## DOF of Micro 4/3 cameras and lenses

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- enricosavazzi
**Posts:**1294**Joined:**Sat Nov 21, 2009 2:41 pm**Location:**Borgholm, Sweden-
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### DOF of Micro 4/3 cameras and lenses

This post is mainly a request for confirmation that I am still sane (at least for what concerns my understanding of DOF). I am sure that Rik will chime in, but any other comments are welcome.

Everything I know about DOF tells me that, at the same lens aperture and field of view, DOF does not depend on film/sensor size (nor lens focal length, because it does not appear in the DOF equation) when comparing pictures displayed at the same size. The only thing that may change is the angle of view (a wideangle renders a distant background as proportionally smaller than a telephoto, even when both lenses render a foreground object at the same relative size). But the angle of view can be kept constant in the following example, to make a comparison easier.

A 16 megapixel full-frame DSLR with a 100 mm lens at (effective) f/2.8 will produce exactly the same DOF as a Micro 4/3 camera with a 50 mm lens at (effective) f/2.8, shooting the same subject from the same camera position (or the same position of the front lens pupil if we want to be real picky). We assume that the lens quality is good in both cases to eliminate any effect of lens aberrations on COC and resolution.

Aside from the different aspect ratios of the two cameras (3:2 versus 4:3), which can be eliminated by cropping both pictures to the same height and width in pixels, there is no way to distinguish which of the two cameras was used to take either picture by looking at their DOF or COC measured in pixels. Is this right?

Then, why do I keep seeing the same statements to the contrary on many web sites, including otherwise respectable ones - at least two of them just today.

For instance, from http://www.dpreview.com/previews/panasonic_12-35_2p8/3:

"In terms of DOF and background blur, the [f/2.8 Micro 4/3] lens behaves like a 16-45mm F3.5 lens for APS-C, or a 24-70mm F5.6 lens for full frame cameras."

Some possible explanations (assuming that my sanity is no longer in question):

Deliberate misinformation?

Full-frame photographers lying in order to preserve their perceived sense of superiority?

Professional photographers who feel they must keep a distance from amateur ones by saying that only their own pro equipment can take good pictures?

Simple ignorance?

Marketing ploy to imply that the more expensive larger-format cameras are intrinsically better in terms of DOF?

Parroting - someone started to say one unsubstantiated thing, and many others are repeating it because it is easier than verifying its truth?

Everything I know about DOF tells me that, at the same lens aperture and field of view, DOF does not depend on film/sensor size (nor lens focal length, because it does not appear in the DOF equation) when comparing pictures displayed at the same size. The only thing that may change is the angle of view (a wideangle renders a distant background as proportionally smaller than a telephoto, even when both lenses render a foreground object at the same relative size). But the angle of view can be kept constant in the following example, to make a comparison easier.

A 16 megapixel full-frame DSLR with a 100 mm lens at (effective) f/2.8 will produce exactly the same DOF as a Micro 4/3 camera with a 50 mm lens at (effective) f/2.8, shooting the same subject from the same camera position (or the same position of the front lens pupil if we want to be real picky). We assume that the lens quality is good in both cases to eliminate any effect of lens aberrations on COC and resolution.

Aside from the different aspect ratios of the two cameras (3:2 versus 4:3), which can be eliminated by cropping both pictures to the same height and width in pixels, there is no way to distinguish which of the two cameras was used to take either picture by looking at their DOF or COC measured in pixels. Is this right?

Then, why do I keep seeing the same statements to the contrary on many web sites, including otherwise respectable ones - at least two of them just today.

For instance, from http://www.dpreview.com/previews/panasonic_12-35_2p8/3:

"In terms of DOF and background blur, the [f/2.8 Micro 4/3] lens behaves like a 16-45mm F3.5 lens for APS-C, or a 24-70mm F5.6 lens for full frame cameras."

Some possible explanations (assuming that my sanity is no longer in question):

Deliberate misinformation?

Full-frame photographers lying in order to preserve their perceived sense of superiority?

Professional photographers who feel they must keep a distance from amateur ones by saying that only their own pro equipment can take good pictures?

Simple ignorance?

Marketing ploy to imply that the more expensive larger-format cameras are intrinsically better in terms of DOF?

