baff
	A program for computing the location and size of baffles
  within a length of tubing.

  Given a length of tubing with entry and exit apertures (e.g. the
  last lens and the image surface), compute the location and size of
  baffles that will put the entire tube wall in the shadow of one of
  the openings.  The basic premise is similar to that given in
  Rutten and van Venrooij ("Telescope Optics -- Evaluation and
  Design", Willman-Bell, Inc., 1988) chapter 19.2.  However, the
  starting point for this algorithm is the reflectance point for the
  extreme rays from the openings.  Baffle locations on either side of
  that are computed iteratively.

  Within the algorithm, allowance is made for baffle aperture
  tolerances and some shadow overlap.  The baffle opening tolerances
  are expressed in terms -0,+tolerance; the aperture is not allowed
  to be smaller, but may be as larger by the tolerance.  The original
  algorithm seems to depict that the the shadows just touch at the
  tube wall.  This may provide minimal coverage, but does not allow
  for errors.  This modified algorithm allows the shadows to overlap
  by a given amount, allowing some tolerance on the positioning of
  the baffles within the tube.

  This program is written to be executed in a Unix/Linux environment.
  However, modification, specifically with respect to input arguments,
  is possible.  The invocation is:

     baff [options]

  where the options are:

	-d tube_diam
	   The interior diameter of the tube.
	-l tube_leng
	   The separation of the entry and exit apertures.  Any
	   sagittas should be subtracted out.
	-e entry_semidiameter
	   The semidiameter of the entry aperture.
	-x exit_radius
	   The semidiameter of the exit aperture.
	-s shadow_overlap
	   The amount of overlap of the shadows from the entry and
	   exit apertures.
	-b baffle_tolerance
	   The tolerance allowed for the baffle aperture semidiameter.

 All dimensional inputs are floating point numbers.  Dimensions here
 are irrelevant, but must be consistently used.

 The output is a simple table of the baffle separations, positions,
 and semidiameters, proceeding from the entry to the exit.  In addition,
 the amount of extra shadow from the first and last baffles is given.
 This is the amount that the first or last shadow would extend beyond
 the end of the tube.