Talk:Depth of field/Archive 1

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Old junk previously not in a section

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

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

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

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

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

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

            o >|<

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

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

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

Sure

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

About the equations

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

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

About the photograph

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

That's a great picture -- thanks for putting it in the article! The only thing that would make it better would be if the text read "A long time ago, in a galaxy far away..." :-)

Atlant 11:52, 31 August 2005 (UTC)

Agreed - love the picture - makes this article super-stylish. --DreamsReign 04:36, 17 May 2006 (UTC)

About the photos provided...

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

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

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

On the other hand...

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

An error and a suggestion

Error: text is missing below the first figure.

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

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

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

New equations 28 August 2006

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

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

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

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

JeffConrad 02:40, 28 August 2006 (UTC)

Jeff, in a previous round of changes, I sought to use equations that are found in the literature and accurate enough, while being much simpler, and at the same time acknowledging the existence of more detailed equations whose accuracy is however limited by the factors they neglect such as pupil magnification.

I haven't really studied the new section carefully yet, but my impression is that by starting with the rather complex equations it will lose a lot of readers, before they get to the simpler ones. Think about it from that point of view and see if you think a different order of presentation could be made workable. I appreciate your effort on helping to clean this up, as you did with EV and LV and APEX system. Dicklyon 03:01, 28 August 2006 (UTC)

Dick, I had the same concern, and almost made a comment to that effect. Perhaps some simplification of the initial presentation is indicated, with more detail later to demonstrate that the basic equations weren't simply pulled out of the air. With this approach, I'd be inclined to keep the basic presentation even simpler than it was. The question is, "To what use would these equations be put, and which equations would be the most useful for that purpose?" A few equation candidates:

1. Total DoF?
2. Front and rear DoF?
3. Near and far limits of DoF?
4. Near:far DoF ratio?
5. Focus and f-number from near and far limits of DoF?

The last equations are almost the only ones that I've ever used, yet they possibly are the least common in the literature. It long has been my impression that DoF discussions concentrating on the object side of the lens are primarily academic exercises; in practice, the task of controlling DoF usually is much easier on the image side:

1. View camera users who calculate DoF usually use the focus spread (difference between near and far image distances) to determine focus and f-number.
2. Small- and medium-format users typically use lens DoF scales to accomplish the same task. At least they did with manual-focus lenses ... except for a few older Canon 35 mm cameras (with the Depth-of-Field AE mode), there is no easy way to control DoF with most autofocus lenses. It's possible, at least in theory, to use object-side relationships in conjunction with lens DoF scales, but the resolution on most AF-lens distance scales is so poor that it's difficult to set the distance with much precision (e.g., it's easy to calculate hyperfocal distance, but tough to set it).

That said, I think getting into the image side probably would lose almost all but the really hardcore readers.

My personal observation on practical control of DoF would be something like:

1. Determining DoF from focus spread or lens distance and DoF scales is reasonably straighforward for distances large in comparison with focal length; as noted, however, even this is no simple task with most AF lenses.
2. Determining close-up DoF with unit-focusing lenses is feasible in theory but quite a chore in practice. With most current small-format internal-focusing long-focus macro lenses that change pupil magnification, internodal distance, and focal length with subject distance, it's almost impossible.

In other words, great accuracy is not needed to determine DoF at moderate subject distances, if your camera will allow you to do it. Don't try to calculate close-up DoF at home ...

JeffConrad 06:18, 28 August 2006 (UTC)

Larger formats -> smaller depth of field

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

Put simply, for the same subject distance, a longer focal length provides greater magnification, and to a first approximation, DOF is inversely proportional to magnification. Hence the reduced DOF. JeffConrad 08:03, 28 September 2006 (UTC)

Okay. Thanks for your quick reply. When I look at the f-numer equation

$N={\frac {f}{d}}$,

i still get confused, however. I read several places that increasing the f-number N increases the DoF. From the equation it looks like increasing the focal length f would have the same effect on the f-number as decreasing the aperture diameter d, which would both lead to an increased DoF. From your reply it seems that this isn't true. Is there simple explanation why?

I should mention that I have no background in optics or photography. My interest is only out of curiosity. Bade, September 28, 2006.

The answer is simple: N is not the only variable in the DoF equation. Dicklyon 13:41, 28 September 2006 (UTC)

I can see that, but if I kept d constant, would a larger focal length f (and thus larger N) result in an increased DoF? In other words: does the DoF depend ONLY on the ratio N, or does it depend also on the absolute values of d and f. Does (for example) N = 50mm/1mm and N = 100mm/2mm (same ratio) give the same result (DoF-wise and otherwise)?

Bade, Thursday, September 28, 2006.

