Talk:Depth of field/Archive 4

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Archive 4

DOF, near:far, and special (edge) cases

I read in the introduction:

"When focus is set to the hyperfocal distance, the DOF extends from half the hyperfocal distance to infinity, and is the largest DOF possible for a given f-number."

This I take to be a general statement. However, I see a few problems with this sentence (really, a conflation of two sentences):

- first, the linked reference within it is external (rather than to the intra-document section "Hyperfocal distance" - which is, I suppose, to be distinguished from the section in this same document, also entitled "Hyperfocal Distance"...); - the reference to "hyperfocal distance" is cataphoric i.e. it hasn't appeared earlier in this document; - and finally, the explanation is sorta-kinda circular i.e. the term is being used to explain itself.

The only reasonable alternative I can think of would be to repeat the opening sentence (or paraphrase thereof) from the section Hyperfocal distance. I have no problem with doing so; as written, it's not completely clear without a re-read that the final phrase refers to DOF rather than focus. JeffConrad (talk) 22:35, 8 November 2009 (UTC)

Since the factors contributing to depth of field (DOF) have, by this point in the text, been introduced, I suggest facilitating discovery, by the reader, of the concept "hyperfocal distance" by giving primacy to the idea of the 'largest DOF possible for a given f-number' or 'maximum depth-of-field', and re-structuring at least the sentence in question to lead the reader from the known to the unknown...

Just about every source with which I am familiar gives primacy to having the far limit of DOF at infinity, which is how the formula for hyperfocal distance is derived. The “greatest possible DOF” is secondary. I think we should stick with this convention. JeffConrad (talk) 22:35, 8 November 2009 (UTC)

After reviewing several sources, I'll concede that a case could be made for either approach; Ray (2000) actually begins by stating, “Maximum depth of field in any situation is obtained by use of the hyperfocal distance”, though he still defines it as the focus distance at which the DOF extends to infinity. The meaning of hyper- is “above” or “beyond”; in this context, it would seem to suggest something to the effect of “beyond which everything is sharp”, and I think the current emphasis is more in keeping with that meaning. But not everyone agrees, even on the definition. An alternative definition is “the near limit of DOF when focus is set to infinity”; its proponents include a man by the name of Adams. Some time ago, I examined half a dozen dictionaries, including the OED, to see if the etymology would be of any help in choosing between the two definitions; alas, the sources were about equally split. The values from the two definitions differ by the focal length, so for practical purposes, they're the same.

I've made a slight change to the sentence in the lead paragraph to eliminate possible ambiguity. I looked at a slightly more expansive statement along the lines of the opening sentence in the section Hyperfocal distance, but at least to me, it seemed a bit unwieldy for the lead section. But perhaps others feel differently. JeffConrad (talk) 23:21, 8 November 2009 (UTC)

Relative to the above, though...

In the (first) section entitled "Hyperfocal distance", I read:

"The hyperfocal distance is the nearest focus distance at which the DOF extends to infinity; focusing the camera at the hyperfocal distance results in the largest possible depth of field for a given f-number (Ray 2000, 55)."

Further on, I read, in the "near:far distribution" section:

"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."

Still further, I read, in the "Close-up" section:

"When the subject distance s approaches the lens focal length, the focal length no longer is negligible, and the approximate formulas above cannot be used without introducing significant error. At close distances, the hyperfocal distance has little applicability, and it usually is more convenient to express DOF in terms of magnification..."

Yet further, in the "Near:far DOF ratio" section:

"... When the subject is at the hyperfocal distance or beyond, the far DOF is infinite, and the near:far ratio is zero. It’s commonly stated that approximately 1/3 of the DOF is in front of the subject and approximately 2/3 is beyond; however, this is true only when s \approx H/3."

I've taken a lens and attempted to focus it at H/3. From what I can tell, this is physically impossible with a prime lens - at least one that is not a macro lens. Put another way, any 'subject' that is at H/3 is necessarily going to be out-of-focus i.e. definitionally outside the DOF. I get the sense that the 1:2 ratio (1/3 / 2/3 notion) is strictly true only when dealing with the high magnification possible with a macro lens. If this is so, I'm supposing that an error has slipped into the text (possibly also the formulae, too). Or perhaps there's a pre-disposition to excessive technical-correctness that is back-firing. In any case, straighten me out if I'm confused, but it seems to me necessary to re-think, re-consider, and re-jig the discussion and the presentation to sort some of these things out. —Preceding unsigned comment added by Curmudgeonistically (talk • contribs) 16:15, 8 November 2009 (UTC)

Um ... by definition, it would seem impossible to have the point of focus outside the DOF.

I don't see the problem focusing at H/3; how are you computing H? Let's take, for example, a 100 mm lens set to f/16, using a circle of confusion of 0.03 mm; the hyperfocal distance is

$H={\frac {\left(100{\text{ mm}}\right)^{2}}{16\times 0.03{\text{ mm}}}}+100{\text{ mm}}=20.9{\text{ m}}\,,$

so H/3 is about 7 m—hardly in the macro region. JeffConrad (talk) 22:35, 8 November 2009 (UTC)

Foreground and background blur

The “format independent” ratio of blur spot diameter to circle of confusion seemed a good one-liner at the time, but we have since expanded the treatment of DOF vs. format, and the assumption of constant subject magnification is inconsistent with our default assumptions (i.e., “same picture” means same angle of view from same camera position) when comparing DoF among different formats, in this article and elsewhere. Consequently, the sentence seemed out of place, and possibly confusing, so I removed it. In retrospect, I should never have added it. JeffConrad (talk) 23:24, 18 December 2009 (UTC)

Depth of field

"The DOF is determined by the subject distance (that is, the distance to the plane that is perfectly in focus), the lens focal length, the lens f-number, and the format size or circle of confusion criterion."

I reread this a number of times and finally realized that "plane that is perfectly in focus" is ment to be the recording or imaging media. This may be more understandable if written "film or sensor plane." Personally I think the additional qualifier "that is perfectly in focus" adds confusion.

"the format size or circle of confusion criterion."

I'm trying to determine where resolution and/or DPI is accounted for here. The statement is true if both formats have the same DPI.

100ASA film has the same grain size (resolution) no matter what format size its made into. Smaller format film cameras would have less resolution and therefore less acceptable DOF when enlarged to the same output size of a larger format film camera. For film, the same CoC has generally been used for different format sizes because the grain size between formats does not change.

The "grain" on a digital camera of different format sizes (and the CoC) may be very very different.

If two different format sizes have the same resolution, the smaller format will have less DOF when enlarged to the same output size of the larger format. (more magnification of the same resoluton)

"When a picture is taken in two different formats from the same distance at the same f-number using lenses of the same focal length, the smaller format has less DOF."

However, if the smaller format has a resolution and CoC equal to or greater than the format size difference multiplyer (or divider)the smaller format will have the same or more DOF than the larger format.

(not sure what to do with the previous comments above, so I left them intact) —Preceding unsigned comment added by Mbloof (talk • contribs) 14:06, 9 April 2010 (UTC)

I think "plane that is perfectly in focus" is the object-space plane. It is the subject distance. The way I think about it, you have an image resolution limit due to pixel size, film ISO, lens quality, and the diffraction limit. If you had perfect Gaussian optics, the depth of field would always be zero in that moving an object away from the plane of focus (in object space) would always result in a measurable defocus blur. It is the imaging resolution limit that gives you finite depth of field. That thickness around the subject distance corresponds to the volume of space that for which the defocus blur is less than the other resolution limits. Does that help? —Ben FrantzDale (talk) 17:04, 9 April 2010 (UTC)

Focus normally refers to object space, and that's indeed where the “plane that is perfectly in focus” is. DoF usually includes just optical effects, so pixel density or film resolution don't enter into the picture. This isn't to say that the imaging medium doesn't affect sharpness, but it's a different effect—the blurring is uniform across the image area. The DoF isn't zero because it's the region that appears sharp, i.e., the optical blur spot is sufficiently small that it's indistinguishable from a point (or is at least acceptably sharp). It probably could be argued that an image given sufficient enlargement would not be acceptably sharp at any point, and thus would have zero DoF, but it's not an argument commonly made. The choice of CoC for the captured image depends on the viewer's visual acuity, the viewing conditions, and the enlargement used to make the final image. If anything is magnified sufficiently, it eventually becomes unsharp. But as long as the blur in the final image is within the final-image CoC, the concept of DoF holds, and the discussion of DoF for different format sizes is correct.

