Talk:Angle of view

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I'm not an expert, but the first sentence of the article seems incorrect to me. Surely all the sample images took up roughly the same area on the 35mm film? Soundray 21:14, 16 Feb 2004 (UTC)

I don't think it's right either, and I don't remember what page I copied that from (they should both be changed). As I recall, I was talking with someone who was trying to explain to me how to define the term without using a circular definition, and used the chance to dump in some photos I'd taken. I believe the definition as is is clumsy and misleading, if not outright wrong (and the fault is, of course, mine--look at the version history). Koyaanis Qatsi 00:15, 17 Feb 2004 (UTC)

This page could really use a chart converting 35mm focal lengths to angle of view. Also, the formula to do this, with the film size as a parameter.

Digital cameras[edit]

I just added the term 'sensor' as the digital alternative for 'film'. But steve's digicams says "Consumer digicam focal lengths are usually stated in terms of their 35mm film equivalents." So should the given focal length then be recalculated for the formula to work?

By the way, that page also says "For digital SLR cameras with interchangeable lenses it's more difficult as different cameras have different size sensors." Which complicates matters. DirkvdM 10:15, 2 February 2006 (UTC)

I haven't used many digital cameras, so I don't know. But for the two Canon cameras that I do have, the real focal length is printed right beside the lens. Using this focal length, I calculated the angle of view of my Canon ZR90 camera to be 37 degrees. The angle of view I measured earlier was 36 degrees, so the calculation was correct (or at least accurate). Also, the size of the sensor (i.e. CCD) can be found on most detailed webpages about the digital camera. Bowlhover 13:45, 4 February 2006 (UTC)


In the "Calculating a camera's angle of view" section there is an error:

In the first formula (ƒ) should be "focal distance" instead of "effective focal length". Effective focal length is something like 28 for wide-angle, 50 for standard, 200 for telephoto objectives (35mm film), but that's not what it is about. It is about how far the object is from the camera (film or sensor), e.g. 50cm or 5m, or 23m.

The thing is, however, that I don't know how to relate this to macro, and other objectives, so someone should correct this article who knows what he is speaking about.

The thing you're calling "effective focal length" is the 35-mm-field-of-view-equivalent focal length. Different beast. Dicklyon 14:58, 12 June 2007 (UTC)
I agree with Dicklyon, the effective focal length describes the FL of your main lens + any optical elements you hang off the front or back (macro dioptres etc); it's like the gross or total FL of all the lenses in that system. It is correct for that formula, because AoV is the same at any object distance. ( 21:18, 27 August 2007 (UTC))
IMO "Working Distance" or "Operating Distance" is the traditional photographer's term for what you call "focal distance". It specifies the distance between the Object and the Film Plane ... and is theoretically irrelevant to Angle of View calculations. In practice, however, pulling focus can affect Angle of View: the simplest method to focus the image onto the film plane is by moving the lens itself along the optical axis, whilst the object-to-film distance remains the same (eg bellows camera, magnifying glass). With this method, very small movements of the lens have a large effect on the film-image focus, and a small (commonly negligible) effect on the Angle of View. Moving the lens away from the Film Plane (for closer focus) increases the size of the image circle, effectively reducing the Field of View recorded on the film/sensor; which is how extension tubes work. (talk) 18:03, 18 August 2008 (UTC)

Optical Axis[edit]

My understanding is that the Horizontal and Vertical Angle of View are traditionally measured across the Optical Axis (centre of the lens / image) to avoid errors caused by Barrel Distortion or Pincushion Distortion. That way the AoV formula also works accurately for non-rectilinear lenses.

Currently the illustration does not show the diagonal, horizontal and vertical AoV arcs 'meeting' as they pass through the optical axis. The description (definition) should read something like the Vertical Angle of View is measured from the centre of the top edge of the image to the centre of the bottom edge of the image ... etc. 00:29, 27 August 2007 (UTC)

Still vs. motion picture 35mm film.[edit]

The frame size is needed to calculate the angle of view. A still 35mm film camera has a VERY different frame size than a 35mm motion picture camera (normal, not vistavision).

