• It seems reasonable to acknowledge that there are formats other than 35 mm.
• Upon further thought, this topic seems to confuse so many people here and elsewhere that it may be good to keep all of the examples.
• I agree that we probably don't need the subscript for the actual viewing distance.

I've revised the proposal accordingly, with some minor additional cleanup. JeffConrad (talk) 03:19, 21 April 2010 (UTC)

As nice as it would be to always be “medium neutral”, after further though, it just isn't practical when dealing with both high-resolution final images like prints and low-resolution final images such as displayed on a computer monitor.The final qualification for the image displayed on the computer monitor will depend on what we conclude for the effect of monitor resolution (if any) on DoF.

Once again, I've revised the proposal accordingly. I've revised the proposal accordingly. I think the wording needs some work. Depending on what we decide for “medium neutral” terminology, some other changes may be needed. JeffConrad (talk) 03:35, 23 April 2010 (UTC)

This proposal doesn't seem to find much support, so for now, I'm pursuing it no further. We can revisit the issue again if someone complains about the lack of a source for the CoC formula or feels that we need additional examples. JeffConrad (talk) 09:09, 28 April 2010 (UTC)

## Resolution of recording and display media

Some comments were recently made in Talk:Depth of field that the article ignores the resolution of the recording medium. That is indeed the case; although that resolution certainly affects the final-image sharpness, every DoF treatment of which I am aware confines itself to optical phenomena. Of course, the resolution of the display medium can also affect final-image sharpness, as is stated in this article:

“If the photo is printed or displayed using a device, such as a computer monitor, that introduces additional blur or resolution limitation, then a larger CoC may be appropriate since the detectability of blur will be limited by the reproduction medium rather than by human vision; for example, an 8″×10″ image displayed on a computer monitor may have greater depth of field than an 8″×10″ print of the same photo, due to the computer monitor having lower resolution; the monitor is less sharp overall, and therefore it takes a greater defocus for a region to appear blurred.”

In revising the Depth of field article to note that the resolutions of the recording and display media are not considered, I added a condensed version of the paragraph above, and noted that it was in conflict with two other notes (unsourced) stating that demosaicing and post-capture processing such as image noise reduction can decrease DoF. Though I don't think there's much dispute that these effects reduce final-image sharpness, as well as making it more difficult to detect which parts of the image were optically sharp, I'm not sure we're correct to say that it changes DoF. In particular, it's clearly possible to draw opposite conclusions from the same effect, depending on how we define DoF:

• The normal definition of DoF is the part of the scene for which unsharpness is undetectable (or at least for which the unsharpness is “acceptable”); with this definition, the additional blurring decreases the DoF, possibly to zero if nothing is acceptably sharp.
• If, alternatively, DoF is simply a region that is uniformly unsharp in the final image, non-optical blurring may increase DoF.

It seems to me that the first definition is the one we need to follow (since we use it in both articles), but I wonder if we aren't going too far in saying that additional blurring reduces DoF, especially absent a source.

H. Lou Gibson (1975) tried to address this issue, making the distinction between depth of field and “depth of sharpness”, with the latter accounting for factors other than the optical blurring in the original image. Lester Lefkowitz (1979) provided an especially good example of a closeup image that exhibited less sharpness over a greater range of distances than a similar image of the same subject taken with a smaller lens f-number. The effect demonstrated was diffraction, so it's not quite what's at issue here, but the effect is similar. Were I to make the call, I'm not sure I could say which image had greater DoF; the effect seems more complex than that. In any event, “depth of sharpness” seems not to have found widespread acceptance, so I don't think it can be taken as anything other than how Gibson described the effect.

And I wonder if the same isn't true here. Might we not be better off simply to mention that other factors can affect final-image sharpness? Whatever we decide is right, I think we should give the same treatment in the Depth of field article and this one. JeffConrad (talk) 04:17, 21 April 2010 (UTC)

I added a {{citation needed}} tag. It pertains only to the effect on DoF; I assume there is no disagreement on the rest of the material in that paragraph. JeffConrad (talk) 08:25, 22 April 2010 (UTC)

In the absence of comment, I've removed mention of a low-resolution display medium increasing DoF. Hopefully what remains still conveys the essence of the effect on image sharpness.

I've made corresponding changes in the Limitations section of the Depth of field article, retaining descriptions of the effects on sharpness but avoiding statements about how they affect DoF. JeffConrad (talk) 08:26, 30 April 2010 (UTC)

## Terminology

This is coming from someone with not much experience, but who likes things to be clear:

Image plane - tick.