Plug some examples into the equation of your choice and see what happens. In general, no; increasing f will give you LESS DoF, not more, if you keep same aperture diameter d. As Jeff points out, the magnification view makes this easiest to see, but any form of the equations should give similar results. Dicklyon 15:14, 28 September 2006 (UTC)

The magnification (and hence the focal length) and circle of confusion scale with the format. See the reference Jeff Conrad's Depth of Field in Depth (PDF) under "Depth of Field and Camera Format" for a discussion of how this affects DOF. JeffConrad 23:33, 29 September 2006 (UTC)

Depth of field versus format size

Dick, I got rid of the sentence

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

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

JeffConrad 07:58, 28 September 2006 (UTC)

I don't know the intent, as I didn't put that (I did edit it a bit). It does seem a bit narrowly put. I doubt that the movements were part of the intent, but that's also a good thing to mention. Dicklyon 13:41, 28 September 2006 (UTC)

So I see ... looks like it was Mr. Anonymous. Had I paid more attention to the history, I'd just have nuked the sentence without comment. Maybe it's best just to leave it out; it's contradictory to mention the greater DOF with smaller cameras and yet claim that the greatest DOF can be had with the largest image format. As the View Camera article mentions, using tilt or swing doesn't really increase DOF, but rather changes the plane of focus to better fit the DOF to the scene. We could add View Camera, Scheimpflug Principle, or Large Format to the "See also" section, but I'm not sure the treatment of movements in any of these articles goes far enough to explain how tilt or swing helps make up for the lesser DOF in larger formats. JeffConrad 22:44, 28 September 2006 (UTC)

What the heck ... I've added a two-sentence mention of movements and tilt/shift lenses to the end of the "Depth of field versus format size" section. I'm not sure that's where it belongs, but I can't think of where else to put it. An article on tilt/shift lenses remains a task for another time. JeffConrad 23:03, 28 September 2006 (UTC)

Isn't

"Consider formats that differ ..."

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

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

Jeff, FYI, a Wikipedia article is never a source; they're OK for "see also", but not as references for sources. It's too transient, and needs to have sources of its own to be verifiable, so list a real source instead. Dicklyon 04:27, 11 October 2006 (UTC)

I chose my words in haste; I never intended to suggest the Wiki article as a "reliable source" in the formal sense, but rather as a guide to Wiki authors. NIST SP 811 obviously is an authoritative source in the USA; NIST SP 330 also is useful. The ISO 31 standards are the definitive references, but unlike the NIST documents, they aren't free. JeffConrad 04:54, 11 October 2006 (UTC)

Edits of 14–15 October 2009

I removed

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

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

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

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

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

That all looks great. Of course, by von Rohr's method, the result is trivial; you can get it from the picture instead of from the algebra. Dicklyon (talk) 04:38, 15 October 2009 (UTC)

I think it shows yet again that there's more than one way to do it; hopefully, at least one will be helpful to the reader. I thought you might add the ref, but included my derivation to make the treatment parallel to that for the more traditional relationship. In any event, I'd say it's adequately sourced. JeffConrad (talk) 05:00, 15 October 2009 (UTC)

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

Delete Circle of confusion computation?

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

Close-up DOF

There are two headings with the same name both starting:

When the subject distance s approaches the focal length

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

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

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

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

Photo clutter

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

I did just add one, but I did so becuase I though an example of close-up DOF was needed. The related section has alot of text on the subject and no image. But mabye you are not refering to me hehe. HighInBC ^{(Need help? Ask me)} 00:06, 17 November 2006 (UTC)

Not you specifically; it's something that's been bugging me for a while. I guess the recent addition just sparked me finally commenting on it. The problem is that your image doesn't really show anything different from any other photograph with a shallow DOF - the first image in the article being a notable example.

The main problem, however, is that there are too many images period. I think that certain other ones may be worthy - such as an image progression showing the same image with different apertures. But beyond one or two examples, what else can you really show about DOF that is different? Let's decide what types of photos should be here and look for the best examples instead of adding photos which are good examples and trying to come up with a pretext for why it should belong to this article. Girolamo Savonarola 00:15, 17 November 2006 (UTC)

I completely agree with Girolamo—this isn't a photo gallery. The only justification for a photo in this article is its illustration of the concept. The best illustration of shallow DoF includes a photo of the same subject showing greater DoF (as do some of the first images submitted). I'm for weeding out the rest; they're gratuitous, detracting from the article rather than adding to it. JeffConrad 00:33, 17 November 2006 (UTC)

Well I am not to attached to the idea of the image being here. I don't mind if it is removed for housekeeping. HighInBC ^{(Need help? Ask me)} 01:27, 17 November 2006 (UTC)

Again, I agree with Giralomo that it isn't just your image. I'd also eliminate "A Cowslip flower ...," "Artistic effect ...," and possibly the kitten and the sequence below it. This may be going a bit too far, but again, the question is, "Does the image really illustrate the concept?" I think Paul van Walree's site is a good example of illustrative images that also happen to be well executed. JeffConrad 01:57, 17 November 2006 (UTC)