I agree that the qualifying phrase adds nothing but confusion; if no one objects, I think we should remove it. JeffConrad (talk) 03:41, 10 April 2010 (UTC)

I've removed this phrase and slightly reworded the description; see if this makes things more clear. JeffConrad (talk) 08:01, 13 April 2010 (UTC)

In todays world, we can use the exact same optics on multiple format sizes. Given that the only difference is the size recording medium (IE: how much of the optics imaging circle is recorded or not) if all formats had infinite resolution the DOF would be the same.

No disagreement that for the same subject distance, lens focal length, and lens f-number, the magnification (and hence the DoF) for the initial images is the same for all formats. With digital capture, of course, it's impossible to view the initial image, so that image needs to be somehow rendered, such as in a print or on a monitor. And then we need to consider the enlargement and viewing conditions. JeffConrad (talk) 15:41, 16 April 2010 (UTC)

If we assume that all formats have the same resolution, (as you mentioned) when smaller formats are enlarged the sharpness of the entire image is decreesed, however the area of acceptable sharpness is also reduced. As an example, if we define acceptably sharp as +/- %3-%5 'perfect focus' then add %3 blur to the entire image (from enlargement), the 'perfectly sharp' area remains within acceptably sharp and what was acceptably sharp no longer is, there by reducing the DOF.

The arguement that the smaller format may require any enlargement to have an output size equal to the larger format in the digital world can't be assumed. There now exists many examples of small format digital cameras which require their images to be reduced in size to equal the output of larger format cameras. Since the resoluton of any given format size can no longer be assumed as it was with film, DOF differences based on format size can't be made. —Preceding unsigned comment added by Mbloof (talk • contribs) 14:27, 16 April 2010 (UTC)

I think you're confusing file size with the physical sizes of the initial and final images. Downsampling to reduce pixel density may reduce file size, but this isn't the same as reducing the physical size of the captured image, and it doesn't change the size of defocus blur spots in the initial image.

I don't disagree that with significantly different pixel densities, extreme enlargement, and very small viewing distances, the pixel density (at least for a digital image) affects final-image sharpness. But for practical consideration of DoF, it's a red herring.

In any event, all relevant factors need to be specified for the comparison to be meaningful, namely, for each format:

• Subject distance
• Lens focal length
• Lens f-number
• Enlargement from initial image to final image
• Final-image viewing distance
• Final-image sharpness criterion

The most logical comparison is the “same picture”, one of the situations discussed in the article. And for that case, DoF is inversely proportional to format size. But the comparison can have almost any conditions, as long as they're specified. Depending on the conditions, the comparative DoFs may change. Again, I think this is thoroughly covered in the article. The method of comparison is hardly new; Stroebel did essentially the same thing in 1976, and to my knowledge, it's not really disputed. If there's something specific that you think is wrong, please indicate what it is. JeffConrad (talk) 15:41, 16 April 2010 (UTC)

Jeff: Forgive me, I'm having issue with format size alone effecting DOF. I think I see where the 'break' is. Let me clarify:

While all else being the same (optics included) on both formats, if I were to take a 4x6" format camera image and a 4x6" crop from a 8x10" format camera the resulting 4x6" printed image would have the same DOF. In this case the smaller format image is simply a crop/section of the larger format. Both have the same magnification and focal length.

If the same lens were used at the same subject distance and the same f-number, yes. This article doesn't claim otherwise. But if the lens focal length is adjusted to give the same angle of view, the larger format has less DoF. JeffConrad (talk) 01:49, 18 April 2010 (UTC)

The article doesn't make it clear that the focal length and angle of view is being adjusted here. Essentially from what I understand if the lens was untouched, so same focal length, subject distance, f-number, then the DOF is unaffected just because the body crops the image. The wording of the article seems to suggest that the subsequent enlargement changes the DOF. This isn't the case I believe, and I don't agree that reduced sharpness due to enlargement is changing the DOF. It is just changing the sharpness of the entire picture. The DOF and COV are surely the same whether you make the entire picture more or less blurred. Oh, and as a side point the same points on cropping are repeated many times in the article. DeadKenny (talk) 08:46, 25 August 2010 (UTC)

I think we clearly state the adjustment of the focal length and angle of view. In the lead,

“When the ‘same picture’ is taken in two different format sizes from the same distance at the same f-number with lenses that give the same angle of view,”

In the section DOF vs. format size,

“For the common ‘same picture’ comparison, i.e., the same camera position and angle of view,”

and

“To maintain the same angle of view, the lens focal lengths must be in proportion to the format sizes.”

We make similar statements in the subsection DOF vs. format size in which we show the mathematical basis for the comparisons. We discuss other comparisons as well, and I think we again state pretty clearly what we're doing.

We mention cropping three times: in the lead, in the section DOF vs. format size, and in the subsection of the same title. I don't see how we could reasonably not say it in each case.

Enlargement indeed affects DOF in the final image—the defocus blur spots become larger and are more easily detected as such than are defocus blur spots from a lesser enlargement of the same initial image at the same viewing distance. Yes, the entire image is made less sharp, but the defocus blur is more obviously unsharp, and in many cases, the softening of the rest of the image is imperceptible.

I think DOF vs. format size gets far more discussion that it merits, here and elsewhere. We cover it extensively here because it came up so often on this page. JeffConrad (talk) 09:34, 25 August 2010 (UTC)

The 'disconnect' in the known formulas (pre digital age) assume that the distance of the optics to the recording medium (and the imaging circle the optics create) is different with each format. While in practical terms this is usually the case however there are now many popular examples (DSLR) of multiple formats sharing the same optics and where the imaging circle remains the same and the 'smaller formats' are only using a crop or portion of the larger formats imaging circle.

There's no “disconnect”; the adjustment of focal lengths for the “same picture” comparison is simply one of the assumptions that need to be stated.

This always seems to come up with fill-frame and “crop format” DSLRs ... and the time and energy wasted discussing it boggles the mind.

General statements about the comparative DoFs of different formats, without stating all the assumptions, are meaningless. With different assumptions, you get different results. Even using the same lens at the same f-number for both formats, it's possible to set up comparisons so that the smaller format has less, the same, or more DoF. If you use the same lens at the same subject distance at the same f-number on a full-frame and crop format DSLRs, the result still depends on what you do with the initial images.

• If both final images are the same size, you get less DoF with the smaller format because of the greater enlargement.
• If both initial images are given the same enlargement (resulting in different-sized final images), the DoF is the same in each format. It would seem to me that this isn't the usual case, but it's certainly a possibility.
• If the subject distances are adjusted so that the field of view at the subject distance is the same for both formats, and the final images are the same size, the smaller format has more DoF.

I thought the the first DOF vs. format size section gives a fairly good summary (and it covers the case of the same lens on two different formats), and the second DOF vs. format size (under Derivation of the DOF formulas) shows fairly well how the results are obtained. But maybe not; perhaps the general equation

${\frac {\mathrm {DOF} _{2}}{\mathrm {DOF} _{1}}}\approx {\frac {N_{2}\,c_{2}}{N_{1}\,c_{1}}}\left({\frac {m_{1}}{m_{2}}}\right)^{2}\,,$

before specific cases are examined, could be added. And perhaps that section could repeating the definitions of the various quantities. Or perhaps the results need to be summarized in a bullet list like the one above.