Recording medium - sus. Sounds like something from the audio field. And it is not a correct description anyway because "recording" implies being stored. Why not "sensor"? It could be defined as: "Sensor - the medium by which the image is captured. e.g. film, CCD/CMOS chip". Film is just a chemical based sensor after all.

Yeah, I hear you on the possible audio implication. But I think it's linguistic legerdemain to suggest that sensor is a reasonable term to represent film. We might find some guidance from the law, at least in the United States. Many jurisdictions have required permits for “commercial” filming, photography, and videotaping; the advent of digital technology has obviously required some changes, and recording medium seems to be one of the more common terms (and video recording is one means of including digital video). Imaging medium is of course an alternative. I think Wikipedia leads only when unavoidable; whenever possible we should follow what others are using (unless it's utter nonsense) to make it easier for the reader to understand what we're saying.

Captured image - tick.

Displayed image - tick.

Go ahead, Jeff. Be bold. Just try to be clear for the sake of newcomers. And instead of cluttering the article with descriptions of these terms, how about listing half a dozen of them near the start, one line each, so that beginners like me can refer to them easily. —Preceding unsigned comment added by Guyburns (talkcontribs) 13:16, 22 April 2010 (UTC)

I have no problem being bold, but I'd also like to be careful that changes would be something that others think is reasonable. If they don't, they'll use different terms in this and other articles, and we'll be right back to where we started. JeffConrad (talk) 00:23, 23 April 2010 (UTC)

There doesn't seem to be much interest in this, so favoring article stability, I'm not going to do anything with it for now. We can revisit if people decide they don't like the current terminology. JeffConrad (talk) 01:35, 3 May 2010 (UTC)

## References

I've added the references for Merklinger and Stokseth. I've also moved the full citation for Coddington the References section for consistency with the others; additionally, it makes the number of references we have more obvious. I need to clean up the full citation to include the original publishing information.

I don't have publishing information for some of the older sources, so I've left the citations inline. JeffConrad (talk) 02:47, 23 April 2010 (UTC)

Jeff, thanks for working on it. If you'd like to do more, find publisher info in Google books by following the "about this book" link and looking near the bottom of the page. For Wall, here, you'll also find "disc of confusion" on a few pages; the indexing doesn't seem to find "circle of confusion", but the quoted passage is on page 92. I emailed you a copy of the Dallmeyer brochure. I'm not sure about the T.H. 1866 page; it seems someone lost all the info I entered with the figure when moving it to commons; I'm sending you a copy of von Rohr's 1899 book pages that mention it. Dicklyon (talk) 05:05, 23 April 2010 (UTC)
I'll see what I can do. And if we can't get it all now, perhaps we'll get it later. The more of this stuff in the References section, the more obvious it will be that this article is fairly well supported. JeffConrad (talk) 05:41, 23 April 2010 (UTC)
I gave it the best shot I could. Everything involved was a scan, so I've used the original dates. Later references, including von Rohr, seem to use arabic rather than Roman numberals, so I followed that lead. I was a bit confused by von Rohr's inclusion of No. 307 for the BJP, so I've left it out. If they published biweekly and numbered the issues continuously from the beginning (1854), this would make sense, but I wasn't able to confirm it. If someone knows that's the case, we can add this information. JeffConrad (talk) 09:15, 24 April 2010 (UTC)

## New section Adjusting the circle of confusion for a camera’s DoF calculator

Cyberland is loaded with discussions, accurate and otherwise, of how to determine the CoC for a photographer's specific conditions. But few address how that CoC is practically applied. It's really quite simple, usually requiring no math, so I've added a brief section discussing it. Hopefully, the section doesn't venture into forbidden “how to” territory. If there is concern about lack of support for some of the statements, we can add a link to the Depth of field article, which derives everything significant from basic considerations. JeffConrad (talk) 09:20, 23 April 2010 (UTC)

Per the discussion in New section needs something below, I've expanded the section to make it more clear how the factor for adjusting the f-number is determined. I've also tried to address the situation with AF lenses. Don't ask me how to determine “the f-number that might otherwise be set”, because I have no idea. But this problem exists with or without adjusting the CoC.

The section has also almost doubled in length. Perhaps the last case (just setting the usual f-number and accepting that DoF with a special CoC is different from that with the standard value) isn't needed.