What many have failed to recognize is that the thumbnails have a whole lot more DOF than the full-size images, and thereby fail to make their point unless clicked on. We need examples that work in a small size. Dicklyon 06:43, 18 November 2006 (UTC)

Demonstrating rather conclusively that "apparent DoF" is redundant. It's tough to see what's sharp and what isn't in a small image (much like looking through the viewfinder of a small-format camera). The primary audience for images here probably are people relatively new to photography, so an illustration should be obvious: what is unsharp should be obviously unsharp, and what is sharp should be very sharp (preferably the result of a tripod-mounted camera). I think the images of the type, the butterflies, and the two white flowers make their points quite clearly; with the other images, the differences aren't as obvious. I think it's especially important for the differences in a sequence of images at different f-numbers to be obvious in the thumbnails, because it's awkward to move among the larger versions. JeffConrad 22:20, 18 November 2006 (UTC)

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

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

I would say, if you haven't had any personal involvement with the creation of any of the images, delete whichever seem most appropriate. As for the sequence, perhaps it would be worth contacting one of the people in the image editing project so that they can be turned into a series of frames for an animation, thus saving the clutter of multiple images of the same thing. Girolamo Savonarola 22:19, 18 December 2006 (UTC)

Jeff, I'd go further and encourage you to "be bold" even if some of the photos are your own. You're the guy who has done the most to refine the content of the article, so there's no way your actions will be taken as anything but constructive. If someone objects to a removal, it can be negotiated, but I don't think anyone's likely to be too attached to their particular images here, or too touchy about trying to prune them. Dicklyon 00:17, 19 December 2006 (UTC)

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

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

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

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

Edits of 11–12 December 2006

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

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

Introductory paragraph

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

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

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

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

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

Dicklyon 19:15, 19 December 2006 (UTC)

Your take is much the same as mine. The angle between the marginal rays from the more distant point always is smaller than the angle between the marginal rays from the closer point; however, this does not establish that the DoF behind the subject is greater than the DoF in front of it. It's simple to construct a diagram showing the far DoF less than the near DoF; such a diagram would, of course, violate the lens conjugate equation.

It's impossible to construct such a contradiction if you ignore the conjugate equation and just draw the "outside-the-box" rays by Moritz von Rohr's method. And it's not that the angle behind is less, but that it's less different from the angle at focus. That angle difference translates to a COC, pretty nearly. But, it's a complicated explanation that hard to see easily. Dicklyon 22:42, 19 December 2006 (UTC)

Perhaps the DoF distribution still is worth mentioning, though I wonder if it's necessary in the opening paragraph. In any event, I think the explanation needs to go. I know of no way to show the DoF distribution other than mathematically; it's easy enough to add this if it's thought that the benefit outweighs the clutter of additional math. JeffConrad 21:49, 19 December 2006 (UTC)

I agree it doesn't belong in the lead, since it takes too much space to explain that the distribution goes all the way from symmetric in macro mode to infinitely more behind is distant mode, with everything in between. In my paper, I explained four regions, one of which is the region around which the popular "rule of thumb" of about twice as much behind as in front is actually nearly true. Should we add explanation of those four regions? Or we could use a picture to illustrate somewhat more behind than in front. I'll see what I have... Dicklyon 22:42, 19 December 2006 (UTC)

My initial reaction, which I didn't state very clearly, was that the conclusion was far from obvious to me without a diagram or some other explanation. A diagram might address that, but at that point we might as well add a derivation. At the very least, we need something to establish the near focused, and far distances from the lens. Although this could be done on either the image or object sides, the concept of DoF necessarily starts with an image-side blur spot, so I think an image-side derivation would be simpler and more appropriate for this article. It's certainly not difficult, though the article already is getting a bit long. It may be simpler to add a few equations; moreover, we've already pointed reader's to several derivations, including two online versions.

I had thought of covering the near:far DoF ratio, but again thought the article was a bit long. Perhaps a simple explanation would suffice; I tend to view the ratio as a continuum, ranging from zero at the hyperfocal distance to a limiting value of unity at high magnification. In particular, the distinction between you regions 2 and 3 seems a bit arbitrary. The continuum works only when using the "exact" equations for near and far limits of DoF; the approximate equations

${\frac {\mathrm {near} }{\mathrm {far} }}\approx {\frac {H-s}{H+s}}={\frac {1-s/H}{1+s/H}}$

would suffice for medium-to-far subject distances, but we'd need another equation, such as

${\frac {\mathrm {near} }{\mathrm {far} }}={\frac {fm-Nc}{fm+Nc}}$

(my Eq. 21, equivalent to your equations that follow Figure 3) for the macro region. I'll put something together in my user space to see if it's worth considering. JeffConrad 23:14, 20 December 2006 (UTC)