But perhaps it just needs to be made more clear at the beginning of the discussion that the results depend on the assumptions. For example, the first section DOF vs. format size begins with, “To a first approximation, DOF is inversely proportional to format size ...”, a general statement of the type I've deprecated above. The key assumptions immediately follow, but perhaps the damage has already been done. And it does seem to presume that the “same picture” comparison is the “proper” one. The “crop format” vs. full-frame comparison may merit additional treatment simply because unless the lenses have been specifically designed for the smaller format (e.g., the Canon EF-S lenses), the lens DoF scales aren't accurate if the final image is the same size as would be made with a full-frame camera. And of course, it depends on the final-image size assumed in generating the DoF scales (e.g., Canon claim their 0.035 mm CoC derives from enlargement of full-frame 35 mm to 5″×7″, so it's not really accurate even with the full-frame format when a larger final image is made). And for most AF lenses, the DoF scales are so small that they're pretty much useless anyway. But that's commentary that's outside the bounds of the article.

One additional comment: please sign your comments with four tildes (~~~~)—it makes discussions easier to follow. The SineBot seems to take care of it pretty quickly, but for a few minutes, it can be confusing. JeffConrad (talk) 01:49, 18 April 2010 (UTC)

This seems to be the topic that tries men's souls ... and that refuses to go away, here as well as other places. Stated otherwise, it seems to confuse almost everyone. Let's see if a slightly different approach makes things more clear.

As I mentioned, the conditions could vary, but for the sake of argument, let's assume the same picture criterion that I mentioned above. With a different criterion, the answer might differ, but the logic used to arrive at it would be similar. Let's also work backwards from the final image (print, projection screen, electronic display, or whatever), and for simplicity, assume that the final-image size, medium, viewing distance, and sharpness criteria are the same for all formats. Let's make it more concrete by assuming the “standard” criteria for the final images:

• Final-image size: 8″×10″
• Viewing distance: 250 mm
• Final-image sharpness criterion: 0.2 mm CoC (or spatial frequency of 5 lp/mm)

For the initial images:

• Same camera-to-subject distance for both formats
• Lens focal length adjusted to give the same angle of view for both formats
• Same lens f-number for both formats

For simplicity, let's not worry about exact format dimensions. If the larger format is 8×10, no enlargement of the initial image is needed, so the initial-image CoC is 0.2 mm, the common value for 8×10. If the smaller format is 24 mm × 36 mm, let's assume the short dimension is enlarged to fill the short dimension of the final image; the required enlargement is then approximately 8×. To achieve the final-image CoC of 0.2 mm, the initial-image CoC must be 0.2 mm / 8, or 0.025 mm—1/8 that for the 8×10 initial image, and slightly smaller than the more common 0.03 mm (which may assume approximately 7× enlargement to fill the long dimension of the final image). In other words, the CoC is in direct proportion to the format size.

A quick glance at the DoF formulas reveals that, for moderate camera-to-subject distances, the DoF in the initial image is approximately inversely proportional to the square of the original-image magnification. The 24 mm × 36 mm initial image is approximately 1/8 the size of the 8×10 initial image; if the lens focal length is adjusted to give the same angle of view in both formats, the focal length is approximately in proportion to the format size, so if the 8×10 image used a 300 mm lens, the 24 mm × 36 mm would use a 38 mm lens. When the subject distance is large in relation to the lens focal length, the magnification is approximately proportional to the focal length, so the magnification is approximately proportional to the format size. Hence the magnification for the 8×10 initial image is 8× that for the 24 mm × 36 mm initial image, and the DoF for the 8×10 initial image is 1/8 × 1/8 = 1/64 that for the 24 mm × 36 mm original image. This difference is partially offset in the final images by the differences in enlargement; precisely, the final-image DoF is approximately inversely proportional to the format size, so the 8×10 format has 1/8 the DoF of the 24 mm × 36 mm format. Equivalently, for the same final-image DoF, the 8×10 format requires 8× the f-number required with the 24 mm × 36 mm format. Few who have actually worked in both formats would dispute this.

Note that none of this has anything to do with grain size or pixel density (or total pixel count). If the resolving power of the film or the pixel density of an electronic sensor were sufficiently low (or the noise sufficiently high from using a zigapixel P&S at high ISO), the characteristics of the imaging medium would eventually become significant—nothing would be sharp, and the image would have, in effect, zero DoF. The same result would eventually obtain given sufficient enlargement of the initial image—as David Hemmings discovered. But either of these scenarios is far removed from most practical photography.

Edits of 18–22 April 2010

I've made a few changes to the lead section, and both of the sections DOF vs. format size in attempt to address some of the recent comments. Quite honestly, I think the coverage given to the topic in the lead section is a bit excessive, but anything less would probably invite even more similar comments. For those who still question what's stated, I suggest carefully reading the two more detailed sections to see if they address some of the concerns. I doubt that what I've added is the last word on this, and perhaps it doesn't help at all. The section that gives the derivation possibly could be slightly better organized to parallel the first section on DOF vs. format size; I simply added the one general equation, which at least presents the big picture with minimal effort.

Let me say it once again: the comparative DoFs of different formats can be almost whatever you want, depending on what is assumed. Those assumptions must be stated or the comparisons are meaningless. JeffConrad (talk) 08:52, 18 April 2010 (UTC)

I've added that we ignore the effects of the imaging and display media to the subsection Limitations. In doing so, I noticed that the stated effects on DoF of some of the factors are contradictory, specifically among items 4–6. All three items describe factors that decrease overall final-image sharpness, yet items 4 and 5 state that this decreases DoF, while the last item that I just added states that this increases DoF (as we state in Circle of confusion#Circle of confusion diameter limit in photography). I've not found much of help in any of the sources for these two articles; the sources seem to follow my previous comments that DoF normally only considers optical blurring. What we end up with is essentially a greater region of uniform unsharpness; what remains is to determine its implication. The concept of DoF may provide the answer: parts of the final image for which the composite blurring is undetectable (or are “acceptably sharp”) are within the DoF; if the composite blurring is such that nothing is “acceptably sharp”, the DoF is arguably zero.

Aside from the last sentence in the preceding paragraph, I don't see an obvious way of stating what's really happening. And I'm not sure we can reasonably go there. A more defensible approach might simply be to avoid any comment on the effects on DoF and just indicate that overall sharpness is reduced.

Thoughts, anyone? JeffConrad (talk) 09:51, 20 April 2010 (UTC)

I've added tags for the last three items under Limitations (including the item I just added). My question applies only to the effects on DoF. JeffConrad (talk) 08:09, 22 April 2010 (UTC)

I've removed mention of the effect on DoF of the last three items in Limitations while retaining mention of the effect on sharpness. If someone comes across a good source, perhaps we can revisit the effects on DoF. I've made a corresponding change to the Circle of confusion article. JeffConrad (talk) 08:41, 30 April 2010 (UTC)

Medium-neutral terminology

It's been suggested here and elsewhere that terminology used in some of the Wikipedia articles on photography has not kept pace with the transition to digital photography, still using terms like film plane, film, print, and so on. We're far from ready to write-off film, so I think we need some terminology that's reasonably “medium neutral” yet readily comprehensible. I've tossed out a few ideas in the Talk for Circle of confusion. JeffConrad (talk) 09:38, 22 April 2010 (UTC)

Dennis Couzin paper

Dcouzin recently added this material to the section Determining combined defocus and diffraction

When taking lens aberration and diffraction into account, Couzin (1982) finds it necessary to disambiguate the concept of DOF according to four questions it might be answering.

