Kevin, et. al,
Depth of field has been discussed in depth several times. |8|| I think the most recent thread is this one last May.
http://www.birdforum.net/showthread.php?t=114462
I attached a .pdf file on Post #7 in which I referred to Binocular DOF like the Emperor's new cloths. Everybody says they see it but it just ain't there. The paper has since been expanded and reviewed, but I'm reluctant to post it again because of BF's 24 hr. policy that makes it too difficult to modify later.
The camera and the eye are examples of focal systems. They focus an image on a receptor array, e.g., film or retina. Each has a defined depth-of-focus/field.
A telescope is an
afocal system. It has no finite focal point, therefore, it also has no finite depth of focus. The focal lengths of the objective and eyepiece components make no difference when we are talking about the instrument as a whole.
When an afocal telescope is coupled to the eye, the only two properties that effect optical DOF are its magnification, m, and the exit pupil if it's smaller than the eye's pupil, i.e., EP < p. The smaller of the two defines the "effective" aperture of the combined system.
As seen in the paper, the DOF of a coupled eye-telescope system can be shown to be the DOF of the eye scaled by m. Hence, all telescopes with a given magnification and EP > p produce the same DOF. It doesn't matter what their component objective or eyepiece focal lengths happen to be.
My initial derivation of these relationships was based on the concept of "acceptable blur," as briefly developed in Warren J. Smith's,
Modern Optical Engineering. Using additional references, it turns out the conclusion suffers no loss of generality at any working distance less than infinity. We have only to use m', which is the "effective" magnification of the telescope. As we all know, effective magnification increases as focusing distance decreases (but not linearly).
Using different theoretical starting points I've been told that others have found a scaling factor of m^2, but I haven't seen the math, just heard assertions. (See Mak's post #9.) The discrepancy may be because I'm missing something, like longitudinal vs. transverse magnification, or because the derivative of 1/m is -1/m^2. A plot of hyperfocal distance, for example, would appear to be quadratic in m. In any case, I don't think there is any dispute about effective magnification and exit pupil diameter being the only relevant variables.
We might keep in mind that DOF is a
monocular property that refers to acceptable limits of
axial defocus, i.e., blur. With a camera it's all very clear because the optics and film are static, and one can observe a print that is decoupled from the eye. It can not be evaluated accurately in a working telescope, however, due to constant accommodation and pupil changes of the eye, which vary the momentary focal length and aperture of the system. Hence, DOF for a telescope is really best determined theoretically, with an idealized instrument, static model eye, and working distance used as a parameter.
A second consideration is that there is great confusion between the concepts of depth of field/focus and
depth/distance perception. Roll that together with your conjecture about flat-field effects on focusing, which I believe is valid, and we have a real Tower of Babble. An ideal flat field has the property of bringing all objects into focus that lie on a plane surface tangent to the circle (sphere) defined by the focusing radius. Nice if your looking at a star field, but not so nice if you move an off-axis object thirty feet away to the center, where it will have to be refocused. Most people don't realize that the field curvature of the eye's optics roughly matches the curvature (spherical cap) of the eyeball where the retina is located. Messing with this has consequences. So, I would agree, in general, that the field curvature will effect focusing—and one's depth illusion.
Ed