It's also possible to avoid discussing the focus spread by starting off with the formula

${\displaystyle \mathrm {DoF} \approx 2Nc{\frac {m+1}{m^{2}}}\,,}$

but it doesn't provide as much useful information, and I don't really think it's any simpler—there's an additional quantity, and it might even take an extra step to make it clear how the formula we want is obtained from this one. Moreover, it throws in magnification, which seems an unnecessary complication for an article that isn't primarily focused on DoF. JeffConrad (talk) 10:49, 24 April 2010 (UTC)

Almost as soon as I wrote this, a quick glance suggested that using the formula above would make things a lot simpler, so I've revised the section accordingly. The section is concerned primarily with adjusting the f-number for a CoC other than the default in practical photography, rather than determining what the f-number should be. The latter problem is covered sufficiently in the Depth of field article, so we really don't need it here.

Citing Ray should deal with any objections that the material is unsourced. That he discusses it under Close-up depth of field does not diminish its applicability here; unlike some other DoF formulas, the “close up” approximation is good for close-up distances as well as moderate distances. It's given in terms of magnification because for close-up work, that's usually more convenient than subject distance. Because we immediately solve to eliminate the magnification, we don't really care how the first formula is expressed.

If it's unclear how the second formula follows from the first, I can add another step if necessary, but I'd rather avoid the math if we can. I'm still not sure we need the last case, but I'm probably not the one to judge—when I care about DoF, I usually let it determine the f-number rather than vice versa.

So no more nodal planes or difficult-to-measure image distances. Hopefully, this will be a bit easier to follow. JeffConrad (talk) 17:45, 24 April 2010 (UTC)

## New section needs something

I saw the new section and my immediate thought was: "Good -- some practical advice." But I couldn't make head nor tail of it.

I feel obliged to indicate my interest in CoC, and my background, in case my above comment elicits the thoughts in people reading this Talk page: "This Burns fellow hasn't a clue. How much of a novice is he?" So here I go: I owned a Olympus OM2n in the 1980s, my first camera, taking thousands of wilderness slides over the years. Virtually every photo was on complete manual, and taken under control of depth-of-field using the markers on the lens. Meaning, sometimes I wanted shallow DoF and at other times maximum DoF. I was always using the DoF markers. I had a clear understanding of what effected DoF in practice, but had never concerned myself with CoC. I didn't need to.

Be assured that many others, myself included, are in the same situation. Sadly, current zigapixel, zigabuck DSLRs cannot replicate what was easily accomplished with your OM2n. My thoughts on this would violate talk page guidelines. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

With the advent of digital SLRs and lenses bereft of DoF markers, and wanting to take photos for showing at 1920 x 1080 at the local cinema, I went to the DoF page for some info on how to calculate DoF. Given a particular viewing situation -- an audience sitting a certain distance from a 1920 x 1080 image -- I wanted to know to deal with DoF using this new technology. The DoF page led me to the CoC page, and after several days I'm still here. Good thing actually. If the CoC had been clearly explained, with clear examples, I would have come and gone in a few minutes. But now I've got the CoC bug and have decided to delve into it as deeply as I can.

Sadly, it's only possible to give the theory. Those who still have manual-focus lenses with decent DoF scales can easily apply what I've described; those with state of the art digital wonders in most cases cannot. The first incarnations of the Canon EOS 1D and EOS 1Ds allowed this to be accomplished in seconds; with later models, it's almost impossible.
Even if camera manufacturers were to rectify the shortcomings in systematic control of DoF, you'd still need to address whether you might sometime make prints of some of your images (perhaps those that wowed the theater audience). In that case, the normal values for CoC would probably work. If you work through what's in the article (and my proposal), I think you'll find that the print criterion will far exceed the requirements of the audience. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

Problems with the new section:

1. I don't understand the heading: "Adjusting the circle of confusion for a camera’s DoF calculator". What is a DoF calculator?

Perhaps “DoF calculator” is too generic—the primary target is small- and medium-format lens DoF scales, but there are similar calculators for view cameras (e.g., as introduced on Sinar view cameras in the 1970s(?)). JeffConrad (talk) 14:17, 23 April 2010 (UTC)

2. "View camera" is introduced in the third sentence. I didn't know what a view camera was, so I looked it up (I assumed it meant one with a view finder). But there it was -- an Ansell Adams type camera. Not a very good example to use, and at odds with the statement in the previous sentence: "how to use that CoC in practical photography". How many people use view cameras today?