In a still camera, the film moves sideways and in motion picture cameras, the film moves vertically. That is why there is a vast difference in the size of the frame.

Therefore any reference to a 35mm camera MUST make it clear if this is a STILL or a MOTION PICTURE camera. Just saying a "35mm camera" or "35mm frame" is WRONG!!!! ~~~~ Robert Elliott (talk) 03:50, 3 January 2008 (UTC)

I inserted "still" in the one place I could find that might remotely have been considered ambiguous. If there are others, just fix them. Dicklyon (talk) 04:44, 3 January 2008 (UTC)

Difference between Field of View & Angle of View in photography[edit]

Despite popular misuse (and I do it too!), saying that Field of View is interchangeable with Angle of View is simply not true! The funny thing is that knowing your Angle of View is relatively useless in practical photography, which is probably why Field of View is the more familiar term.

Field of View means simply how much of this scene is included in my picture. A larger FOV can be obtained by either increasing the AOV, or increasing the camera-object distance.

"Field of View" and "Depth of Field" are measures of distance (so many feet or so many metres) - they are concerned with objective dimensions. Angle of View is not dimensional, angles are dimensionless. FOV size increases proportionally with distance whereas AOV does not.

  • The most important point is that objective dimensions (size and distance) are much easier to measure/estimate than relative angles. Angles of view may be useful to surveyors and astronomers, allowing them to calculate unmeasurable distances, but if I ask you to imagine the difference between a 18 degree elevation and a 26 degree elevation, you would be pretty hard pressed. However if I ask you to imagine looking at a 10ft wall from a distance of 30ft and then at a distance of 20ft, it gets a lot easier to visualise.
  • Focal Length, Image Format, Minimum Focal Range, etc are always given as dimensional values - usually mm. Aspect Ratios describe proportions between rectilinear lengths, not angles and arcs. Converting between angles and dimensions involves more complex mathematics such as arctangent tables which you can't do in your head. For practical photography, these conversions are completely unnecessary and only add to confusion. The FOV formula is so simple you can do it in your head and it gives you useful information. (talk) 02:56, 15 March 2008 (UTC)

FOV formula in practical photography[edit]

In landscape, architectural, underwater, macro and aerial photography, sizes and distances can be so large or critical that 'stepping back a bit' and 'zooming out a bit' are not enough to give the photographer the FOV he wants. Therefore photographers have devised a user-friendly FOV formula - as opposed to the AOV formulae given in the article - for use when 'setting up a shot' on location with minimum fuss.


  • FOV = Field of View as the dimension of the Objective Frame,
  • F = Focal Length of the lens,
  • I = Image (D, H or V dimension of the Sensor) and
  • D = Distance between object and camera:
FOV = D * I / F

D is going to be the most variable factor, so if you let D = 1, then you get a FOV:D ratio of Objective Frame-Size : Distance. This ratio is constant for this prime lens on this camera. Note that the AOV is also derived from I and F (2 arctan (I / (2 F))), but FOV size increases proportionally with distance whereas AOV does not. With practice, and familiarity with the focal lengths of your lenses, this method of setting up a shot is extremely quick and efficient. Even zoom lenses have minimum and maximum AOVs and 'sweet spots' measured as focal lengths.

  • Eg1 If I use my 28mm lens: I/F = 36mm/28mm so my FOV:D ratio is 9/7 which means I need to stand at least 70ft away from a 90ft building to get it all in frame.
  • Eg2 Using a normal lens, 36mm/50mm gives me FOV:D ratio of 72%. If I want to photograph a 70mm-ish butterfly full frame with my normal lens, I need to get the camera about 100mm from the insect. However, I also know that the minimum focal range of this lens is 300mm, so I need to change the lens to get this shot. If I do this before I shove the camera at the butterfly, it's more likely to still be there when I'm ready to take the picture.

