Patrick Powers wrote:
> It is simply the pin hole camera effect again. Light passing through any
> small aperture is focused . As the hole's size is changed the focusing
> parameters are changed too. So with a fixed distance from hole to plate
> there will be one size that works. A different size would be needed for
> different image distances.
The pinhole doesn't really do any focussing. It allows a small beam of
light from a point on the subject to travel to the image. The fact that
the pinhole is small allows small areas of the subject to be sampled
and therefore produce a reasonable copy of the subject, without mixing
different points on the subject too much.
However, the light doesn't pass through the pinhole, or any aperture,
without being affected by diffraction, which causes the image of a point
source to turn into a diffraction pattern consisting of a central disk
surrounded by alternating dark and bright rings.
For a circular aperture, the linear size of the diffraction disk is
determined by the size of the aperture, the distance to the image,
and the wavelength of light involved. One common theory says that the
smallest image is produced when the diffraction disk is the same size
as the pinhole.
The linear diameter of the diffraction spot (Airy disk) produced by
a pinhole of a given diameter is:
spot = (2.44 * wavelength * focal_length) / diameter
The optimal size is where spot = diameter, so:
diameter * diameter = (2.44 * wavelength * focal_length)
diameter = sqrt (2.44 * wavelength * focal_length)
An example of a pinhole for a distance of 100 mm and a wavelength of
550 nm is:
diameter = sqrt (2.44 * .000550 * 100) = sqrt (.01342) = .366 mm
The zone plate does have a focussing effect due to the interference
between the light coming from the various zones. For an explanation
see:
http://www.freeyellow.com/members6/glsmyth/zone_Plate.htm
http://www.stanford.edu/~cpatton/pinhole.html
