> To understand how a pin hole works (and if mathematics comes easy),
> start with Huygens' Principle, then get into Fresnel's Extension.
> Basicaly, Huygens stated that every point of a wavefront acts as a point
> source becomeing a source of secondary wavelets. Fresnel, more than a
> hundred years later, assumed that the secondary waves interfered with
> each other according to the principal of superposition. This
> interference results in the effect of causing a "focus" of an "image" of
> the source of the light ("subject"). Any good optics textbook should
> explain the math. The best way to investigate the details of pin hole
> properties is with math. Have fun.
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. That is also why making the
hole smaller increases the resolution. (Until the diffraction limit is
reached of course.) The smaller hole casts a smaller point of light on the
plane. It is also the reason why you can use larger pinholes with longer
focal lengths.
Since you don't actually focus the hole, the usual concept of depth of
field doesn't apply, and since the light rays are not bent or otherwise
distorted by a lens there is no linear distortion.
The most concise treatment of pinhole physics I've yet read was written by
one of my colleagues here at NIST. The article is:
Young, Matt, The Pinhole Camera, The Physics Teacher, December 1989
I can send you a copy if you'd like.
Now, has anyone tried building the opposite of a pinhole camera? You
should be able to get an image from the shadow cast by a pin speck. The
physics is the same.
- Wayde
(wallen@boulder.nist.gov)