I have an expanded Basis of the DOF formulae section (which I've retitled) at User:JeffConrad/DoF equations. I think it addresses the issues raised, though I'm not convinced that we need all (or any) of it. Although it's convenient to have a self-contained derivation, the article keeps getting longer ... I am now convinced it is easier to show the near:far DOF distribution algebraically rather than with a diagram. Although it's easy to make a diagram showing greater DOF beyond the subject, it's not so easy to show that it must be so. JeffConrad 02:59, 21 December 2006 (UTC)

I'm against making an encyclopedia article too "mathy". You and I can follow all that and appreciate what it means, but to many readers it just becomes increasingly intimidating--a bigger chunk they have to skip and feel bad about. However, it might be good to summarize the result, that the 1/3-2/3 rule applies at H/3, and that the DOF is more symmetric when closer, more skewed when further. And I agree that it's easier to show the near:far ratio algebraically if you want to get quantitative, but I think it's easier to show diagramatically if you just want to show that it's greater on the far side. It takes a few words to motivate von Rohr's method, but then it becomes obvious, by construction, for whatever size circle you want to put in the field plane. Dicklyon 04:24, 21 December 2006 (UTC)

Depends on the article, I suppose, but as I said, I'm not convinced we need any of it. Quite frankly, I think the entire section Basis of the DOF formulae could be eliminated, pointing the mathematically inclined reader to any of the external links that cover this stuff in detail (I'd probably retain the image-side formulae for focus and f-number simply because they are among the few that actually are useful in the field). I see little reason to say anything about asymmetrical lenses except perhaps to mention that they aren't accurately described by the simple formulae. To my mind, the basic derivation would be far more useful (and less intimidating). In earlier edits, I simply retained many formulae that I probably would not have included in an article such as this.

One either gets into the mathematical detail or one does not, and when one does, the discussion gets quite lengthy, as both my paper and yours illustrate. The middle ground is tough to cover; I originally had a much shorter version, without formulae that I thought no one would ever miss. Of course, almost all the comments I got were about the formulae I had "overlooked."

It's easy to make a simple diagram using von Rohr's method, but really understanding it requires understanding the concept of projecting the image-side blur spot onto an object-side blur spot; easy enough, perhaps for Abbe, Kingslake, and von Rohr, but, to me, more difficult to grasp than the math, and definitely more obscure than the conventional image-side approach. The diagram on my page requires only first-year algebra and geometry, and the derivation certainly is no more complex than yours in the Circle of confusion article.

My original suggestion was simply to eliminate the last sentence of the introductory paragraph. Perhaps this could be tempered by adding a sentence elsewhere stating (but not demonstrating) something to the effect of

"The DOF beyond the subject is always greater than the DOF in front of the subject. When the subject is at the hyperfocal distance or beyond, the far DOF is infinite; as the subject distance decreases, near:far DOF ratio increases, approaching unity at high magnification. The oft-cited 'rule' that 1/3 of the DOF is in front of the subject and 2/3 is beyond is true only when the subject distance is 1/3 the hyperfocal distance."

Such a passage might be subject to challenge, of course, but that is always a possibility with a statement that is not supported. Again, however, the reader could be directed to one of the references or external links for substantiation. JeffConrad 07:50, 21 December 2006 (UTC)

OK, I'll let you worry about whether some simplification can be had by "overlooking" some formulae. I'll put von Rohr's method into his article, since it is, as you say, a rather unusual treatment for a mainstream DOF article. Dicklyon 16:16, 21 December 2006 (UTC)

I think putting von Rohr's method into his article makes perfect sense; perhaps the DOF article can include a link. Including the translation is a big help for those of us who retained little of our high school German.

I've revised the introductory paragraph, added a section Near:far distribution of depth of field, added the image-side equations to the DOF formulae section. I've left the derivation section for now, including the added material. See my further comments under that section on this page. JeffConrad 21:36, 21 December 2006 (UTC)

Showing DOF in front and behind

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

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

Dick, no question about the conclusion, which follows using either the image-side or object-side approach. However, I think the conclusion is far from obvious without considerable additional explanation. Might it suffice simply to say that the DoF is greater beyond the subject and approaches a 50/50 split at close focus?

That might suffice. It shouldn't take many words to explain the picture. It's a lot easier conceptually than the image-side approach that requires invoking the lens equation. Dicklyon 05:36, 20 December 2006 (UTC)

Incidentally, I think adding the Dominic Groß translation would make the Moritz von Rohr diagram much easier to follow. JeffConrad 01:21, 20 December 2006 (UTC)

OK, I'll add that. Dicklyon 05:36, 20 December 2006 (UTC)

Edit of 21 December 2006

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

Derivation of the DOF formulae

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

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