I did include a WL to view camera... Actually, quite a few people still use view cameras; see the Large Format Page for a good intro. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

3. "If vn and vf are the image distances that correspond to the near and far limits of DoF, c is the CoC, the f-number N can be determined..." I read that and thought "Bewdy! That's what I want. I'll put in the DoF, divide by 2C and set the f-stop." However, the next sentence says: "The image distances are measured from the camera’s image plane to the lens’s rear nodal plane". What does that mean? I assumed the instructions referred to distances from me to objects that I want to photograph. But it looks like they refer to in-camera distances measured in mm.

See the next answer. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

4. What is a "lens’s rear nodal plane"? How do you measure from there to the camera's "Image plane" in practical photographer?

I'll add a WL ... It's tough to measure, which I mention. But as I also mention, you don't need to measure it. On a view camera or a small-format camera. On a view camera, one focuses on the far, and notes the distance between the front and rear standards; one then focuses on the near, and again notes the distance between the front and rear standards. The focus spread vnvf is then used to calculate the required f-number.
On a small- or medium-format camera, as I mention, it's tough to measure the focus spread. But you don't need to; that's what the lens DoF scales are for. They're used in much the same manner as the calculation above:
1. Focus on the far; note the position of the focusing ring.
2. Focus on the near; note the position of the focusing ring.
3. Set the focusing ring so that the focus index (i.e., the focused distance) is midway between the two previous positions.
4. The near and far positions previously noted should align with numbers on the DoF scale; that's the f-number from the DoF “calculator”; adjust it accordingly.
I talk about “position of the focusing ring”; in most cases, you can look at the values on the distance scale and use them as references. But if the lens is tilted, as when using a tilt/shift lens, the marked distances aren't meaningful. But the “position of the focusing ring” always works.
The greater issue is that the DoF scales on most AF lenses are so small that they're almost useless. And even if they were usable, you'd need to forgo AF ... ridiculous. Canon had a feature, “Depth-of-Field AE”, that did quite a good job of it, but for reasons known only to Canon, it was dropped in the middle of 2004. This article cannot deal with such issues. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

5. The second last paragraph assumes too much, with too little explanation. The example given just happens to end up with a 1.4 ratio, exactly the ratio between f-stops, and the reader is expected to know that the relationship exists and to understand the connection: i.e. "Oh, the ratio of CoC is 1.4 -- obviously I change the aperture by one f-stop."

Perhaps some expansion is needed. Let me think about it. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

Jeff, you and I will make a good team fixing up this article. Your technical knowledge to correct my inexperience, and my skill at detecting your unclear explanations. Please submit a second draft to this Talk page, and I suggest it be for "practical photography" i.e. a DSLR with a zoom lens right at the start, and then if you must, go into the more esoteric cameras.

Alas, the typical AF zoom lens is the weak point of everything; most of the dual-ring type do not even have DoF scales. Bottom line: yer screwed ...
Actually, there is a way to to determine focus and f-number for current DSLRs, but you need a laser rangefinder and a programmable calculator or PDA or smart phone or something similar.
1. With the rangefinder, note the distance to the object that is at the far limit of DoF.
2. Again with the rangefinder, note the distance to the object that is at the near limit of DoF.
3. Along with the CoC (your custom value), the lens focal length (one of the drawbacks of object-side calculations ...), enter the near and far object distances into the calculator. Your program will give you the f-number and object distance.
4. Scan the scene with the rangefinder until the distance matches the focus distance just calculated; remember what in the scene is at that distance.
5. Point the camera at that point and use AF to set the focus.
6. Set the calculated f-number.
Is this nuts? You bet ... but quite honestly, I don't know of a good alternative at present. I still have a Canon EOS 1v, with which I can get the nominal values in seconds with three button presses; I then just close down one stop.