Parroting - someone started to say one unsubstantiated thing, and many others are repeating it because it is easier than verifying its truth?

--ES

- rjlittlefield
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**Posts:**21198**Joined:**Tue Aug 01, 2006 8:34 am**Location:**Richland, Washington State, USA-
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### Re: DOF of Micro 4/3 cameras and lenses

Enrico,

I do not like to talk about sanity, so let's talk about DOF instead.

From http://www.dpreview.com/previews/panasonic_12-35_2p8/3:

In contrast:

The issue of DOF and f-number has been discussed at length in previous threads. The best single reference I know is http://www.photomacrography.net/forum/v ... 8376#78376. See http://www.janrik.net/DOFpostings/PM1/D ... _Size.html for a direct illustration of corresponding DOF between large- and small-sensor cameras.

In brief, to get the same FOV and DOF from two different sensor sizes, you have to scale the

The underlying theory is very simple -- the trick is to set aside the math and just think about the light. The appearance of an image is determined by what light was used to make it. Same light, same image. As a result, at same FOV and final image size, DOF is determined by the angular width of the entrance cone. That angle is determined by the location and diameter of the entrance pupil. If you keep the entrance pupil at the same location, then you also have to keep the same diameter. Of course the distance from lens to sensor will have to scale in proportion to sensor size. Effective f-number can be computed as that distance divided by the aperture diameter, and that's why the effective f-number also scales in proportion to sensor size. It's almost insanely simple.

Where things get complicated is to understand the correspondence between the above simple and correct intuition and the far less simple but equally correct standard math formulas for DOF. I'll leave that as an exercise. Check back if you can't make it work out.

By the way, I have great sympathy for people who get confused by DOF, sensor size, and camera settings. The history of my own coming to grips with how things work is mostly recorded for posterity in our own forums, starting over 6 years ago HERE. It's been quite a journey!

--Rik

I do not like to talk about sanity, so let's talk about DOF instead.

From http://www.dpreview.com/previews/panasonic_12-35_2p8/3:

The above statement is correct to within rounding error and aspect ratio."In terms of DOF and background blur, the [f/2.8 Micro 4/3] lens behaves like a 16-45mm F3.5 lens for APS-C, or a 24-70mm F5.6 lens for full frame cameras."

In contrast:

The above statement is also correct, but only if the word "aperture" is interpreted asenricosavazzi wrote:at the same lens aperture and field of view, DOF does not depend on film/sensor size (nor lens focal length, because it does not appear in the DOF equation) when comparing pictures displayed at the same size.

*diameter*, rather than its usual meaning*f-number*. If "aperture" means "f-number", then the statement is not correct.The issue of DOF and f-number has been discussed at length in previous threads. The best single reference I know is http://www.photomacrography.net/forum/v ... 8376#78376. See http://www.janrik.net/DOFpostings/PM1/D ... _Size.html for a direct illustration of corresponding DOF between large- and small-sensor cameras.

In brief, to get the same FOV and DOF from two different sensor sizes, you have to scale the

*effective f-number*in proportion to the sensor size.The underlying theory is very simple -- the trick is to set aside the math and just think about the light. The appearance of an image is determined by what light was used to make it. Same light, same image. As a result, at same FOV and final image size, DOF is determined by the angular width of the entrance cone. That angle is determined by the location and diameter of the entrance pupil. If you keep the entrance pupil at the same location, then you also have to keep the same diameter. Of course the distance from lens to sensor will have to scale in proportion to sensor size. Effective f-number can be computed as that distance divided by the aperture diameter, and that's why the effective f-number also scales in proportion to sensor size. It's almost insanely simple.

Where things get complicated is to understand the correspondence between the above simple and correct intuition and the far less simple but equally correct standard math formulas for DOF. I'll leave that as an exercise. Check back if you can't make it work out.

By the way, I have great sympathy for people who get confused by DOF, sensor size, and camera settings. The history of my own coming to grips with how things work is mostly recorded for posterity in our own forums, starting over 6 years ago HERE. It's been quite a journey!