Lens Manufacturers use the Diagonal AOV reference because it corresponds the diameter of the Useful Image Circle and is unaffected by Aspect Ratio. However, FOV traditionally refers to the Horizontal FOV, because this is most frequently the one a photographer wants to use. Aspect Ratio? easy: if my AR is 4:3, my vertical FOV is going to be 3/4 of my horizontal FOV. (That doesn't work with AOV!) (talk) 02:56, 15 March 2008 (UTC)

Angle of Coverage[edit]

When comparing the actual size/area of the lens' Useful Image Circle to the actual size/area of the camera Sensor, a (dimensionless) "Angle of Coverage" is just useless. The "back focal length" of a lens gives you this information in a useful form, but as this property of a lens system is certainly not adjustable and conforms incredibly precisely to the BFL defined by its Lens mount system, I see no reason to reinvent it here. It would make more sense to talk about a "Field of Coverage at the Focal Plane", but that is exactly what a lens' "Image Circle" is. Even in View Cameras, it is the size of the Lens' Image Circle which is important to Shift, not the angle of divergence of its peripheral rays - and the Tilt angle is relative to the optical axis (the angle of the lens' focal plane is always perpendicular to its optical axis) so again a "Back AoV" just doesn't come up. (talk) 02:56, 15 March 2008 (UTC)

Non Rectilinear Lens - Radial Distortion[edit]

Quantifying Radial Distortion in Non-Rectinlinear Lenses is no mystery if you realise that Radial Distortion increases with distance from the optical axis. The corners of a rectangular image are furthest away from the optical axis and thus most distorted. As long as you measure Vertical and Horizontal FOV through the optical axis, ie between the mid-points of opposing sides of the frame, you will get accurate Focal Length readings. Radial Distortion of a lens can be quantified objectively by measuring the Diagonal FOV empirically and comparing it to the calculated (rectilinear) dFOV for the lens' focal length. Barrel distortion stretches the dFOV, whereas PinCushion Distortion shrinks the dFOV in proportion to the hFOV or vFOV. It is that simple. For the 'worst case' measure of radial distortion, you would compare the shortest FOV (usually the Vertical) to the longest (always the Diagonal). Of course marketing 'specs' for lenses usually employ different ways of measuring radial distortion in order to exaggerate how 'rectilinear' the lens is. As with all serious photographic equipment, price is a better indication of quality than marketing material. (talk) 02:56, 15 March 2008 (UTC)


There should be a graph of angle of view vs. focal lenght if not here, on crop factor or focal length. Here's a start: Matlab/Octave code to make such a plot:

fl = 17:300; 
loglog(fl, 2*atan((repmat([36; 24; 36/1.6; 24/1.6],1,size(fl,2))./2)./repmat(fl,4,1)) * 180/pi); 
xlabel('Focal length');
ylabel('Angle of view');
legend('135 film width','height','1.6 crop width','height');
grid on;

Feel free to finish it up, or I may get back to it. —Ben FrantzDale (talk) 17:03, 22 June 2008 (UTC)

I don't see how that plot is very useful. There are many formats beside these two. A plot as a function of FL / format might be more useful; you could mark the normal, wide, and tele ranges on it. Also, 135 is a film size, not a format. At least three different formats are shot on this film size. Dicklyon (talk) 17:12, 22 June 2008 (UTC)

Effective focal length[edit]

The definition of “effective focal length” in this article seems at odds with common usage (e.g., Sidney Ray's Applied Photographic Optics, 3rd ed, p. 47) and with that in the article focal length. I think what's meant is simply “image distance”. JeffConrad (talk) 00:21, 7 August 2008 (UTC)

Yes, I agree, that's the wrong thing to call it. Dicklyon (talk) 01:17, 7 August 2008 (UTC)

Merge proposal[edit]

From out-of-the-blue WP:content fork, Field of view (image processing). Dicklyon (talk) 01:50, 11 October 2008 (UTC)

