[Leica] OT pinhole lenses

[Malcolm McCullough <MM4@mm-croy.mottmac.com>]

D Khong stirred the pot with:

>If I am not mistaken, pin-hole lenses are used in architectural
>photography. Straight lines must be strait, everything is in focus, the
>image is distortion free.

Dan,
I wonder if you are referring to glass lenses with a very very small 
aperture rather than a plain pinhole (hence the term 'pinhole lens')? 
Despite what someone or other claims, a plain pinhole does not focus light 
rays (LUGgers please contact me off-list if you disagree with that 
statement) so the image they produce always looks rather blurred. The 
addition of a simple refractive (eg glass) element to a pinhole that is not 
diffraction limited improves the image significantly because it brings the 
light rays to a focus. The aberrations created by the refractive element 
will be small because of the very small aperture. This is a really easy 
experiment to carry out if you have a close-up lens.

So-called 'Pinhole Lenses' are frequently used in surveillance video cameras 
and the like. These are generally a bit of a misnomer, because they are 
small refractive lenses (often glass in the better ones) of very short focal 
length and wider aperture than a plain pinhole. Typical specs might be an 
f/2 4mm lens or an f/1 2.8 mm lens. They can have focussing mounts - which a 
plain pinhole would not need because it doesn't focus.

For distortion-free images with a pinhole the film should be held on an arc 
with the pinhole at the origin (strictly speaking the film should be held on 
a spherical surface - beginning to look a bit like an eye).

The diffraction-limited resolution is dependent upon the 'focal length' of 
the pinhole. The formula for diffraction limiting can be easily re-written 
to give the pinhole diameter in terms of the 'focal length':

d^2 = 2 * wavelength * focal length

This gives the following lengths (in mm), pinhole sizes (in mm), f stops and 
resolutions (in lppmm) using the wavelength of red light:
28    0.20  f/141  2.5 (eg a Leica body cap with a hole in it)
35    0.22  f/158  2.3
50    0.26  f/189  1.9
75    0.32  f/231  1.5
100   0.37  f/267  1.3
150   0.46  f/327  1.1

Regards,
Malcolm