--Rik

- enricosavazzi
**Posts:**1294**Joined:**Sat Nov 21, 2009 2:41 pm**Location:**Borgholm, Sweden-
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Thanks Rik,

I did the homework and came up with the following results, which clearly show the DOF difference at a subject area of 360x240mm, and still a significant difference at 36x24. No significant difference at 3.6x2.4 and lower, where we usually "live", although there seems to be something still going on in the last few decimals. The area shaded in green contains computed values. D is of course the DOF.

So it is true what they say about the different DOF of the different sensor sizes, although it is not so relevant in photomacrography (but still good to know about in macrophotography).

I think I need to add the following corollary to my notes on DOF:

"Whenever you think you understand DOF well enough that you don't need to do the calculations, do the following:

1) Open mouth

2) Insert foot

3) Start Excel"

PS- the Excel file is available at http://savazzi.freehostia.com/dof.xls. I used the non-approximated equations for Dn and Df, because anyway I am not the one doing the calculations. I did not bother to take the hyperfocal distance into account, so the spreadsheet is probably going to bomb at very large subject sizes.

I did the homework and came up with the following results, which clearly show the DOF difference at a subject area of 360x240mm, and still a significant difference at 36x24. No significant difference at 3.6x2.4 and lower, where we usually "live", although there seems to be something still going on in the last few decimals. The area shaded in green contains computed values. D is of course the DOF.

So it is true what they say about the different DOF of the different sensor sizes, although it is not so relevant in photomacrography (but still good to know about in macrophotography).

I think I need to add the following corollary to my notes on DOF:

"Whenever you think you understand DOF well enough that you don't need to do the calculations, do the following:

1) Open mouth

2) Insert foot

3) Start Excel"

PS- the Excel file is available at http://savazzi.freehostia.com/dof.xls. I used the non-approximated equations for Dn and Df, because anyway I am not the one doing the calculations. I did not bother to take the hyperfocal distance into account, so the spreadsheet is probably going to bomb at very large subject sizes.

--ES

- rjlittlefield
- Site Admin
**Posts:**21198**Joined:**Tue Aug 01, 2006 8:34 am**Location:**Richland, Washington State, USA-
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Enrico,

Different people get best results from different sets of rules. I have seen standard formulas misused so many times (and done it myself!) that I no longer have much faith in calculations alone.

As a result, my own set of rules now includes these steps:

- Predict result from "first principles"

- Compute result using standard formulas

- Set up a test and measure an experimental result.

- Compare the three results and resolve any big discrepancies.

In the current discussion, your spreadsheet surely has something wrong. After much study, I think it's a matter of labeling, but it's an important matter. You have a line labeled "N (effective f/number)". It contains the value 4 even for the case of a 3.6 mm subject on a 36 mm sensor (10X). But of course effective f-number is equal to nominal f-number multiplied by the quantity (magnification+1). So, saying "effective f/4" at 10X is implying a nominal lens of f/0.36(!). This by itself is suspicious. Further, the number that you end up computing for D shares more than four significant digits with the number computed by Lefkowitz's macro DOF approximation that

TDF =2*C*f_r*(m+1)/(m^2) ,

where f_r = 4 is the "relative (marked) aperture", not the effective aperture.

So, I think that your spreadsheet's value for N is not the

I hope this does not sound like nitpicking. As you know, there is a huge difference between "effective f-number" and "nominal f-number" at high magnification. With that one little word wrong, this table becomes actively misleading to anyone else who would need it in the first place. (

Now, you mentioned that "there seems to be something still going on in the last few decimals" even at high magnification. Again, this can be understood by thinking about the entrance cone. When magnification is high, the angle of the entrance cone depends almost entirely on the nominal f-number of the lens. But not quite entirely. When you go from 10X on a full-frame sensor to 5X on a micro four-thirds sensor, the lens moves relatively a little farther away from the subject. This little increase in relative distance makes the entrance cone a little narrower, and it's that narrowing of the entrance cone that gives the little more DOF with the smaller sensor. (It also gives a little more diffraction blur.)

I would like to go back to the basic issue of sensor size, since I think this is still not well understood by many.

Again, diffraction imposes a strict tradeoff between resolution and depth of field. This tradeoff is identical for all sensor sizes -- if you stop down to get the same DOF, then you get the same diffraction blur in the same final image.

So, when you are stopping down to get maximum DOF with acceptable diffraction blur, the main advantage of a larger sensor is to get less noise by capturing more light.