Merging the article would be fine with me. The Lamb of God (talk) 23:14, 13 October 2008 (UTC)
Good. Since it's all your work, can you find out what part is not already represented here, and add a section or two as needed? Dicklyon (talk) 23:18, 13 October 2008 (UTC)
Yes I can. It might now be right away but I will do thatThe Lamb of God (talk) 15:22, 14 October 2008 (UTC)

Thanks for starting on the merge. But there's still a lot of work to do, to get to a coherent article that respects WP:MOS (esp. MOS:BOLD and equation formatting). The big section on Field of view (image processing) is very unclear in its relationship to the rest. The statement "industry standards refer to it most often as FOV" really needs a source; if we could look at what the standards are, or who has drawn such a conclusion, it could guide the integration effort. If different fields prefer different terms, we should be able to clarify that. Etc. I'll be happy to help. Dicklyon (talk) 16:41, 14 October 2008 (UTC)

I agree it is not exactlly clear on how the articles relate to one another. However, they certainly do. I am unsure how to merge it in a more coherent manner without deleting my own thing. Yet, by deleting my own things I feel that it makes the section incomplete. Your help would be welcome. I can add an "industry standard" reference that may or may not be sufficient, if not some one should be able to find one somewhere on the "SPIE", "NI", or "ISO" web sites.The Lamb of God (talk) 16:52, 14 October 2008 (UTC)

In addition, the content seems to be completely incoherent and uninterpretable. You introduce variable names and then don't use them in the example calculations. New terms like "angular extent" are used for no apparent reason. And parenthetical like "(in radians)" appear to not have any actual motivation, as it appears that any system of angular measurement would work equally well, and so need not be specified there. The stuff about display pixels and target sizes is as clear as mud, and in my estimation probably incorrect. The linked sources don't take you where you can attempt to verify.

My recommendation would be to step back, take out your own thing, see what's missing, and add that back in a more integrated way. Dicklyon (talk) 16:55, 14 October 2008 (UTC)

It seems that the variables I introduced are the variables I used. angular extent is not a new term its explained in the first sentence of the article. radians doesn't have any actual motivation yes, it is simply just what is used. Miliradians or degrees are just as fine so you have a point there. Stuff about display pixels and target size is correct by the estimation of the optics industry. I will notify EOI that they need a better web link. The incoherency does not seem as incoherent to me, but that is probably just because I am used to seeing it that way. Too technical is probably more accurate than incoherent. The page can be moved back to Field of view (image processing) for the time being.The Lamb of God (talk) 18:01, 14 October 2008 (UTC)
It's not too technical; rather, too incoherent. In the section Example calculation of angular extent, there are variables defined, and there's a calculation, but there's no formula with the variables in it to show what you're calculating. And you don't need the term "angular extent" when the article already calls it angle or view and field of view, do you? Or is this angular extent different from the angle of view? Just be clear, clean up the style issues, etc. It's better to do it here (or some in your sandbox if you like) than in a content fork. Dicklyon (talk) 18:22, 14 October 2008 (UTC)
Dick I think the best solution would be to do what I originally did and just give my thing its own article. This article is more focused on photography and the "angle of view" of a lens while my intended audience is in the digital imaging community and meant for digital imaging . "The field of view of an imaging sensor." My thing is too incoherent as it relates to this article any way. I am going to move it back therefore. —Preceding unsigned comment added by The Lamb of God (talkcontribs) 16:21, 16 October 2008 (UTC)
No, I don't think that's acceptable. See WP:CFORK. You're going to have to face up to learning how to make good wikipedia articles, and you can't really make progress on that by trying to make your own article to get around having to fit material in with what others have done. Dicklyon (talk) 03:54, 17 October 2008 (UTC)
I finally figured out what your formulas are trying to say. The "angular extent" is the angular size of the virtual image of the target, which is at infinite distance; this angle in radians is the ratio of physical target size to focal length of the imaging system that makes the virtual image at infinity, which in this case is the collimator's main mirror. The FOV or AOV of the camera is just how much more it sees than the target, which has been totally confused by calling the camera's image size "Vertical Dimension of Display (pixels)" and such; it's about the camera, not the display; or it's about the size of the full camera image on your display, if you want to measure in that space. These are all things that could be cleared up if you'd edit with others, explain what you're up to, etc.

