Assertions that DoF is dependant on pixel pitch leads me to believe not all the assumptions about DoF and DoF itself are understood.

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Since this is a long and somewhat technical discourse, let me try to motivate the potential reader by summarizing the conclusions which I think it demonstates:

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Digital is different. Pixel pitch affects DoF in a serious way, and (except in the exceptional case when pixel pitch is exactly proportional to sensor size), the "M x A rule" and similar rules of thumb, or DoF tables based on film-camera concepts, will be inaccurate and misleading.

Both Nikon and Canon are widely rumored to be contemplating introducing large-MP full-frame "Super DSLR" models. But a "Super DSLR" such as our hypothetical 27MP "D3Z" will have considerably less DoF that existing 10-16MP full-frame DSLRs. As a practical matter, the DoF penalty for such a camera, arising from its necessarily finer pixel pitch, may be so large as to make it effectively impossible to get enough DoF for landscape photography, for example, by simply stopping down. The only recourse would seem to be using lens movements, of the type view-camera users have long been obliged to learn, in a new generation of well-corrected "Tilt & Shift" lenses. Let us hope that Nikon and Canon will attend to this task, as well.

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The mathematics of calculating DoF from the CoC are described in any standard optics text (for example, Chapter 22 of Sidey Ray's Applied Photographic Optics); the basic idea is that if the image of a scene element K units in length can be covered by a "Circle of Confusion" of diameter C on the film, it wiil not be perceived in detail, and will be in the "out-of-focus" zone; while one whose image is too large to be covered by the CoC will be detectable on the print, in the "in-focus" zone. For a camera focused on a subject u meters away, the near and far camera-to-object distances, S < u and and R > u, at which a K-sized element would just span the CoC, define the near and far limits of the "in-focus" field. The Depth of Field T is defined as T = (R-S), and for "normal" (i.e., non-closeup) distances, it can be calculated from the equation

T = (2*u*u*N*C)/(f*f)

where u is the camera-to-subject distance, f is the focal length of the lens, C is the diameter of the CoC, all in meters, and N is the relative aperture, a pure number (2.8, 4, 5.6, etc.). The CoC (value of C) is chosen in view of the intended enlargement, and distance at which the print is to be viewed; a value of 30 microns (millionths of a meter) would be typical for a 35mm negative, enlarged 8x to a 8" x 12" print, to be viewed at 10-12 inches (the 30-micron CoC would thus be enlarged to a 8 x 40 = 240-micron blur spot on the print).

To apply this apparatus to digital, we must re-express the CoC in terms of pixels, not microns, as explained in my previous post.

But let's first apply it to FILM cameras, which have no pixels, to the calculate the DoF's of full-frame vs APS. For concreteness, suppose we're using a full-frame 35mm SLR to photograph an object 10 meters away, using a 100mm lens (f = .1), using a CoC of 40 microns, at an arbitrary aperture N. If we work out the arithmetic (keeping track of all the zeroes) we find that T = .3N, implying a DoF of 1.2 meters at f/4, or 2.4m at f/8, etc., which is in the ballpark with the DoF scales engraved on a typical 100mm SLR lens.

Now suppose we take the same shot from the same vantage point with an an "APS" (16 x 24mm frame) body, using a wider lens (because of the "crop factor") to get the same FoV; the proper lens to use is one of focal length f' = (2/3)f = 68mm. Moreover, because the APS negative is only 2/3 as large, it will have to be enlarged more to yield the same final print size, by a factor of 3/2; hence, in order to end up with the same-sized blur spot on the print, we must take a smaller CoC, C' = (2/3)C. All other factors in the equation are the same, so the DoF for the APS shot, T', is

T' = [2*u*u*N*C']/f'*f' = [2*u*u*N*(2/3)C]/[(2/3)f*(2/3)*f] = (3/2)T = (3/2)*.3N

Thus, at the same aperture, the DoF in the APS image is 3/2 as large; to get the same DOF we would have to open up the aperture to N' = (2/3)N. Or, to put it the other way around, the DoF for a full-frame camera, using a longer lens to give the same FoV, is only 2/3 as deep, compared to the APS camera; and to get the same DoF we would have to stop down the full-frame's longer lens by the "crop factor" of 3/2: if the APS image (using the 68mm lens) were shot at f/4, we would have to stop down the 100mm lens on the full-frame camera to f/6.