However, larger sensors also allow larger apertures, which can reach combinations of shallower DOF and less diffraction than you can get with smaller sensors. This is obvious and important at very low magnification, for example in landscape photography. The potential improvement is less at higher magnifications and becomes negligible for microscopy.

I hope this helps!

--Rik

Different people get best results from different sets of rules. I have seen standard formulas misused so many times (and done it myself!) that I no longer have much faith in calculations alone.

As a result, my own set of rules now includes these steps:

- Predict result from "first principles"

- Compute result using standard formulas

- Set up a test and measure an experimental result.

- Compare the three results and resolve any big discrepancies.

In the current discussion, your spreadsheet surely has something wrong. After much study, I think it's a matter of labeling, but it's an important matter. You have a line labeled "N (effective f/number)". It contains the value 4 even for the case of a 3.6 mm subject on a 36 mm sensor (10X). But of course effective f-number is equal to nominal f-number multiplied by the quantity (magnification+1). So, saying "effective f/4" at 10X is implying a nominal lens of f/0.36(!). This by itself is suspicious. Further, the number that you end up computing for D shares more than four significant digits with the number computed by Lefkowitz's macro DOF approximation that

TDF =2*C*f_r*(m+1)/(m^2) ,

where f_r = 4 is the "relative (marked) aperture", not the effective aperture.

So, I think that your spreadsheet's value for N is not the

*effective*f-number, but is actually the*nominal*f-number, uncorrected for magnification.I hope this does not sound like nitpicking. As you know, there is a huge difference between "effective f-number" and "nominal f-number" at high magnification. With that one little word wrong, this table becomes actively misleading to anyone else who would need it in the first place. (

*End rant.*)Now, you mentioned that "there seems to be something still going on in the last few decimals" even at high magnification. Again, this can be understood by thinking about the entrance cone. When magnification is high, the angle of the entrance cone depends almost entirely on the nominal f-number of the lens. But not quite entirely. When you go from 10X on a full-frame sensor to 5X on a micro four-thirds sensor, the lens moves relatively a little farther away from the subject. This little increase in relative distance makes the entrance cone a little narrower, and it's that narrowing of the entrance cone that gives the little more DOF with the smaller sensor. (It also gives a little more diffraction blur.)

I would like to go back to the basic issue of sensor size, since I think this is still not well understood by many.

Again, diffraction imposes a strict tradeoff between resolution and depth of field. This tradeoff is identical for all sensor sizes -- if you stop down to get the same DOF, then you get the same diffraction blur in the same final image.

So, when you are stopping down to get maximum DOF with acceptable diffraction blur, the main advantage of a larger sensor is to get less noise by capturing more light.

However, larger sensors also allow larger apertures, which can reach combinations of shallower DOF and less diffraction than you can get with smaller sensors. This is obvious and important at very low magnification, for example in landscape photography. The potential improvement is less at higher magnifications and becomes negligible for microscopy.

I hope this helps!

--Rik

- enricosavazzi
**Posts:**1294**Joined:**Sat Nov 21, 2009 2:41 pm**Location:**Borgholm, Sweden-
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Hi again Rik,

Barring further mistakes, the results still show in both cases that the DOF differences of the sensor sizes are important in ordinary photography, still worth knowing about in close-up and macrophotography, and essentially negligible in photomacrography (within the range of available optics).

Definitely not nitpicking, and very important. Thank you for pointing it out. And in fact, this raises a further question. Should we compare the DOF at a constant nominal aperture or a constant effective aperture? There are good reasons for either choice. Unfortunately, at the photomacrography end, geometric optics no longer gives answers usable in practice (as anyone who tried 10x with a nominal f/4 aperture should know by now) and some of the apertures are unattainable with present technologies. However, the comparison is still interesting because it emphasizes the trends already present when using a smaller range of apertures and magnifications. So here is the spreadsheet modified to give both comparisons:rjlittlefield wrote:Enrico,

...

I hope this does not sound like nitpicking. As you know, there is a huge difference between "effective f-number" and "nominal f-number" at high magnification. With that one little word wrong, this table becomes actively misleading to anyone else who would need it in the first place. (End rant.)

...

