Re: Resolution at long focal length settings

Detail Man wrote:

Ron Tolmie wrote:

Ian:

The angular resolution (in arc sec) is inversely proportional to the aperture diameter:

sin (angle) = 1.22 x wavelength/aperture diameter

The focal length is not a factor in determining the angular resolution. If the lenses in a view camera and a miniature camera have the same angular angular resolution they will appear to be equally sharp. If the aperture diameter is 3mm and the lens has no optical aberrations then the image will be acceptably sharp, and it doesn't matter if the focal length of the lens is 4mm or 4000mm. If the aperture diameter is 1mm the image will be soft, irrespective of the focal length.

In comparing lenses that have the same focal length (such as the 50mm lenses used in FF cameras) it is a common practice to resort to a linear measurement (lines per mm) because it is easier to make such measurements. Unfortunately that leads to confusion if you try to compare lenses that have different focal lengths. If you have two lenses of equal quality (i.e. the same angular resolution) but different focal lengths the short FL lens will deliver more lines per mm even though it is not any better than the long FL lens. To make a useful comparison of the lenses you would need to divide the l/mm number by the focal length.

My statement about diffraction as a function of the aperture diameter was correct. If you want to make comparisons between measurements made at different focal lengths then you need to measure the angular resolution, not the l/mm. Otherwise you end up in a state of confusion.

Hi Ron,

Have a look at the mathematical approximations and the correspondng identies in this section:

http://en.wikipedia.org/wiki/Airy_disk#Cameras

What do you think ? It seem (to me) to make sense (for small angles) to be able to restate your the correct identity quoted above to be of the form (in units of distance):

Distance = (Wavelength) * (F-Number)

If you disgaree, I would be very interested in learning from you - as I must have missed something.

The derivation makes an assumption that a (symmetrical, thin) lens is focused at "infinity". The Effective Focal Length being Focal Length (for "infinity" focus) multipled by [ 1 + M/P ] (where M is Image Magnifictaion, and P is Pupillary Magnification factor), it seems that this is the form that one might want to use for analyzing notably "close-up" shooting conditions.

As well, see these identities relating to F-Number (as opposed to the entrance-pupil diameter):

http://en.wikipedia.org/wiki/Diffraction#Diffraction-limited_imaging