Finally, all questions above are rhetoric. There's no need to answer them. I can look up the answers if I need to. —Preceding unsigned comment added by Guyburns (talkcontribs) 12:01, 23 April 2010 (UTC)

I don't know quite what to say ... in essence, I've said that systematic control of DoF is almost impossible with current DSLRs and AF lenses (aside from my ostensibly tongue-in-cheek procedure above). But if we take that too literally, there's no point (other than historical interest) in having this or the Depth of field article. Although there are some serious obstacles to practically implementing most of what's covered in either article, I think the information still has some value.
What this section really needs is support from camera manufacturers. Perhaps they will eventually get the message, though I'm not holding my breath.
Ultimately, if the new section is of no value, we can just get rid of it. JeffConrad (talk) 14:17, 23 April 2010 (UTC)

### Simplification

Jeff, it would be much easier to correct the f-number than the distances when changing the CoC that a DoF scale or calculator is based on. For example, if your 35-mm-format lens has a DOF scale, and you want to use it on a DSLR with 1.5 crop factor, then you need to reduce the CoC by a ratio 1.5, which means you need to a smaller aperture by 1.5 than the scale says. So stop down 1 stop or so; set f/8 when it says f/5.6 and you'll be close enough. Dicklyon (talk) 18:11, 24 April 2010 (UTC)

Dick, I'm not quite following; aren't you and I saying the same thing? Where did I say anything about distances? Or is this a reference to the last case in which the f-number is the same but the DoF varies? JeffConrad (talk) 20:34, 24 April 2010 (UTC)
Maybe we're saying the same thing. I didn't really read it carefully, but it looked over-complicated. Shouldn't really need formulas for this; just use a smaller aperture if you need a smaller CoC, proportionately. Dicklyon (talk) 21:04, 24 April 2010 (UTC)
Perhaps obvious enough to you and me. But it's been news to many people in various photo forums, and Guy had said that even with the one formula in the original version, it wasn't obvious how the ratio was arrived at. Key is that for given DoF, the f-number is inversely proportional to CoC, and I'm not sure I've seen a good source that mentions this seemingly obvious relationship except to show it in a formula, and even then without intentionally addressing this issue. So it seemed to me that just saying something like “adjust the f-number by the ratio of CoCs” (it might not always be an increase; the format change with the same lens is only one application) might lead many to ask, “Why?” and “Where did you get it?”, and perhaps even to tag the statement. And I think I'd have a hard time explaining the general case without a formula. But perhaps I underestimate most readers; if this procedure is that obvious, we probably don't need this section at all. But perhaps the last case is really superfluous; getting rid of it would also eliminate a formula.
It still seems to me that the far greater problem is how to pick the right f-number in the first place with most AF lenses, even if they have DoF scales. The same is true even for some MF lenses, like the new Canon and Nikon tilt/shift lenses, which have very small scales that are hard to read with any accuracy. The subject of DoF is discussed to death in cyberland, yet little seems to be said about how one actually chooses the f-number with most AF lenses.
Anyway, if this section is superfluous, I'll just get rid of it. JeffConrad (talk) 23:54, 24 April 2010 (UTC)
Here's the explanation from Ray (2002, 229), under Depth of field scales, displays and calculators:
“The scale may not be accurate enough in some circumstances and is for a fixed value of C. For critical work, halving the value approximates a closure of aperture by two stops to obtain the necessary depth.”
Merklinger (1992, 57), under More on Distance Scales [referring to a DoF scale in Figure 8 on page 17], says
“Using the scales as provided, I set the infinity mark opposite the right-hand depth-of-field marker for the f-stop I intend to use: let’s say f/16. The focus pointer points to the hyperfocal distance, about 15 feet. I want the circle-of-confusion to be one-seventh of what was assumed. I can get this by either of two methods. I can set the infinity mark opposite where the f/2.3 marker would be, or, I can refocus from 15 feet to 7 times 15 feet, or 105 feet.”
Both are saying the same thing that I'm saying, but I think the way I've put it is easier to follow and easier to apply to more general circumstances. But perhaps others don't see it that way. JeffConrad (talk) 08:38, 25 April 2010 (UTC)
Right, sorry I didn't read it more carefully before. I was thrown off by the approximate formula and the discussion of magnification. There's no need for any of that, as the actual blur circle diameter also varies in direct proportion to the aperture diameter, exactly. Adjusting the CoC is just a proportionate adjustment of the aperture. Not much else needs to be said. Merklinger's distance approximation is good, but not general (only applies to hyperfocal shooting). And it's probably not necessary to mention AF lenses as a proxy for poor DOF scales. Dicklyon (talk) 15:05, 25 April 2010 (UTC)