--Rik

Barring further mistakes, the results still show in both cases that the DOF differences of the sensor sizes are important in ordinary photography, still worth knowing about in close-up and macrophotography, and essentially negligible in photomacrography (within the range of available optics).

--ES

- rjlittlefield
- Site Admin
**Posts:**21198**Joined:**Tue Aug 01, 2006 8:34 am**Location:**Richland, Washington State, USA-
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To my mind, the most meaningful comparison is neither of those.enricosavazzi wrote:Should we compare the DOF at a constant nominal aperture or a constant effective aperture?

Instead, it is to compare DOF at an effective aperture that is scaled in proportion to the sensor size, for example f/16 on a full-frame 36x24 mm sensor versus f/8 on a hypothetical 18x12 mm sensor.

This comparison is particularly simple because then the DOF and diffraction blur are identical for both sensors.

Thinking about it this way works well to highlight the advantages of larger sensors at low magnifications, especially if you want those nice blurred backgrounds.

At very low magnification the advantages are strong. Example: shooting a shallow DOF portrait at f/1.4 on the full-frame sensor is simple; shooting the same portrait at f/0.7 on the smaller sensor is not feasible.

At macro range, the advantages are still significant, but fading. Example: shooting at 1X and effective f/8 on the full frame camera is simple (use nominal f/4); shooting the same FOV at 0.5X and effective f/4 on the smaller camera is not so simple but still doable (requires nominal f/2.67). If you stop down to a more common effective f/16 on the full frame camera (f/8 nominal at 1X), then this is easily matched on the smaller camera with effective f/8 (f/5.3 nominal at 0.5X).

This is true, but I think it's not very relevant to the current discussion.Unfortunately, at the photomacrography end, geometric optics no longer gives answers usable in practice

When the effective aperture is scaled to match the sensor size, the results apply to both geometry and wave effects. It's a wonderful unification.

--Rik

The practical progress is that it used to be more difficult to compare different lens and sensors at once. With mFT, Nikon 1 or Pentax Q it is possible to compare to DSLR using the same lens over substantially different sensor crops; or one can find suitable lenses for equivalences.

I think the comparison approach is not just about equivalences but depends on the sports discipline in question:

- stacking with unlimited light (at peak sharpness)

- non-stacking unlimited light (at diffraction tradeoff)

- handheld non-stacking in limited light (where small sensors win)...

This is a helpful thread, thanks guys!

What happens to DOF if not white light, but UV (or IR) would be used?

What happens to DOF if not white light, but UV (or IR) would be used?

Klaus

http://www.macrolenses.de for macro and special lens info

http://www.pbase.com/kds315/uv_photos for UV Images and lens/filter info

http://photographyoftheinvisibleworld.blogspot.com/ my UV diary

http://www.macrolenses.de for macro and special lens info

http://www.pbase.com/kds315/uv_photos for UV Images and lens/filter info

http://photographyoftheinvisibleworld.blogspot.com/ my UV diary

- enricosavazzi
**Posts:**1294**Joined:**Sat Nov 21, 2009 2:41 pm**Location:**Borgholm, Sweden-
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Hi Klaus,kds315* wrote:This is a helpful thread, thanks guys!

What happens to DOF if not white light, but UV (or IR) would be used?

the wavelength affects the amount of diffraction. In practice, with the same aperture, magnification etc. and changing only wavelength, in the NIR the image resolution is more degraded by diffraction than in visible light, in the NUV it is less affected. Or, to put it another way, to get the same CoC in the NUV you can stop down a little more than in visible light and get a slightly higher DOF. It is not a major difference, but it is there and can be seen e.g. in macrophotography (around 1x) with nominal apertures around f/11-f/16.

--ES

Thanks Enrico, exactly as I (also) had experienced that. I was more looking for a formula for that...the scientist/engineer I am

Klaus

http://www.macrolenses.de for macro and special lens info

http://www.pbase.com/kds315/uv_photos for UV Images and lens/filter info

http://photographyoftheinvisibleworld.blogspot.com/ my UV diary

http://www.macrolenses.de for macro and special lens info

http://www.pbase.com/kds315/uv_photos for UV Images and lens/filter info

http://photographyoftheinvisibleworld.blogspot.com/ my UV diary

- enricosavazzi
**Posts:**1294**Joined:**Sat Nov 21, 2009 2:41 pm**Location:**Borgholm, Sweden-
**Contact:**

I can tell you what I usually do, which is not the only way.