At the deletion discussion Wikipedia:Articles for deletion/Field of view (image processing) there are lots of opinions, but generally support for some kind of a merge. So I've restored the merge and started to make it fit better. On review it became clear that the other article was mostly about a test method for measuring FOV, as opposed to calculating it from the camera parameters (sensor size and f.l.); so I made an appropriate section head for it. I went ahead and did some editing to move the style in the right direction, but there's still a lot of work needed, and it needs to be a lot shorter. I'll go redirect the other now... Dicklyon (talk) 06:12, 20 October 2008 (UTC)

Lens asymmetry[edit]

I added the angle of view formula for asymmetric lenses (most photographic telezoom lenses are of this type). I realize that I really also should edit the derivation section, but to be honest this would take more time then I am willing to at the moment. The reference provides a full derivation for those interested and/or willing to draw the new picture etc.

Arjan Mels (talk) 21:13, 24 January 2010 (UTC)

Chapter Characteristics, first sentence - I don't think it is right to say that that longer lens has shallower depth of field. DOF is almost exclusively dependent on the aperture. Focal length could be ignored here... Cheerz, Mike. — Preceding unsigned comment added by (talk) 23:57, 31 July 2011 (UTC)

The statement is definitely incorrect without qualification. To good approximation, DOF depends on magnification (which includes the effect of focal length and camera-to-subject distance) and aperture. JeffConrad (talk) 00:28, 1 August 2011 (UTC)

Possible Error![edit]

Location of possible error: 2nd Paragraph, last sentence.

Quote of possible error: "If the angle of view exceeds the angle of coverage, however, then vignetting will be present in the resulting photograph."

I think this is perhaps backwards. It would seem to be more correct (at least according to the preceding sentences of the article if they can be trusted), that it should read instead:

"If the angle of coverage (area of the sensor) exceeds the angle of view (image coming from the lens), however, then vignetting will be present in the resulting photograph."

This re-write would seem to make more sense simply because, if the angle of view (image coming from the lens) (which is a circular image) is bigger (exceeds) the area of coverage (size of the sensor) then you would get your standard cropped rectangular picture and no vignetting.

I wanted to put this into discussion first because I am not 100% certain and don't want to edit the main page. — Preceding unsigned comment added by Jettatore (talkcontribs) 15:27, 14 October 2011 (UTC)

You sound right to me. —Ben FrantzDale (talk) 17:41, 14 October 2011 (UTC)
No, he's backwards. Angle of view is determined by the sensor, and angle of coverage by the lens, opposite to his stated interpretation. Dicklyon (talk) 17:45, 14 October 2011 (UTC)
Aah, yes. I skipped his definitions and went directly to agreeing that the image plane beyond the image circle is vignetted. —Ben FrantzDale (talk) 15:03, 17 October 2011 (UTC)

Has anyone come to any conclusion. It still sounds to me, with the article yet to be modified, that the original author either has definitions reversed, or has accidentally reversed their terms or perhaps they used "exceeds" instead of "fails to match or exceed". Without adjusting one of these, and I wouldn't know what to adjust or even be sure if I am correct, that there is still some error remaining in that paragraph. Jettatore (talk) 21:09, 26 October 2011 (UTC)