I may have been thinking useless, but I think poor is a bit more pejorative than I implied. The case could be made that because this section is about adjusting the f-number obtained from a lens DoF scale (and the title now reflects this), discussion of circumstances for which the f-number cannot be obtained from the DoF scale in the first place is irrelevant.
Yet another possibility for the main thrust of the section: include only the first equation, and following it with a more general paraphrase of the excerpts from Ray and Merklinger above, to the effect of
“The f-number determined from a lens DoF scale can be adjusted to reflect a CoC different from the one on which the DoF scale is based. When the subject distance is much less than the hyperfocal distance the DoF is given to good first approximation by (Ray 2000, 55–56),
${\displaystyle \mathrm {DoF} \approx 2Nc{\frac {m+1}{m^{2}}}\,,}$
where N is the lens f-number, c is the CoC, and m is the magnification. Because the DoF is proportional to the product of the f-number and the CoC, an increase in N is equivalent to a decrease in c, and vice versa. For example, increasing the f-number by 1 stop, a factor of approximately 1.4, is equivalent to decreasing the CoC by the same factor. If it is known that a lens DoF scale is based on a CoC of 0.035 mm, and the actual conditions require a CoC of 0.025 mm, the f-number determined from the DoF scale must be increased by a factor of 0.035 / 0.025 = 1.4, if it is known that a lens DoF scale is based on a CoC of 0.035 mm, and the actual conditions require a CoC of 0.025 mm, the CoC must be decreased by a factor of 0.035 / 0.025 = 1.4; this can be accomplished by increasing the f-number determined from from the DoF scale by the same factor, or about 1 stop, so the lens can simply be closed down 1 stop from the value indicated on the scale.
The same approach can usually be used with a DoF calculator on a view camera.
On many autofocus lenses, the DoF scales are small and may be difficult to read accurately, and many autofocus zoom lenses do not even include DoF scales, so the f-number may need to be determined by other means.
I think this is more general and more complete that either of the excerpts above. I think we need to keep the first formula for two reasons:
1. It sources the statement that follows.
2. Seeing the Nc product in the formula makes the statement that follows easier to follow.
Perhaps the mention of the view camera DoF calculator is optional, but there still are many Sinar cameras out there, and this provides a simple way of using other than the default CoC for someone who wants to view a 16×20 at 250 mm.
After Guy's comment, it seems to me that other people may ask, “On what planet does this editor spend most of his time? How can anyone possibly apply this with AF zooms?” But if others think the last paragraph is superfluous, I don't have strong feelings one way or another—I didn't include it in the first version. Perhaps with the current section title, the requirement of a lens DoF scale is now obvious. JeffConrad (talk) 17:04, 25 April 2010 (UTC)
I think the AF zoom comments are not very relevant. The real point is very simple, and the sentence that starts "When the subject distance is much less..." seems like just a distraction away from the point. The point is that in all DoF equations, exact or approximate, the quantity cN is the only way that c or N appears. Neither of your sources saw the point, it appears. We could write it sensibly, but I don't know what to use for a source. Dicklyon (talk) 03:12, 26 April 2010 (UTC)
Not strictly true; the exact formula is
${\displaystyle \mathrm {DoF} ={\frac {2Nc\left(m+1\right)}{m^{2}-\left({\frac {Nc}{f}}\right)^{2}}}\,.}$
Ray says, “halving the value approximates a closure of aperture by two stops” [emphasis added]. Hard to say what he means, but one interpretation is that he's accounting for the approximation that I mention. In deriving the “close up” DoF equation, Ray notes that terms in the denominator can be neglected; this is true enough for short and even moderate distances, but not for longer ones. Ray had restricted the equation to close-up use, so the disclaimer wasn't that important.
Ray is wrong about it being approximate, and your equation shows exactly what I said: "the quantity cN is the only way that c or N appears." Approximations come in if you want to talk about changing the DOF distances, but not if you stick to aperture diameter. Sticking to that simple observation could keep the section concise. Dicklyon (talk) 19:36, 26 April 2010 (UTC)
I agree that the formulas are equivalent as long as the Nc product is the same. “DoF is proportional to the Nc product”. Perhaps I was getting sidetracked by insisting too much on including something to the effect of “DoF is proportional to the product of the f-number and the CoC”, which seemed like a simple way of supporting “an increase in one is equivalent to a decrease in the other”. I'll concede that insisting on that introduces some complication, but it seems to me that just saying, “In DoF formulas, N and c only appear as the product Nc, so an increase in one is equivalent to a corresponding decrease in the other” is asking the reader to accept a lot on faith—as obvious as the behavior may seem, it's hardly ever mentioned in most published sources. But perhaps a better approach would be to just give an exact formula and include a WL to the appropriate section of the Depth of field article for support. I suppose we could also just make the statement and direct the reader to the Depth of field article, but I wonder if that isn't asking a bit much—I'd certainly rather be able to look at the formula above to immediately see the basis for the statement.
I've made a new proposal, in a new subsection, so it doesn't get lost in the clutter here. It seems to me that much of this discussion has arisen from not reading each others' comments carefully enough. Hopefully, I've not overlooked anything significant this time. JeffConrad (talk) 23:20, 26 April 2010 (UTC)
The second term in the denominator is small at small to moderate distances, but it becomes significant as the hyperfocal distance is approached, and at the hyperfocal distance, is equal to the first term. Which was my point; the “close up” approximation is better than many common DoF equations commonly used, but it fails very badly at large subject distances, much as the common
${\displaystyle \mathrm {DoF} \approx {\frac {2Nc}{m^{2}}}}$
(which is about the only practical one to use when making a general comparison of DoF for different formats) fails badly at very short distances. I'll admit that most sources (including Stroebel) seem to skip these details (Bob Atkins seems to be one of the few that doesn't), but some pretty significant errors can result. I don't think this is being any fussier than mentioning that the blur spot usually isn't round, or that the edges are soft—most sources skip that, too. We skipped it in the DoF article until someone called us on it.
Ray and Merklinger both treat depth of focus as numerically (if not quite conceptually) conjugate to depth of field (Ray again acknowledges the approximation). The harmonic mean of the image distances is alway less than the arithmetic mean used in constructing most DoF scales; in most cases, the difference is small, but with a large focus spread, setting focus to the arithmetic mean will focus slightly in front of the desired point.
In casual conversations, I've often discussed the “close up” DoF equation as if it were exact. But strictly, that's not correct.
I agree that we could drop “the DoF is given to good first approximation by” without much loss; that's kinda what “≈” means.
The only point with AF zooms (assuming they're all dual ring) is that this approach can't be used with them. But perhaps that's now obvious with DoF scale in the title. As I said, I saw no need to include it prior to Guy's comment, and I have no strong attachment to it now. JeffConrad (talk) 05:49, 26 April 2010 (UTC)