The traditional definitions of CoC (circle of confusion) and C (the maximum acceptable CoC) are formulated for evaluating photographic prints of "normal" size, seen from a "normal" observation distance by an observer with "normal" vision.

This does not make much sense to me, because we rarely do this in digital photography. Instead, we generally look at dimensionless digital images on computer screens, and we usually display images at 1:1 pixel ratio to evaluate sharpness and resolution. What I typically do to determine C, instead, is look at the maximum practical resolution visible in a digital image, measured in pixels. On a "typical" Bayer sensor with a "typically" strong antialias filter and demosaicking algorithm, in my own judgement and with the cameras I own, this is slightly more than 6 pixels per line-pair if I look at real test images of variously oblique line-pairs (in addition to just vertical or horizontal ones). I generally use a value of 6.2 as a compromise of several factors. Others may choose different values - in the end, the principle remains the same. I take this value as C.

The Airy disk is given by the approximate formula x/f=1.22 l/d, where l is the wavelength (here is where it comes in), x the diameter of the Airy disk and f the distance from the lens to the focal plane (not the focal length). The (effective in this case) lens aperture is f/d (which is where the aperture comes in). As long as you know the physical spacing between sensels (closely approximated by the linear size of the sensor / number of sensels along this dimension), you can compute the diameter of the Airy disk in sensels.

The "diffraction barrier" is hit, from a perceptual point of view, when the diameter of the Airy disk > C (or, more precisely, when it becomes sufficiently larger to be detected as fuzziness). When I compute my tables of acceptable effective apertures and magnifications, for simplicity I use a yellow color (=warning, diffraction is getting in) when CoC >= C, and red (=don't use, diffraction territory) when CoC >= 2C.

The traditional DOF formula does not take diffraction into account, only geometric optics. You must plug in a rule for verifying whether diffraction is large enough to play a role, like the above one. To make things simple, I approximate by ignoring diffraction when Airy < C and use the Airy instead of CoC when Airy >= C, although this is not strictly true.

The traditional definitions of CoC (circle of confusion) and C (the maximum acceptable CoC) are formulated for evaluating photographic prints of "normal" size, seen from a "normal" observation distance by an observer with "normal" vision.

This does not make much sense to me, because we rarely do this in digital photography. Instead, we generally look at dimensionless digital images on computer screens, and we usually display images at 1:1 pixel ratio to evaluate sharpness and resolution. What I typically do to determine C, instead, is look at the maximum practical resolution visible in a digital image, measured in pixels. On a "typical" Bayer sensor with a "typically" strong antialias filter and demosaicking algorithm, in my own judgement and with the cameras I own, this is slightly more than 6 pixels per line-pair if I look at real test images of variously oblique line-pairs (in addition to just vertical or horizontal ones). I generally use a value of 6.2 as a compromise of several factors. Others may choose different values - in the end, the principle remains the same. I take this value as C.

The Airy disk is given by the approximate formula x/f=1.22 l/d, where l is the wavelength (here is where it comes in), x the diameter of the Airy disk and f the distance from the lens to the focal plane (not the focal length). The (effective in this case) lens aperture is f/d (which is where the aperture comes in). As long as you know the physical spacing between sensels (closely approximated by the linear size of the sensor / number of sensels along this dimension), you can compute the diameter of the Airy disk in sensels.

The "diffraction barrier" is hit, from a perceptual point of view, when the diameter of the Airy disk > C (or, more precisely, when it becomes sufficiently larger to be detected as fuzziness). When I compute my tables of acceptable effective apertures and magnifications, for simplicity I use a yellow color (=warning, diffraction is getting in) when CoC >= C, and red (=don't use, diffraction territory) when CoC >= 2C.

The traditional DOF formula does not take diffraction into account, only geometric optics. You must plug in a rule for verifying whether diffraction is large enough to play a role, like the above one. To make things simple, I approximate by ignoring diffraction when Airy < C and use the Airy instead of CoC when Airy >= C, although this is not strictly true.

--ES