"If the angle of view exceeds the angle of coverage, however, then vignetting will be present in the resulting photograph" is correct, as far as I can see. Is it confusing you? Or is there some other issue I'm not seeing? It could be made more explicit as "If the diagonal angle of view exceeds the angle of coverage, however, then vignetting will be present in the resulting photograph." Dicklyon (talk) 21:12, 26 October 2011 (UTC)
well I guess it's still confusing to me if the entire paragraph is without error. I'll try to explain myself in full. Vignetting is when there is a darkening of the border of the image circle or frame, and in this case would be caused because there is not enough projected image to fill up the sensor. So if we listen to what he's said, "If the angle of view exceeds the angle of coverage..." this would appear to me that you have more of a picture to project onto the sensor and instead of "vignetting" you would get "cropping". Again, the reason I started this as a discussion and not an edit is because I am just not fully certain but appreciate any clarification or new understandings or someone else confirming and editing. cheers Jettatore (talk) 21:40, 26 October 2011 (UTC)
Indeed, it's not really well defined what happens outside the image circle. You might call it cropping, but typically it's a gradual falloff, not abrupt, so here it was called vignetting. Dicklyon (talk) 22:33, 26 October 2011 (UTC)
Here is a great source about all that. Dicklyon (talk) 22:35, 26 October 2011 (UTC)
The more I read this the more I agree that it's at least confusing. Usually in photography the "angle of coverage" of a lens isn't emphasized -- there are very few lenses that are designed to make an image circle smaller than the sensor of the camera they are designed for. The wide-angle crop-sensor lenses that wouldn't fill a 35mm sensor are designed not to mount on a 35mm body (e.g., the Cannon "white square" lenses). There exist lenses with a relay and an internal field stop that produced a sharp image circle (or square or any shape you like) that has no vignetting at the edges. Of course, most camera lenses have no relay and so no proper field stop; they may have lens hoods which may act as out-of-focus "field" stops, but strictly speaking, I think if it's out of focus it's vignetting, not field-stopping, so a typical relay-free camera lens will necessarily vignette at the edge of the image circle. As both of you point out, there's ambiguity in what the "angle of view" is when the image circle doesn't fill the sensor. One could define it to be the pinhole angle of view given the focal length and the sensor radius, or one could define it as the actual angle of image-forming rays. I tend to go with the latter. When I spec an optical design, I ask for an angle of view and possibly spec vignetting falloff (or insist on none). I would be pretty disappointed if the designer came back saying "It's got the angle you asked for, it just doesn't let any rays form an image there. Also, vignetting may be OK within the coverage of the lens (unless you define coverage to be coverage without vignetting), so then the sentence is misleading in that it implies that full coverage means no vignetting. Dick's link says that the image circle does have vignetting toward the edge, implying that the diameter is the diameter that gets any light at all. How about this?: "For most cameras, it may be assumed that the image circle produced by the lens is large enough to cover the film or sensor completely (possibly with some vignetting toward the edge). If the angle of coverage of the lens does not fill the sensor, the image circle will be visible, typically with strong vignetting toward the edge, and the effective angle of view will be limited to the the angle of coverage." —Ben FrantzDale (talk) 11:58, 27 October 2011 (UTC)
More or less OK, but "for most cameras" ignores the class of cameras for which it's an issue; e.g. view cameras with interchangeable lenses that interchange between cameras of different format. Dicklyon (talk) 14:46, 27 October 2011 (UTC)
How about "Typically, the image circle produced by a camera lens is large enough..."? (I see "typically" used as a less-quantitative version of "most" on Wikipedia.) I'll be bold with that version. Also, in that paragraph it implies that angle of coverage is the angle of chief rays emerging from the exit pupil -- that can't be right: digicam lenses are often image-space telecentric. —Ben FrantzDale (talk) 12:34, 28 October 2011 (UTC)

Formula for FOV when using a known zoom factor[edit]

Given an initial field of view for zoom level 1 (normal image - no zoom) I know a formula for computing the fov given a zoom level.

Is it ok to have the formula in some paragraph?