Upon re-read, the proposal seemed a bit convoluted, so I've reworded it to make the statement more direct. I also added the missing “at the hyperfocal distance,” to a comment above so that it makes sense.
I suppose we could eliminate the formula and say something like “When the subject distance is much less than the hyperfocal distance, the DoF is proportional to the product of the f-number and the CoC, so an increase in N is equivalent to a decrease in c, and vice versa”, but this is somewhat pulling it out of the air because we've not previously given a DoF formula in this article. This relationship may be second nature to you and me, but I doubt it's that obvious to most readers. And for me, even though I'm very familiar with this relationship, trying to describe even simple math solely in words is excessively abstract, akin to using SVG code to describe a drawing. JeffConrad (talk) 19:14, 26 April 2010 (UTC)

### New proposal for CoC adjustment section

Perhaps we could try something to the effect of

“The f-number determined from a lens DoF scale can be adjusted to reflect a CoC different from the one on which the DoF scale is based. It is shown in the Depth of field article that
${\displaystyle \mathrm {DoF} ={\frac {2Nc\left(m+1\right)}{m^{2}-\left({\frac {Nc}{f}}\right)^{2}}}\,,}$
where N is the lens f-number, c is the CoC, m is the magnification, and f is the lens focal length. Because the f-number and CoC occur only as the product Nc, an increase in one is equivalent to a corresponding decrease in the other, and vice versa. For example, if it is known that a lens DoF scale is based on a CoC of 0.035 mm, and the actual conditions require a CoC of 0.025 mm, the CoC must be decreased by a factor of 0.035 / 0.025 = 1.4; this can be accomplished by increasing the f-number determined from the DoF scale by the same factor, or about 1 stop, so the lens can simply be closed down 1 stop from the value indicated on the scale.
The same approach can usually be used with a DoF calculator on a view camera.”

This strikes me as concise as well as reasonably supported. With the formula provided, I can see at at glance that the next statement logically follows. I'll concede that this isn't the most common form of the total DoF equation, but it's the only exact formula we give in that article. And I think it's just as digestible as the more common form

${\displaystyle \mathrm {DoF} ={\frac {2uNc{{f}^{2}}\left(u-f\right)}{{{f}^{4}}-{{N}^{2}}{{c}^{2}}{{\left(u-f\right)}^{2}}}}\,,}$

for which, offhand, I don't have a handy source.

