<< You are making this much too difficult. Dick Sullivan basically had it
correct. The pinhole image is simply the shadow (or anti-shadow rather)
of the pinhole at a continuum of points across the image plane. Each
point in the image plane is simply illuminated by the light that can be
seen through the pinhole at that position. >>
Al Hazen predicted that 1000 years ago, but Geber hasn't prepared yet the
photo emulsion to confirm the statement.
Seriously calculation of the optimum diameter for pinhole imagery from Al
Hazen, Petzval, Rayleigh, Hardy & Perrin, Wood, Kingslake, Selwin,
Sayanagi, to Keneth Connors and others, is going on Esoterica.
Who cares about the MTF ( modulation transfer function) of a zoom lens ?
Sharpness and resolving power are good for a glass lens isn't it ?
To my point of view the advantage of the pinhole image is the noisy effect
it shares with the film emulsion, after this it's an artist business.
For Pin speck photography or the anti-pinhole photography discovered by
Adam Lloyd Cohen of Loyola University in Chicago, there was an article by
Jearl Walker in the Scientific American Nov. 1981.
For my part I discovered in 1982 the reflected pinhole photography, based
on the use of a micro-mirror, I used several material for that, diamonds
zirconiums etc.,
It's just like the reflection of the image of a pin hole, without a pin
hole but a small reflecting mirror or any plan surface, beware refraction !
Moulay El Ouazzani
http://www.worldnet.fr/~ouazzani
Enjoy