Iulian-Nicu Șerbănoiu 14:37, 10 November 2011 (UTC) — Preceding unsigned comment added by Iulian.serbanoiu (talkcontribs)

What's a "zoomLevel"? Where does this formula come from? Dicklyon (talk) 16:01, 10 November 2011 (UTC)

Example: when magnifying a picture twice (200%) you will have zoom level 2 (you will see only half of a 'fullscreen' object in the same picture size ). This means that the seen width of a object occupying the entire screen of the newly obtained image will be width / zoomLevel. Given those parameters the formula is fairly easy to obtain (considering the distance D from the camera to the object):

If we divide we obtain the formula above (D is simplified). — Preceding unsigned comment added by Iulian.serbanoiu (talkcontribs) 23:34, 10 November 2011 (UTC)

Yes, given that definition, the derivation is trivial. But "zoomLevel" is not a normal term, is it? And is this formula sourced? Dicklyon (talk) 00:07, 11 November 2011 (UTC)
I used this formula on Android devices (an augmented reality application) to compute the fov of the camera when zooming, and it worked fine. I don't know (yet?) any resources where this formula is mentioned. Iulian-Nicu Șerbănoiu 06:49, 11 November 2011 (UTC) — Preceding unsigned comment added by Iulian.serbanoiu (talkcontribs)
Unfortunately no sources for this formula were found. Is this acceptable in case of such an article? --Iulian-Nicu Șerbănoiu 10:16, 14 November 2011 (UTC) — Preceding unsigned comment added by Iulian.serbanoiu (talkcontribs)
I don't disagree with your math. It appears that "zoomLevel" is the reciprocal of the fraction of the full image size being used. The thing is, "zoomLevel" isn't standard. This equation (or one like it) may belong on crop factor where the conversion between sensor size and angle of view is relevant, but "zoomLevel" isn't a standard photography/optics term, I don't think. I suppose it's probably the same as the "zoom factor" the "×" used in, e.g., "10× zoom"... in that case there may be a place for this equation... hmm... —Ben FrantzDale (talk) 12:43, 14 November 2011 (UTC)

I understand. Maybe the right place for such formula will be indeed the crop factor page. I will see. Thank you. --Iulian-Nicu Șerbănoiu 12:33, 15 November 2011 (UTC) — Preceding unsigned comment added by Iulian.serbanoiu (talkcontribs)
Yea, the more I think about it, the more it makes sense to have that equation on crop factor. For long lenses (small angle) those trig terms go linear, but for wide lenses, it is interesting that the effect on the angle of view is different from the effect on the linear extent of a rectangular projection. Of course, if you have a lens with distortion, that messes with things... PS, sign your comments by writing ~~~~ at the end of your posts; it gets auto-replaced with a signature line. —Ben FrantzDale (talk) 17:28, 15 November 2011 (UTC)
Yes, I always used the 4 tildes but unfortunately my signature was not good. I changed that now. --Iulian.serbanoiu (talk) 10:39, 16 November 2011 (UTC)

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Maybe wrong tables[edit]

I transposed both tables for better readability. While reviewing both tables, I noticed that something should be wrong, some component may be missing in the calculation of the values at shorter focal distances. If you see lenses for APC sensors, a 4.5mm lens, is a fish eye or super wide angle 180 degrees or more lens. While the second table says 146 degrees at 4mm diagonal. The first, projects a circular image. According to the first table, 0mm corresponds to 180 degrees. Those tables do not consider the refractive and physical shape of lenses. There are optical design techniques that allow to project a circular 220 degrees image with a 6mm focal length fish eye lens for full frame sensors, having the lens closest to the sensor at a distance greater than 6mm to have a gap for the mirror travel. Earlier nikkor fish eye lenses could only be used in cameras that can lock the mirror. The same design technique is used in focal reducers. the opposite of those tele converters fitted between the lens and the sensor in DSRLs or 4/3 cameras. That allows to design 220 degrees fish eye lenses, which according to the table would be impossible to make, if 0mm. the closest focal distance, has 180 degrees. — Preceding unsigned comment added by (talk) 14:24, 30 October 2016 (UTC)