(User.programs)
Item: 324 by _nwallace at hpcvbbs.cv.hp.com
Author: [Nelson W. Wallace]
  Subj: Rectangular Geometry Fresnel Diffraction
  Keyw: diffraction, fresnel, optics, light, physical optics
  Date: Mon Sep 02 1991

Rectangular Geometry Fresnel Diffraction

   Chapter 10 of John M.  Stone's book "Radiation and Optics" contains
equations for calculating the irradiance in a Fresnel diffraction pattern at a
normalized lateral distance "s".  Lateral distance is measured in a direction
perpendicular to the light's propagation direction and also perpendicular to
the diffracting edge.  Three cases are treated in the book and are modelled in
this series of HP-48SX programs.  The cases are for the diffraction pattern in
the region irradiated from an aperture in an oqaque screen (GENERAL), for the
irradiated region near an edge (EDGE), and for a narrow obstruction in a beam
(OBSTRUCTION).  The programs take their arguments from stored variables, and
leave their result on the stack.  As a result, the programs can be run alone,
or in conjunction with the program MAIN.  MAIN prompts for the case (geometry)
of interest, and also prompts for values of relevant variables, including the
range of distance over which the Fresnel diffraction function is to be plotted.
Next MAIN plots the intensity versus normalized lateral distance.  The programs
have been verified by accurately reproducing Figures 10-5, 10-6, and 10-8 in
Stone's book.

   The GENERAL and OBSTRUCTION programs must evaluate four Fresnel integrals
for each data point, while EDGE uses two Fresnel integrals, and hence runs
faster.

   Example: Press MAIN, and then press OBSTR.  Type in 0.6 for delta v, then
press the down arrow once in order to position the cursor at the right of
:s0min:.  Type in 0.  for s0min, then press the down arrow again, type in 7.2,
then press the ENTER key.  The calculator display will briefly show
'OBSTRUCTION', which is the name of the program that will be plotted.  Then
MAIN begins to plot the diffraction pattern for a narrow obstruction.  The
program will take about an hour or more to complete, depending on how full your
memory is.  (Fresnel integrals take time.)

   The program XiEQN uses Stone's equation 10-3 to translate from the axial
observation distance (r20 in Stone's book), the lateral distance (x), and the
wavelength (lambda), in units of length, into the normalized lateral distance
"Xi" (as used in Stone's book) which for want of a greek character is "s" in
these HP-48 programs.  "s" is dimensionless.  The incoming light is assumed to
be collimated (r10 very large).  (Do not confuse "s" with "S", the Fresnel sine
integral.)

   The subdirectory takes about 2400 bytes.

   Warning: the MAIN program has given anomalous results when available memory
was below 600 bytes.

   Please report bugs to Nelson Wallace, (818) 703-6496.