  Q1: Over what distance range is a fixed low standard of sharpness achieved?
  Q2: Over what distance range is a fixed high standard of sharpness achieved?
  Q3: Over what distance range is there practically no falloff of sharpness?
  Q4: At which f-stop is the range from D to D' covered with the best sharpness?

Couzin, Dennis. 1982. Depths of Field. SMPTE Journal, November 1982, 1096–1098. Available as .pdf at [1].

I have several issues with this material:

1. The presentation is marginally encyclopedic at best, and offhand, I don't know how to fix this because I don't really how most of the cited article relates to this section; the part dealing with diffraction seems to be the only relevant part.
2. The cited article expresses some strong opinions that border on polemic, and for the most part gives no basis for them. For example, the article makes statements like, “Some chartmakers have yielded to the temptation to increase the sharpness standard in the Q1 formula and to produce a chart supposed to answer Q2” without providing any context.
3. The article cites “a formula for calculating small aperture answers to Q4 for any good lens:”

$1.22f{\sqrt {{\frac {1}{D}}-{\frac {1}{D'}}}}$

focal length f is in mm D and near distance D and far distance D′ are in ft,

without providing a source or derivation; it appears that the result refers to the f-number, but this isn't clearly stated. The formula is dimensionally inconsistent, and the quantity under the radical isn't dimensionless, so there's obviously some constant and unit conversion whose origins have not been made clear.

I don't suggest that the formula is wrong; in my paper, I arrive at

${{N}_{\text{opt}}}=20{\sqrt {\,\Delta v}}\,,$

where N_opt is the “optimal” f-number, and Δv is the focus spread v_n − v_f in mm. The focus spread is related to the focal length and object distances by

${{v}_{\text{n}}}-{{v}_{\text{f}}}={\frac {\left({{u}_{\text{f}}}-{{u}_{\text{n}}}\right){{f}^{2}}}{\left({{u}_{\text{f}}}-f\right)\left({{u}_{\text{n}}}-f\right)}}\,.$

If both object distances are large in comparison with the focal length, this simplifies to

${{v}_{\text{n}}}-{{v}_{\text{f}}}\approx {\frac {\left({{u}_{\text{f}}}-{{u}_{\text{n}}}\right){{f}^{2}}}{{{u}_{\text{f}}}{{u}_{\text{n}}}}}$

and

${\sqrt {{{v}_{\text{n}}}-{{v}_{\text{f}}}}}\approx f{\sqrt {\frac {{u}_{\text{f}}-{{u}_{\text{n}}}}{{{u}_{\text{f}}}{{u}_{\text{n}}}}}}=f{\sqrt {{\frac {1}{u_{\text{n}}}}-{\frac {1}{u_{\text{f}}}}}}\,,$

which is equivalent in form to Couzin's formula. Hansma (1996) arrives at a similar formula using a very different approach, further suggesting that Couzin's formula is reasonable. All three equations deal with only part of the picture, however. I think both Hansma's and my use of “optimal” is misleading because the f-number given is really a maximal rather than optimal value; i.e., choosing a greater f-number will actually result in less sharpness because of increased diffraction. Moreover, the f-number given by these equations applies only to the sharpness at the DoF limits. In general photography, that's often the appropriate choice (motion-blur considerations permitting), but in closeup photography, there are tradeoffs between sharpness in the plane of focus and overall sharpness, as Gibson (1975) and Lefkowitz (1979) illustrate. All three formulas are invalid for closeup work; Hansma's and mine require an additional factor of 1 / (1 + m) when the magnification is significant. Additionally, my formula is empirically derived from calculated MTFs, and is specifically tied to a final-image resolution of 6 lp/mm.

It's not clear to me that Couzin is citable under WP:RS; the original publication, the SMTPE Journal is certainly credible, but I have concerns with the strong POV and the lack of support for many of the statements. In any event, the material here needs to more encyclopedic and better fit the context of the section; the part of the cited article that deals with diffraction seems to be the only part that's relevant. Perhaps the equation could be mentioned, but I'd like to see some additional support from a source that provides more context. JeffConrad (talk) 01:43, 20 May 2010 (UTC)

For the sake of completeness, I reviewed Hansma's article, and specifically looked at his equation for optimal f-number:

${{N}_{\text{opt}}}\approx {\sqrt {{\frac {{K}_{\lambda }}{2}}\Delta v}}\,,$

where K_λ is a constant that depends on the wavelength of light. Substituting for Δv from the last equation above,

${{N}_{\text{opt}}}\approx f{\sqrt {\frac {{K}_{\lambda }}{2}}}{\sqrt {{\frac {1}{u_{\text{n}}}}-{\frac {1}{u_{\text{f}}}}}}\,.$

Hansma used a value of 750 mm⁻¹ for K_λ; for u_n and u_f in ft rather than mm, this becomes

${{N}_{\text{opt}}}\approx f{\sqrt {\frac {750}{2\times 304.8}}}{\sqrt {{\frac {1}{u_{\text{n}}}}-{\frac {1}{u_{\text{f}}}}}}\approx 1.11f{\sqrt {{\frac {1}{u_{\text{n}}}}-{\frac {1}{u_{\text{f}}}}}}\,,$

which is close to the equation given by Couzin. The choice of K_λ is somewhat arbitrary, and some have criticized Hansma's value, so Couzin's result is probably reasonable.

Couzin's article is interesting because it implies an analysis similar to Hansma's at least 14 years before Hansma presented it. In fact, Hansma's analysis is quite similar to Gibson's, but I've been unable to find an equation similar to Couzin's in his 1975 work. In any event, though Couzin's article is interesting, I think we need something more than just a final result to justify including it here. JeffConrad (talk) 07:14, 20 May 2010 (UTC)

The questions look better when properly formatted, but I think it's akin to rearranging deck chairs ... As I've stated, the first three questions are absolutely unrelated to this section, and probably to the entire article as well. Although the equation given in under the fourth question is interesting because of its timing, I think its lack of context makes of little value to this article. Absent a good reason to retain this material, I'm going to remove it. JeffConrad (talk) 22:34, 14 June 2010 (UTC)

There has been no comment, so I've removed most of this material—it's clearly unrelated to the section. I question the value of the formula for optimal f-number (under Q4) without any mention of its basis, but I've retained a brief mention because it shows that a simple formula was published (and probably forgotten) long before Hansma's article.

If someone thinks it's important, we could give both Hansma's formula and the one Couzin presents, though they probably should be given context with a new subsection that includes some of the material above. JeffConrad (talk) 20:20, 22 June 2010 (UTC)

Variables

I think this page could be rephrased to clarify the variables responsible for depth of field. The way I see it there are just two critical criteria that completely determine the depth of field and the size of the bokeh:

1. entrance pupil diameter
2. subject distance
3. resolution in object space

Equivalently, you could replace (1.) with object-space numerical aperture. Basically you need to know the geometry of the pencil of light around an in-focus point, and need to know the resolution to know how far away from nominal would start to look fuzzy. You can change the sensor size or the focal length or the f/number, but if you were to keep these three things fixed, your depth of field would remain the same, as would the size of the bokeh. Given most photographic lenses have variable subject distance, and that subject distance is part of composition, that really leaves entrance-pupil diameter. So assuming no pupil magnification, a 50mm f/1.2 has a 41.6mm entrance-pupil diameter, a 135mm f/2: 67.5mm, a 85mm f/1.2: 70.83mm, and a 400mm f/2.8, 142.86mm!

This explains why compact cameras will (short of computational-photography tricks) never give bokeh like SLRs -- many compact cameras are ~50mm across and so just can't fit these world-class entrance-pupil diameters, even at f/2.8 or faster.