The math? It seems to me that the one formula that's included is a lot less imposing than the math in the section that follows. JeffConrad (talk) 23:20, 26 April 2010 (UTC)

I'd say that's better, but I might still argue that the formula is not the best way to get to the understanding. You don't need a formula for DOF to know that it will be unchanged if you change your c criterion and make the corresponding change to your aperture diameter. Dicklyon (talk) 00:06, 27 April 2010 (UTC)
You know this provided that you know that N and c occur only as the product Nc. Since we don't have a source to support this, showing the formula (which is derived from basic principles in the Depth of field article) seems like the most reasonable way to support the statement. Even if we had a source, seeing the formula right it front of me makes it easier to accept the statement. Again, the issue is verifiability (or reasonable facsimile thereof) as much as truth. I've developed an inherent distrust of almost anything on the web, especially if it relates in any way, shape, or form to depth of field. Even with presumptively reliable sources, I want to know the basis for a claim.
In retrospect, I may have erred in thinking that “DoF is proportional to the product Nc” was inherently easier to grasp than “N and c occur only as the product Nc”, and accordingly using an approximate equation for which the former is true. It now appears that using the exact formula is by far the simpler approach. If we decide to keep this section, I'd like to go with what I've just proposed unless there's a strong objection—it seems to me a reasonable compromise. Again, the math is much less and is no more gratuitous than that in the following section. JeffConrad (talk) 00:52, 27 April 2010 (UTC)
Right, no source, so what can we say? Only what's obvious? It's obvious from a ray diagram that the actual CoC of an object point at any distance can be changed, by changing the aperture, proportionately. And that if we fix a DOF, and consider only object points at the near and far limits, then we need to change aperture if we change CoC, proportionately. No equations needed. Of course, it can also be supported by either exact or approximate equations. Dicklyon (talk) 03:01, 27 April 2010 (UTC)
What could we do?
1. Find a source that makes a similar statement.
2. Make a diagram and use that to explain the reciprocal relationship.
3. Show a formula that's either sourced or derived.
I couldn't find a source that makes a sufficiently similar statement. And I didn't have a diagram that made this clear. The only sourced equations I could find were approximate, throwing in additional complications, so showing an exact equation that's derived in the WL'd article seemed a reasonable next step. Even if I had a diagram, I don't think I could explain this as succinctly as I could by providing the equation.
The behavior may be obvious to anyone who could derive the DoF equations from a diagram. And had a diagram or was willing to make one. How many readers of this article would qualify? I don't think we need a citation for every sentence, but I also don't think we can treat everything as self evident.
I think the discussion is starting to repeat itself. I'm not comfortable making the statement without the equation, and if you're not comfortable with it, perhaps we should just delete the section. As I've mentioned, with the majority of lenses in use today, it's almost impossible to get an accurate f-number from the DoF scale, so there's nothing to adjust. JeffConrad (talk) 03:58, 27 April 2010 (UTC)

Looking at the section DOF limits in the Depth of field article, I can't see a reasonable explanation not including the figure and just about everything up to and including the substitution for d, leading to something like
${\displaystyle {\frac {v_{\mathrm {N} }-v}{v_{\mathrm {N} }}}={\frac {v-v_{\mathrm {F} }}{v_{\mathrm {F} }}}={\frac {Nc}{f}}\,,}$
which makes it clear that as long as the Nc product is unchanged, the image distances (and hence the DoF) don't change. To me, this seems a lot more complex than just including a DoF equation; in essence, it's repeating a derivation rather than making use of a relationship that has already been derived. I also can't see just referring the reader to a diagram and derivation in the Depth of field article to support the point, especially since that derivation doesn't explicitly make the point on which we would rely.
Perhaps a mere glance at the diagram suffices to make the point for some, but I doubt that it's very many. So I more or less stand by what I've suggested. I think a glance at the Nc product in a DoF equation is a far simpler and quicker read than forcing the reader to follow a derivation. JeffConrad (talk) 21:41, 27 April 2010 (UTC)
Because there seems to be consensus that what I proposed above is an improvement, I've updated the article accordingly. If it still doesn't work, I suggest we get rid of the section entirely—the article has somehow survived without it, and presumably would continue to do so. JeffConrad (talk) 09:06, 28 April 2010 (UTC)