Equipment & Techniques > Cameras, Lenses and Shooting gear

DoF, sensor size, and pixel pitch

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gkramer:
Sidney Johnson's analysis of DoF ("Lens Equivalents") is based on a film-camera era treatment of the topic, and is not valid for digital. The basic problem is that it is implicitly based on the "enlargement factor" as measured by the ratio, in terms of linear dimensions, by which the film negative (or positive) is enlarged to to produce the final print (thus a 35mm negative, which measures 24 x 36mm = 1" x 1.5", when enlarged to produce an 8" x 12" print, has an "enlargement factor" of 8x).

This is inappropriate for digital: the relevant "enalrgement factor" depends only on the pixel count, and is idependent of the physical dimensions of the sensor. A 6MP, 2000 x 3000-pixel image file will produce the 6.7 x 10" print at "native" 300ppi resolution, irrespective of whether it was captured by a 24mm x 36mm full-frame sensor, a 16mm x 24mm APS-C sensor, or a tiny, quarter-inch sensor from a pocket point-n-shoot.

Johnson suggests setting the CoC to (sensor diagonal)/1500, which for a fullframe 24mm x 36mm sensor gives a CoC of 29 microns diameter. For the Canon EOS-1Ds, with a pixel pitch of 8.9 microns, this means the CoC on the sensor is 29/8.9 = 3.25 pixels in diameter; at 300ppi, this would be about .011" on the print.

The Nikon D2X has about the same MP count (12.2MP), on a smaller APS-C sensor, with a much smaller pixel pitch, 5.5 microns; but suppose Nikon decided to produce a full-frame DSLR by simply scaling up the D2X's sensor (it would be an impressive 27MP). Then the CoC on the sensor would be 29/5.5 = 5.27 pixels in diameter, and would produce a blur spot on the print 1.6 times larger, or .017". The difference on the prints (viewed under identical viewing conditions) would be clearly visible.

Of course the print produced by the 27MP Nikon D3Z (let's call it) would be much larger than the 11MP Canon's; at "native" 300-ppi resolution, the "D3Z" image would be 9.5" x 14.3", versus the Canon's 6.8" x 10.3"--roughly the difference between a double-page spread in Audobon magazine, and a shot that would fit comfortably on a single page. But, viewed at the same distance, the blur spot used to define DoF of the D2X image would be visibly larger; or, put differently, the apparent DoF of the D3Z image would be less.

To correctly calculate the DoF for the D3Z, we must use a smaller CoC, of 29/1.6 = 18 microns.

One implication of this is that the DoF scales engraved on lenses are meaningless when the lens is attached to a DSLR, since they do not take account of either sensor size or pixle pitch; and even tables like Johnson's, which do take account of sensor size, are off the mark. I'm working out a corrected one, which I hope to post later.

howiesmith:
Anyone with a basic understanding of DoF knows CoC is determined by the photogtapher, not the camera (or its maker) or sensor type or size or pixel pitch or kind of film being used, lens, or whatever.  It is simply a number decided on by the photographer when designing a print.

It makes no sense of course to select a CoC smaller than can be resolved by the camera system, be it digital or film.  There is a distinct difference between DoF and maximum DoF.

Sidney Johnson made some assumptions about the size of enlargement and viewing conditions in order to deteremine a CoC, but that CoC is valid only for his set of assumptions.

BJL:

--- Quote ---Sidney Johnson made some assumptions about the size of enlargement and viewing conditions in order to deteremine a CoC, but that CoC is valid only for his set of assumptions.
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Give it a rest Howard. The DOF perceived by a viewer of a print depends amongst other things on print size and viewing distance, and so these conditions are a necessary part of any DOF calculation or comparison. These are "assumptions" only in the same sense that reference to a particular focal length, aperture ratio and focus distance are "assumptions": they are all just explicit parts of the statement.

And in fact, so long as one only assumes that different prints from different combinations of focal length, aperture, subject distance etc. are assessed via prints of the same size, viewed from the same distance, by a viewer of the same visual acuity, Johnson's conclusions hold: equal aperture size d=F/N, combined with equal perspective, equal FOV, equal image size and equal viewing distance will give about equal DOF.

Johnson does make some assumptions, mostly rather harmless. Firstly that we are not in the "macro" range, where some of the optical approximations made might become less accurate. Secondly that the sensor resolution is not an issue because it is more than the viewer can make out under the stated viewing conditions, and that lens aberrations are likewise low enough to be ignored.


It might be interesting to rework Johnson's calculations in terms of statements about the effects on angular resolution of various parts of the image from the combination of OOF effects (the various circles of confusion at different parts of the image), Airy disks, pixel sizes, etc. This is more the spirit in which astronomers approach resolution.

howiesmith:

--- Quote ---Give it a rest Howard.   ...

Johnson does make some assumptions, mostly rather harmless. ...

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No.

I didn't say Johnson's assumptions were not harmless or even unusual.  I merely said that assumptions were made and that the reader must understand those assumptions in order to understand Johnson's results.

Not knowing or acknowledging assumptions often leads to results becoming "facts."  Like, DoF is determined by the engraved scales on the lens' barrel, without even caring what the CoC is.  The engraings are true for and only for, prints that are made according to the applicable assumptions.  Canon assumes a print size, viewing dsitance and CoC.  These assumptions do nat have to be made.  Or that the DoF preview in the view finder works (what is the "print size" (maybe 1x1.5"), what is the viewing distance, and isn't the viewfinder dimmer than the print viewing area?).  Or the assumptions for DoF calculators are not provided, but simply provide a CoC value for the camera/lens being used.

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

BJL:

--- Quote ---I merely said that assumptions were made and that the reader must understand those assumptions in order to understand Johnson's results.

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