So yea, I think this is a much easier way of thinking about the issue. I'm going to start by replacing this:

"The DOF is determined by the camera-to-subject distance, the lens focal length, the lens f-number, and the format size or circle of confusion criterion."

since these five variables really include two extras that just confuse the matter.

Comments? —Ben FrantzDale (talk) 10:36, 14 June 2010 (UTC)

I sympathize with the problem, but this is the conventional way it's done. The "outside the box" or "von Rohr's method" approach is seldom seen in literature on DOF, so we shouldn't introduce it as the main approach here. Also, let's don't introduce the unneeded neologism "bokeh" in the lead; you can refer to later if you want to, but it's not part of any traditional discussion of DOF. Dicklyon (talk) 16:04, 14 June 2010 (UTC)

Hi Dicklyon. I hadn't heard of Moritz von Rohr; thanks for the reference. Whatever way the literature usually approaches it, this seems to be the simplest way to explain what is going on. The only simpler way would be to punt on the definition of "in focus" and instead just talk about the size of the geometric blur circle. (I actually would prefer that in that I think people get hung up on a binary notion that cameras are "in focus" for some distance around the subject and then "out of focus" everywhere else.)

I really dislike the intro as you reverted it because discussion of f/number and film format only complicate things. Not only do they introduce extraneous variables (sensor size and focal length), but depending on those variables makes this article inaccessible to those who don't fully understand sensor size, focal length, and f/number. I imagine (although I am just guessing) that entrance pupil diameter (properly introduced) and subject distance are much more approachable to someone with minimal photography background. I can see avoiding the term "numerical aperture" since it's rarely used in photography.

Are you open to some version of an introduction that emphasizes the geometry of the pencil of light and downplays sensor size and f/number? —Ben FrantzDale (talk) 19:46, 14 June 2010 (UTC)

As Dick said, the lead as it's written is almost always the way the subject is approached in the common sources, so there would seem an obligation under WP:WEIGHT to at least make it the primary treatment. Mention is made of von Rohr's approach, briefly in this article and in considerable detail in Circle of confusion, so I think it's certainly given reasonable coverage.

I strongly disagree that image format and f-number complicate the issue. As the article mentions, lens controls are marked in f-numbers (to facilitate setting exposure) rather than in in entrance-pupil diameters (to facilitate setting DoF). A person wishing to use the latter approach in practical photography would need to calculate the entrance-pupil diameter from the f-number and the focal length, so it could easily be argued that looking at the entrance-pupil diameter and the pencil of light introduces unnecessary complication. Moreover, DoF tables and DoF calculators are based on the main approach taken in this article. Reasonable (as well as unreasonable) minds may differ on which approach is better, but the common approach is as it is, and the more we deviate from it, the less accessible the article becomes for most readers.

The direct phenomenon related to DoF is the image-side blur spot, which is covered thoroughly in this article in much the same manner as the common sources. In this article and in Circle of confusion we clearly relate it to the final-image sharpness, which ultimately governs DoF. The entrance-pupil approach requires the additional concept of projection of the image-side blur into object space, which may be easier to follow for some than for others.

It might be reasonable to add a section expanding on object-side analysis, but the section should be well-sourced or completely explained in a manner that a person with, say, reasonable mastery of high-school mathematics and physics would understand it (depending on the approach, the derivation in Circle of confusion might suffice for much of the explanation).

I agree with Dick that bokeh is an unnecessary neologism. Moreover, it's a largely subjective term that depends on characteristics of the lens design as well as on entrance-pupil diameter.

I think any mention of numerical aperture in the lead section is off the wall. Though the term is common in microscopy, it's seldom used in practical photography. JeffConrad (talk) 21:29, 14 June 2010 (UTC)

Right. I agree with Ben that the "outside the box" method might be "much more approachable to someone with minimal photography background." But for wikipedia purposes, and for photographers, Jeff's point is more relevant. It's not up to us to make up new ways to formulate the material. Von Rohr's approach is exceedingly obscure (I had to prowl libraries and get translations to find it and understand it), even though I and several others sort of "re-invented" it more recently. There are at least 1000X more publications that do DOF in the image side. Ben, if you want to do a modest expansion of the section on object field methods, that might be OK. Dicklyon (talk) 04:01, 15 June 2010 (UTC)

I think this article, directly and indirectly, covers the object-side approach better than 99% of the other sources. But perhaps the direct treatment could be expanded. If it is, I'd agree with Dick that the section Object field methods would be the appropriate place. Preferably what's covered in Circle of confusion would be referenced rather than repeated. And I'd take a look at what's already mentioned; the relationship of DoF to the absolute aperture diameter (for thin or symmetrical lens, the same as the entrance pupil) is discussed in the subsection DOF vs. format size under Derivation of the DOF formulas. Note also that the external links include the Carl Zeiss article as well as Dick's paper. JeffConrad (talk) 06:56, 15 June 2010 (UTC)

One additional comment: for the most part, the introduction of pupils in this context is a needless complication. Except at fairly significant magnification with a lens with a pupil magnification that differs considerably from unity, the effect asymmetry on DoF is negligible. Accordingly, most of this article, like most other treatments, considers only a thin lens, so that the entrance pupil, exit pupil, and aperture diameter are equivalent. I see no reason for a different approach in an object-side treatment. JeffConrad (talk) 08:02, 15 June 2010 (UTC)

Zone focusing

I don't think the reference to the midpoint of reciprocal distance is quite correct. To extend the DoF between a given near and far distance, focus would ideally be set to the harmonic mean of the near and far object distances, which is the reciprocal of the midpoint of the reciprocal distances. The ideal image distance would also be the harmonic mean of the near and far image distances. There are a couple of complications, however:

1. The marked distance on most small-format lenses is the distance to the image plane, so in addition to the object distance, it includes the image distance and the internodal distance (hiatus).
2. Rotation of the lens barrel (at least on a unit-focusing lens) is proportional to the change in image distance. Because most f-number markings are symmetrical about the focus mark, the midpoint is actually that of the near and far image distances; in other words, the set image distance is the arithmetic rather than harmonic mean of the near and far distances.

In most cases, the approximation from using the lens DoF scale (or the midpoint of the focus spread on a view camera) works just fine, but focus is set slightly closer than the harmonic mean of the object distances.

The strictly correct behavior is described in the two sections Focus and f-number from DOF limits; the question then is how we describe it in the Zone focusing section without getting too complicated while staying consistent with the later sections. We could

1. State that the focused distance corresponds to the reciprocal of the midpoint of the reciprocal distances. Even if this were strictly correct, I think it would lose most readers.
2. State that the focused distance is the harmonic mean of the near and far distances. Strictly, this isn't correct, and it would strike me as gratuitous technicality for this introductory section.
3. State that the focused distance is the optimal focus to have the DoF extend from 1 m to 2 m, leaving the reader to ask, “Why?”
4. State that the focused distance corresponds to the midpoint of the near and far image distances, which is correct, though it might leave the reader wondering how we even got into image distances. We could direct the reader to the detailed discussion in the later section (even though we already have a link at the end of Zone focusing, it's far enough away that it may not catch the reader's attention).
5. Say nothing, as was previously the case. This obviously avoids undue technicality and statements that aren't really correct, but perhaps it could leave the reader wondering what's going on. It's nonetheless the approach that seems to be taken by the few sources that even cover lens DoF scales.

