Digital Resolution
How to match your lens and your camera for best results

Theory

Test
Shots

Early
2004

Late
2003

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-numberFocal Length / Lens Diameter (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)

back  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

back 

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

Max.Mag. = 

Again the formula in the main text is for orange light

 

E-mail Paul Burrows