This relationship, and the rule "stop down by the crop factor" is a general one, which does not depende on the numerical specifics of our example. This type of ananlysis is the basis for similar "rules", such as Alexander's "CoC =Diag/1500" rule, and Wrotniak's "M x A" rule.

But now let's apply this apparatus to digital, taking account of pixel pitch, specificaly to the issue of DoF on APS-C versus full-frame DSLRs, and using the D2X (an APS-C, 12MP camera with a pixel pitch of 5.5 microns) as a baseline.

The DoF of a 100mm lens focused at 10m, using a CoC = 30 microns, is T = .3N, as shown above (irrespective of the sensor size); so for the D2X, the relevant "CoC" measured in PIXELS--call it the DCoC--is 30/5.5 = 5.5 pixels in diameter. A 300-ppi print has about 12 pixels/mm, so the resulting blur spot would be about 420 microns in diameter, somewhat larger than the film-camera example used above; but this calculation ignores the effects of demosiacing & sharpening, and is close enough for illustrative purposes (suppose we're viewing all the digital prints at a somewhat greater viewing distance.) Thus the DoF for a D2X shot taken with a 100mm lens, focussed on an object 10 meters distant, is also given by T = .3N

Now let's compare the D2X image with one taken by a full-frame DSLR, in which the pixel pitch has been increased (by a factor of 3/2) to make the sensor large enough to fill the full 24 x 36mm frame. The pixel count is the same, so both cameras will yield the same (300-ppi) print size. To get the same-sized blur spot on the print, we must choose a DCoC 5.5 pixels in diameter, which for these larger pixels reqiuires a CoC of C' = (3/2)C. To get the same FoV, because of the "crop factor", we would use a lens of f' = (3/2)f = 150mm; so plugging these into the equation

T' = [2*u*u*N*C']/[f'*f'] = [2*u*u*N*(3/2)C]/[(3/2)f*(3/2)*f] = (2/3)T = (2/3)*.3N

This follows "stop down by the crop factor" rule, as did the film-camera example above.

But now suppose we use a full-frame camera--the "D3Z"--which uses the same pixel pitch as the D2X. Its 27MP image will yield a consdierably larger, 300-ppi print; but suppose we still view it at the same distance, using the same blur-spot size to define the in-focus field. To get the same blur-spot on the print, we must use the same CoC, C' = C = 30 microns, which is still 5.5 pixels in diameter; so, taking account of the longer lens, we have:

T" = [2*u*u*N*C']/[f'*f'] = [2*u*u*N*C]/[(3/2)f*(3/2)*f] = (4/9)T = (4/9)*.3N

There is now less than half the DoF; for the full-frame camera to get the same DoF as in the D2X shot, we must now stop down by the SQUARE of the "crop factor", in this case by (9/4). If the D2X shot were taken at f/4, we would have to stop the D3Z's 150mm lens to f/9--which is approaching the limit (f/11, according to Thom) at which D2X users have found that diffraction-induced blurring effects increase objectioanlly (basically because the diameter of the Airey disk exceeds the 2-pixel Nyquist limit).

There are a couple of morals to this story.

Digital is different. Pixel pitch affects DoF in a serious way, and (except in the exceptional case when pixel pitch is exactly proportional to sensor size), the "stop down by the crop factor" and similar rules of thumb, or DoF tables based on film-camera concepts, will be inaccurate and misleading.

Both Nikon and Canon are widely rumored to be contemplating introducing large-MP full-frame "Super DSLR" models. But a "Super DSLR" such as our hypothetical 27MP "D3Z" will have considerably less DoF that existing 10-16MP full-frame DSLRs. As a practical matter, the DoF penalty for such a camera, arising from its necessarily finer pixel pitch, may be so large as to make it effectively impossible to get enough DoF for landscape photography, for example, by simply stopping down. The only recourse would seem to be using lens movements, of the type view-camera users have long been obliged to learn, in a new generation of well-corrected "Tilt & Shift" lenses. Let us hope that Nikon and Canon will attend to this task, as well.