My preference would be either of the last two approaches, because at least they're correct, and aren't too unwieldy. I'd probably move the explanation from the caption to the text to keep the caption short and be more likely to catch the attention of the reader who doesn't read captions. JeffConrad (talk) 06:51, 16 June 2010 (UTC)

My intent was just to change the 1.4 m to a more correct value, like 1.3 m or 1.33 m, but I thought it would be worth explaining. My language of midpoint in reciprocal distance space was intended to mean the same as harmonic mean, or reciprocal of mean of reciprocals; the 1.4 suggested a geometric mean, which is not correct. I'm OK any way you want to change it, except for invoking the image space midpoint. Somehow, maybe not in this section, it would be good to convey the approximate linearity of focus scales in reciprocal distance, so people can envision better how interpolation works on such scales. Dicklyon (talk) 14:13, 16 June 2010 (UTC)

Any value we give for distance is a guess because we don't know what the internodal spacing is. But I agree that 1.33 is probably a better guess than 1.4 (but giving it as 1.3 would probably be better). It obviously helps when the value is calculated; the problem with most DoF scales is that accurate visual interpolation of image plane–to–subject distances is almost impossible. Were the interpolation done on the image side, it would be linear and easily done.

Perhaps introducing image space is a complication whose purpose is not obvious. But at least it's accurate, we cover it in detail, the mathematics is quite simple, and the same formula works for all types of cameras (the rotation of the lens scale is just convenient way to measure image distance). The midpoint of reciprocal distances (implied but not quite fully described in Ray 2002, 228–29) is not covered at all in this article, and the math is considerably more complicated. There is another significant advantage to the image-side approach: it works even with tilts and swings. Consequently, the DoF scales on tilt/shift lenses are still usable if the near and far points are determined visually; the distance marks can be used for references for the positions of the focusing ring (essentially, the near and far image distances) as long as there is no attempt to relate them to distances from the camera.

We could possibly expand this section to cover the theory and layout of distance and DoF scales, but the required expansion would be considerable. What is ostensibly a simple topic is, on further examination, not quite so simple—I'm not sure I've seen a really comprehensive but straightforward treatment of how inverse distance relates to lens distance and DoF scales. Merklinger (1992, 56) notes that the rotation of the focusing ring is proportional to the lens extension from infinity focus, so that

$v-f={\frac {f^{2}}{u-f}}\approx {\frac {f^{2}}{u}}\,,$

so the rotation is approximately proportional to inverse object distance. Of course, in the usual case in which the marked distances are for image plane to subject, there is an additional approximation that's not mentioned. Ray goes a bit further in relating this to distance and DoF scales, but still doesn't describe quite how the calculation is accomplished. Even though I'm quite familiar with this topic, I need to provide the missing steps to understand how it works.

Though solving for the optimal focus distance for given near and far DoF limits would seem self evident, it's hardly even mentioned in most sources. Merklinger (1992, 19) gives it, quoting the 1949 4th edition of the Ilford Manual of Photography; I cannot find it in the 9th ed. Ray (2002, 222) does cover it, but as luck would have it, his Equation 22.11 is missing the factor of 2 in the numerator. Shipman 1977, 42–47) gives an accessible but comprehensive treatment of DoF and DoF scales, yet completely overlooks the harmonic mean focus or the simple way of achieving it with the lens DoF scales.

In any event, I've changed the section to refer to the harmonic mean; I qualify it as approximate and direct the reader to the more detailed section for a more comprehensive discussion. I've retained the second WL to that section in the last paragraph because it's in a slightly different context, and prefer to make it easy for the reader who's interested. I've changed the focus distance to a 1.33 m (Interpolate to three significant figures? Seriously ...), and moved the explanation from the caption to the text. As you did in the caption, I've tried to make it more clear in the text that focus is set to the midpoint of the distance markings. See if this works for now. JeffConrad (talk) 23:50, 16 June 2010 (UTC)

Edits of 29 June – 3 July 2010

Under Limited DOF: selective focus

“A subtler issue is the effect of angle of view on background blur, due to scaling—given a fixed distance, in a shot taken with a wide-angle lens, the background is smaller and thus appears less blurred in absolute terms than an equivalent shot taken with a telephoto lens. This gives rise to the wide-spread misconception that focal length affects depth of field, that wide-angle lenses have less depth of field. This is incorrect—they have less (absolute) background blur (due to the background being smaller), but the same depth of field.”

The use of scaling here seems a neologism, and should have a source if it is to remain. There also seems a conflation of two different issues: angle of view and magnification; the latter is what's operative here. Presumably, it was intended to say that that the misconception is that wide-angle lenses have greater depth of field; in any event, wide-angle lenses actually do have greater DoF, though the effect is significant only as the distance approaches hyperfocal, as we discuss in the second Close-up section (which may not be the best place for it). We either should qualify the statement that wide-angle lenses don't have greater DoF or eliminate it (my preference). The background blur and its relationship to the background magnification is discussed fairly extensively, with a supporting derivation, so I'm not sure discussing it here adds anything.

“note that ‘selective focus’ may be used broadly to refer to shallow DOF generally, or narrowly to refer to tilted focal planes specifically.”

I'm not quite sure what this means; it seems to say that “selective focus” is sometimes used to specifically refer to the use of tilt. If that's what's meant, it needs a reliable source—this is the first I've heard that “selective focus” may imply the use of tilt.

Under Near:far distribution

“approaching unity at high magnification—the ratio is (just above) 1:1.”

The near:far ratio is always less than unity, so I assume just below was meant. But this seems redundant, because we've just said as much.

“A 1:2 ratio is ‘average’ in the sense that 2 is the harmonic mean of 1 and ∞, as 2/((1/1)+(1/∞)) = 2/(1+0) = 2/1 = 2.”

This seems pretty off the wall; the focused distance would be the harmonic mean of the near distance and ∞ (in less obtuse terms, twice the near distance), but this has nothing to do with the near:far DoF ratio. In any event, I have a problem with claiming a 1:2 ratio (or any finite ratio) applies to a situation in which one element is infinite, especially because it was just stated that the ratio is 1:∞. Moreover, nothing has been included to support the assertion that having the DoF extend to infinity is “average”, so the statement seems inappropriate. This sentence needs a source if it is to remain. JeffConrad (talk) 02:27, 30 June 2010 (UTC)

Edits of 3 July 2010

I've removed some of the material cited above because no sources have been provided, and some of it was obviously wrong.

I've moved a few things around in the derivation section; in particular, I put DOF vs. focal length in a separate section so it isn't buried under Close-up as before. The second Close-up section is now pretty minimal; perhaps it's no longer needed, but I thought that removing it completely would give the appearance of an oversight. I removed material that was already covered under DOF vs. focal length, but we could put some of it back if we think some readers might skip the earlier section. I don't think anything other than the transition from the “exact” equation in terms of magnification would be needed. JeffConrad (talk) 08:09, 3 July 2010 (UTC)

Subsectioning

I recognize that we already have very heavy subsectioning for a Wikipedia article; however, some material is easily lost in the plethora of information, as we have seen from some edits that were apparently made without awareness that the material was already covered. Accordingly, I added a few quaternary headings to highlight subtopics. I think that a simple bolding would suffice for visual separation of subtopics, as well as to guide a reader who was interested in that subtopic but did not wish to wade through the other material to find it; I used the headings with the assumption that this better accords with WP practice. A side effect, of course, is that it makes the TOC even longer. I'm fine with either the headings or simple bolding, but would defer to WP practice on this if one exists. JeffConrad (talk) 04:38, 22 July 2010 (UTC)

Article structure: keep two formula sections?

As more and more was added to the original DOF formulas section, the reader who just wanted a simple formula had a lot of material to wade through to find that formula. Accordingly, we created a fairly simple DOF formulas section for the reader not especially interested in the math, and put the rest of the math in the Derivation of the DOF formulas at the end so that a reader who wanted to avoid most the math could do so. As always, it seems impossible to please everyone, and a few readers have complained that the duplication (or at least the appearance thereof) is confusing.

At one time, I was ready to eliminate the second section. But despite the amount of material that section includes, I don't think it includes anything that hasn't come up in at least one online forum in the past year or so (and that's only in the handful in which I participate), so the material is probably worth keeping. The DoF vs. format size is a good example; without a comprehensive statement of everything that is assumed, it is simply impossible to make a conclusive answer to the question.

