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As you may remember from the physics you were taught in school if
you shine a beam of light through a slit and place a white card behind it you
will see a pattern of dark and light stripes. Generally in photography you can
ignore this phenomenon as a 'slit' with the diameter of a typical lens with a
card as far behind it as the film or digital imager would produce an invisibly
fine pattern of stripes.
But especially in digiscoping and even with digital SLR's with
extreme telephoto lenses this effect will produce a blurring that imposes an
absolute limit of resolution in practical terms. In practice there would be
little point in having pixels in the imager spaced any closer than the spread of
this blurring. For digital SLR's this can very conveniently be expressed as a
maximum F-number
(minimum aperture) for any lens and is derived from the number of pixels/mm in the
sensor as follows.

Maximum F-number for a digital SLR with 'perfect' lens
click here for details of derivation
This is the theoretical best performance of a lens. Due to spherical aberration and other
problems the best performance that can be expected of a real lens would be worse
than this. On the positive side the sharpening that can be done by processing
the image after it has been taken improves resolution by bringing out otherwise
hidden detail (provided this low contrast detail has not been lost in noise from
high ISO). In a practical test I performed recently (see
here) the improvement over theory was slightly more than the detriment.
So taking an estimate of this for a real image. However as the highest
magnification shot I could take was not significantly blurred the factual
could be higher.

Maximum F-number for a digital SLR with 'real' lens
These formulas only apply to the maximum
aperture for a given lens, stopping down with the lens's diaphragm does not
have the same effect because the diaphragm is usually near the rear of the lens
where it has much less impact on resolution. In fact stopping down by 1 or 2
stops usually improves the resolution. See these example
shots. But they do apply for adding teleconverters and for the F-number changing
with zoom.
|
Camera |
Max. F-number
(possibly higher) |
|
Nikon D1h |
f/17.5 |
|
Nikon D1x |
f/17.5 vertically
f/8.7 horizontally |
|
Nikon D100,
Canon D60,
EOS 10D |
f/11.5 |
| Nikon D2h |
f/14 |
If you know the number of megapixels (M.P.) and the focal
length multiplier (f.l.mult.) of a camera then

Maximum F-number for a digital SLR with 'real' lens
This would also give you the correct result for
images taken at reduced resolution.
For digiscopers all this talk of F-numbers is not
so convenient but the same theory can be manipulated to produce the maximum
useful magnification. Long axis pixels is the larger number when the sensor size
is quoted as e.g. 3000x2000 pixels. 
Maximum Magnification for digiscoping with 'ideal' telescope of lens diameter D
click here for details of
derivation
Again real optics will
introduce extra blurring to this theoretical picture. Digiscoping will always
have greater opportunity for aberration compared to SLR photography due to the
intermediate image in the telescope and the necessary extra optics. The
opportunity for sharpening after shooting is similar so there is probably no
improvement between ideal optics and real post-processing images. 
Maximum Magnification for digiscoping with 'real' telescope of lens diameter D
|
Lens Diameter |
Max. Magnification
(2500 pixels) |
|
80mm |
30x |
|
60mm |
20x |
The magnification of a digiscoping setup being the
magnification of the 'scope with the eyepiece used times the quoted
magnification of the camera's lens. The latter is quoted somewhat variably. For
a 35mm film SLR 1x magnification (i.e. nominally equivalent to the human eye) is
given by a 56mm lens, and for a smaller sensor a proportionately smaller lens.
Unfortunately magnification can be slightly over-quoted to make a lens sound
more impressive.
This can be circumvented by calculating the number of pixels
across an image of the full moon (always the same angular size) at the optimum
magnification. This also has the advantage of being true for any sensor. For
digiscoping multiply lens diameter by 8
|
Lens Diameter |
Pixels/Moon |
|
80mm |
1100 |
|
60mm |
820 |
Appendix (minor approximations not
shown)
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For Fraunhofer diffraction by a
circular aperture of diameter D (meters) the angle (radians) from the axis
to the first dark ring of monochromatic light of wavelength l
(meters) is |

This is also the angular resolving power of the
aperture.
At a screen L (meters) behind this aperture

Matching the resolution to the spacing of
pixels on a sensor W (mm) wide with x pixels along that axis and using the
definition of F-number that is is equal to the
focal length of a lens divided by its diameter to find the correct spacing for orange light (red would have the
worst resolution for visible light) yields

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To calculate
the maximum useful magnification take the angular resolution as calculated
above view of a 56mm lens on a 35mm camera (defined as 1x) which is
0.6 radians along the long axis, thus
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Max.Mag. = |

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Again the formula in the main text is for orange
light
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