As even more material has been added, often to support something that was challenged, the second section (and the article) has become more unwieldy. I wonder if it's feasible to move a few of the more common formulas from the first formulas section into sections that discuss the behavior covered, and move everything else to the more complete section at the end. The down side, of course, would be that a reader who wants no math would be faced with at least a little of it. Another issue would be deciding which of the “basic” formulas should be covered in the sections to which they apply. JeffConrad (talk) 02:10, 23 July 2010 (UTC)

Image of wolf spider

There have been a couple of complaints on Talk:Focus stacking about the image of the wolf spider making that article inaccessible to people with arachnophobia. It has been suggested that the image be replaced with one of comparable quality that would not aggravate any phobias. Though the issue hasn't been raised here, I assume the same considerations would apply. JeffConrad (talk) 00:33, 24 July 2010 (UTC)

The wolf spider image in Focus stacking has been replaced with one of a tachinid fly; the new image seems comparable in quality to that of the spider. Unless there is a good reason not to do so, I'll make the same replacement here. JeffConrad (talk) 09:44, 17 August 2010 (UTC)

New image for DoF derivation

Ben, a small point, but would you put the subscripts in the image in roman rather than italic so they match the text? They're descriptive, so both ISO and NIST call for them to be roman. JeffConrad (talk) 03:19, 27 September 2010 (UTC)

They are. Somehow Wikipedia is rendering them wrong. With Firefox, if I click through to the .svg, they are Roman. —Ben FrantzDale (talk) 23:50, 28 September 2010 (UTC)

Images September 2010

I've moved several images, including BenFrantzDale's new aperture-effect diagram, in attempt to put them in the contexts of the concepts they illustrate—see if what I've done works. I removed the Lensbaby image because I was running sort on room, and because most of the blurring is the result of field curvature rather than tilt, so I don't think it ever really belonged in this article.

Some time ago, several of us noted that we were pushing it with respect to WP:NOTREPOSITORY, and several images were accordingly removed. I think we're again at that point. The second two images in the lead section are the most recently added, and I don't think they really provide relevant illustration that we don't already have. I recommend that we remove them unless there's a strong reason to keep them; a case might be made for using the image of the boy to illustrate that blurred highlights have the shape of the aperture stop. JeffConrad (talk) 03:46, 28 September 2010 (UTC)

I totally agree, although I think my image might be useful at the top along with one photograph, since the photo shows the effect and the diagram explains how. Most of the images are redundant. There are some images we could add to show specific things (like maybe an Airy disk from, e.g., the image of a star at f/32 to illustrate how depth of field could be finite rather than zero). But we don't need multiple pictures of things close up, isolating subjects from their background. —Ben FrantzDale (talk) 23:57, 28 September 2010 (UTC)

I think your image belongs in the section where we talk about the effect of aperture, from which an illustration was sorely lacking. Matching pictures should show both large and small DoF; I think the flowers might show this better than the current four pictures (given their sizes, I find it hard to see any differences among the images—perhaps we should just remove them). I'm not sure an image of an Airy disk is relevant, because it's a different spot than the uniform defocus blur spot we assume for most of this article, consistent with most other treatments of DoF. The real spot, of course, is a combination of both, and I think we discuss this sufficiently in the Circle of confusion article. JeffConrad (talk) 02:07, 29 September 2010 (UTC)

I would add, the latter part of the article needs thinning. It has to be possible to explain this more concisely. I'm thinking an illustration comparing format sizes would help. —Ben FrantzDale (talk) 00:18, 29 September 2010 (UTC)

Could you be more precise about what constitutes the “latter part of the article”? I think we devote far too much space to the effects of format sizes, especially in the lead section, but we've added it because people have raised so many questions about it. It's complex because there are so many different combinations of assumptions, most of which are left unstated when claims are made about various effects of format. In particular, we devote far too much space to the effects of “crop” sensors, but it seems to be an obsession for many, including some who've commented here. So we've tried to address it so that at least the treatment is correct.

I think it would be nice if we could eliminate the two math sections, by putting the more important formulas in sections that discuss them, but my suggestion to do this didn't seem to find support, so I've not pursued it. JeffConrad (talk) 02:07, 29 September 2010 (UTC)

Though I'm not sure it addresses BenFrantzDale's concerns, I've added a couple of quaternary headings to the DOF vs. format size derivation so that it's a bit easier to wade through.

Though an illustration might help, I think we'd need several just to address the most common situations, even if the final-image size is assumed to be constant:

• “Same picture”
• Same focal length, same distance
• Same focal length, same field of view at subject distance

The case could be made that we'd even need one for cropping, and perhaps one for the situation where the absolute aperture size is constant. I've seen every one of these situations come up in recent Internet discussions that sometimes never manage to get to what Stroebel stated in 1976.

Yet another approach would be to create a separate article on this topic, though I'm not sure that could really justified.

Subheads and the TOC

As I've previously mentioned, the TOC becomes more monstrous with every additional subhead. If it's too much to take, I think we could reasonably replace the quaternary headings with simple bolding and a line break after the heading text, as I've shown here.

DOF vs. format size

>Excerpt - "If pictures are taken from the same distance using the same lens and f-number, and the final images are the same size, the original image (that recorded on the film or electronic sensor) from the smaller format requires greater enlargement for the same size final image, and the smaller format has less DOF."

Same distance, same lens, same f-number. What does 'same size' mean? In such a case, wouldn't the smaller format record a smaller part of the picture? If so, then it is the large-format picture that would need an enlargement (and cropping) to match with the smaller format? The whole paragraph is quite dense and involved, perhaps illustrations are needed to highlight the differences. Preroll (talk) 00:36, 13 October 2010 (UTC)

I'm not sure I understand the question about same size. There is some potential ambiguity when the two formats have different aspect ratios (size then could refer to the long dimension, the short dimension, or the diagonal); this is discussed in DOF vs. format size under the section Derivation of the DOF formulas. But for the conditions Preroll cites, the most common comparison is between 24 mm × 36 mm and a “crop” format, so the aspect ratios are the same.

Implied is that the both images are enlarged without cropping to give same-size final images, so that enlargement is in proportion to format size; perhaps we need to mention this explicitly, though it might make the paragraph even more dense. Though perhaps the wording could be improved, I don't see a way to reduce the complexity. Unless all relevant assumptions are stated, a comparison is meaningless. Unfortunately, quite a few assumptions are relevant.

With the additional qualification of no cropping, the smaller format would require greater enlargement. The angle of view with the smaller format would of course be smaller. The image from the larger format could of course be cropped so that both final images had the same field of view at the subject distance. Both “same distance” and cropping are discussed at some length under DOF vs. format size, though we don't specifically mention cropping the larger-format image to match a smaller-format image taken with the same lens and f-number at the same camera-to-subject distance.

If we add an illustration for this comparison, it seems to me we'd also need illustrations for other possible comparisons, as I mentioned under Images September 2010 above. I'm not sure what such illustrations should depict; it would be simple to show the camera position and angle of view for each format, but less simple to show the effects of f-number and enlargement. JeffConrad (talk) 03:49, 13 October 2010 (UTC)

I reviewed it and I agree it's correct, though a bit dense. Introducing aspect ratio would only complicate it further. Later in the paragraph, however, I found a bug, which I believe I have corrected. Please review. Dicklyon (talk) 04:34, 13 October 2010 (UTC)

In answer to Preroll's question "wouldn't the smaller format record a smaller part of the picture?", yes, the smaller format would record a smaller part of the scene (like a crop of the larger format's picture). That's why it goes on to say that "The pictures from the two formats will differ because of the different angles of view." Maybe it would be better to say "different fields of view"? Dicklyon (talk) 04:36, 13 October 2010 (UTC)

Perhaps we could break the paragraph up into bullet points for the different situation, outline form. At the top levels, the situations to compare across formats are same lens and same field of view. For the same lens case, the situations to compare include same position and same field of view at subject distance. We could get elaborate and consider same f-number versus same aperture diameter in the same angle of view case, to make it clear when "the same camera position and angle of view, DOF is, to a first approximation, inversely proportional to format size" is applicable and when not. Dicklyon (talk) 04:41, 13 October 2010 (UTC)

The assumptions of same-size final image, same viewing conditions, and same sharpness criteria hold for the entire section, so I moved this to the front. Should we add that except where stated otherwise, the images are enlarged without cropping? For now, I've retained subsequent mentions of same-size final images, but they arguably are unnecessary and could be removed to make for an easier read.

I think we should continue to say “same angle of view” when that is assumed, because it's more general an more common. But I'll concede that, in this specific instance, “field of view” might more directly address Preroll's question.

I agree that there's still work to be done. Though I think this article has the most comprehensive coverage of the topic that I've seen, the point is obviously still not getting across to many readers. A bullet list might help; a similar approach would be to include subheads for each situation that we describe (if we do that, ensuring that the informal and formal treatments have parallel structure might be a good idea). Or we could have a bullet list and subheads; whatever it takes to make clear that several comparisons are possible and that the relevant assumptions need to be stated for each case. Things were much simpler for Stroebel; until recently, the “same picture” comparison was the only usually even considered. JeffConrad (talk) 05:54, 13 October 2010 (UTC)

Your same-size assumption is violated for the case where it says "The final images will, of course, have different sizes." Dicklyon (talk) 06:04, 13 October 2010 (UTC)

So I see ... I suppose we could add “except where stated otherwise” or a similar qualifier.

In that same comparison, does “and if judged with a COC criterion as a fraction of the image size will have different DOFs” really make sense? I cannot imagine why anyone would do this. The DOFs would also be different if the images were viewed at different distances ... Of course, I'm not sure I can imagine anyone giving equal enlargements to images taken in two different formats, either. Could we eliminate this example? I think I included it only to give an example of when images from two formats would have the same DOF. But does that really matter?.

Perhaps we could briefly mention the effect of enlargement at the beginning. We cover the topic quite well in Circle of confusion, but perhaps it's unreasonable to expect the reader to follow the link to that article. We talk about sharpness in Acceptable sharpness, and even mention the effect of format size on lens choice, but we don't seem to say anywhere that the initial-image CoC must be smaller by the ratio of the enlargement (it's hinted by the mention of different enlargements for 35 mm and 16 mm films, but this assumes that enlargement has an effect). I've added a brief mention of enlargement and rearranged a few paragraphs to have the ideas introduced in logical order—see if what I've done works for now.

Perhaps we should mention enlargement in both sections. Or perhaps we should move all the material on the effect of format size to the section under discussion. I think I've left the sharpness section alone because still photographers have pretty much hijacked this article, and I wanted to leave something that related to filmmaking. But perhaps it should just be moved to this section.

It almost seems that we've devoted more time and effort to the effect of format size than to everything else in the article combined ... JeffConrad (talk) 09:52, 13 October 2010 (UTC)

You can't imagine why one would use a COC criterion as a constant fraction (e.g. 1/1500) of the print size? I thought that was the usual convention, based on "comfortable viewing distance", per Horder's Encyclopedia of Photography and such. I agree that eliminating this case may be the best course of action; is there any source that talks about this case? Dicklyon (talk) 17:51, 13 October 2010 (UTC)

The final-image CoC is based on visual acuity at a comfortable viewing distance. If two final images were viewed at the same distance, their sizes would have no effect visual acuity; the fraction-of-the image-size criterion relates to the original image, under the assumption that the image will be enlarged for viewing.

I'm not aware of a source that describes the “same enlargement” comparison, but I'm not sure that's the real factor. Does this comparison serve any purpose? The more I think about it, the less sense a format comparison seems to make unless the final sizes and viewing conditions are the same. Given the several comments we've had about the density of this section and related material in other sections, removing something that's not needed may well improve the article. Upon reflection, I don't think it adds much except clutter, so I've removed it. We have more than enough practical comparisons to deal with.

I've also added some subheads to make the different situations more obvious; they don't quite parallel those under Derivation of the DOF formulas, but they're close. I think additional work is needed, but see if this is on the right track. The final sentence under Same DOF for both formats seems a bit out of place, but I'm not sure where else to put it; perhaps at the beginning of this section?

If necessary, we could precede the detailed discussion with a bullet list of the cases to be covered. I'm against needless repetition, but this is a topic that seems to baffle most photographers, here and elsewhere.

To me, the formatting of the subheads is a bit visually intrusive; simple bolding such as I suggested in the previous section might suffice to separate the cases. If we do it here, I think we also should do it in place of all quaternary headings.

I've replaced the subheads in this section with bold text followed by line breaks to make the subdivisions less garish, as well as to keep the TOC from expanding out of control—see if this works. If it doesn't, revert; if it does, we can use the same approach elsewhere, as I suggested above. JeffConrad (talk) 07:09, 15 October 2010 (UTC)

Hmmm ... it seems that I can't count—we only have tertiary headings. Thank goodness ... I'd replace some of them nonetheless. JeffConrad (talk) 07:35, 15 October 2010 (UTC)

As I think again about the discussion of motion-picture formats under Acceptable sharpness, I think the format comparisons are worth retaining because “same picture” criterion seems self evident—I cannot imagine a filmmaker taking a different approach when shooting in different formats. This isn't to say that the FF/“crop” discussion isn't important, but simply that it's possible to get carried away.

I've removed

“At the same f-number and subject distance, the same lens provides the same blur in the image plane at any distance for all formats.”

because it's a nonsequitur with the deletion of the “same enlargement” comparison, but I think we should mention it somewhere, perhaps under Acceptable sharpness. One question, though: does “at any distance” refer to “any defocused objects”?

“The same blur in the image plane” raises an interesting question about the use of “original image” in the context of digital capture. It's technically a misnomer because the original image in the size of the field stop doesn't exist in tangible form. I suppose the same could be said of undeveloped film, but at least after processing, an image does exist in the format size. The proper description as you've used it here works well; unfortunately, it may be unwieldy to use a technically correct description in some other contexts. One approach would be to continue to use the term as we have, but add a footnote explaining the true situation. It was a lot easier when Ansel could just refer to “the negative”. JeffConrad (talk) 00:58, 14 October 2010 (UTC)

Addition of same absolute aperture to Same DOF section

Though I agree that the absolute apertures are the same, mention of that in this subsection is completely out of context of what directly precedes and follows—this section deals with derivations, and at the point of mention, we haven't yet shown what obtains from the same absolute apertures in both formats. Accordingly, I think we should remove its mention here.

I think we cover it quite well in the section specific to absolute aperture, where we show that constant absolute aperture gives constant DoF. Though the absolute-aperture approach is probably more direct, it's not the way lenses have been marked for well over 100 years, so its mention should probably be confined to the section in which discuss it in detail. JeffConrad (talk) 04:01, 14 October 2010 (UTC)

I think a forward reference would solve the problem. The reason to mention is here is nothing about how lenses are marked or what the formulas are, but rather the simple explanation that makes the stated result easy to remember. Dicklyon (talk) 05:59, 15 October 2010 (UTC)

My concern here was that we hadn't previously mentioned absolute diameter, and the equation that followed the statement didn't include d, so it seem a bit of a nonsequitur. We now have it forward linked and back linked, so the bases should be covered; hopefully the equivalence is obvious enough that we can state it without an explicit proof. JeffConrad (talk) 07:09, 15 October 2010 (UTC)

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