Mirror Test Data Processing

PROGRAM

SIXTESTS.EXE

RESTRICTIONS

SIXTESTS.EXE is a DOS program, which can be run in a Win95 DOS window.
A coprocessor (80387, 486/DX, or Pentium) is required.
The mirror must be 1 m diameter or smaller.
A maximum of 50 zones.
The program is designed to process data from any of six tests: fixed- or
moving-source Foucault, caustic, or poor-man's caustic.

PURPOSE

SIXTESTS uses a series of test measurements to compute the mirror
profile errors, several mirror evaluation parameters, and the resultant
diffraction pattern.

METHOD

This program merges FOUCAULT.EXE and CAUSTIC.EXE plus processing for the
poor-man's caustic test.  The general theory of these tests is described
in Ref. [1], and more specific information is in Refs. [2] and [3].

USAGE

At the DOS prompt,

sixtests <filename>

where <filename> is the name of an input file described below, including
the path if the file is not in the current directory.
INPUT

The input file structure is:
                                                 Line
Comment line                                      1
Primary and obstruction (if any) diameters, mm    2
Test type (Foucault, Caustic, Poor-man)           3
Source distance (0 for moving source), mm         4
Comment line                                      5
measurements:  y, X(y)[, Y(y) for caustic], mm    6-EOF

The data is free-format with spaces or tabs between items, and integers
may be supplied for decimal data, e.g., the primary diameter can be
either 254 or 254.0.  In lines with required numerical data, the data
must be at the beginning of the line; the rest of the line (after a
space or tab) can be a comment.

OUTPUT

Screen output:  focal length of best-fit parabola; mirror's surface and
wavefront P-V and WRMS, and the Strehl ratio.  After <Enter> is pushed,
a plot of mirror deviations from the best-fit parabola is shown.

ASCII Plot file (MIRROR.GGP):  measurements, interpolated measurements,
measurements for the best-fit parabola, and mirror deviations vs. zone
radii; Airy and PSF brightness, and EER vs. far-field angle.

EXAMPLES

Sample input files are included:
   SPHERE:  moving-source Foucault,
   SPHERE_P:   moving-source poor-man,
   BANERJEE:  fixed-source caustic [4],
   BANER_P:  fixed-source poor-man,

The BANER_P input file is

----------------------------------------
8"f/4 parabola, Banerjee numbers.
200.0             Primary diameter, mm.
poorman
1600 => fixed source.
zone,     X, mm.
17   1600.54
33   1602.04
50   1604.69
67   1608.43
83   1612.96
92   1615.94
----------------------------------------
The screen output from a run (i.e., sixtests baner_p) is

----------------------------------------
8"f/4 parabola, Banerjee numbers.
Fixed-source poor-man

Focal length of best fit parabola = 800.0 mm.

          Surface   Wavefront
               nm   (550 nm)    Goal

      P-V     0.5   1/593.1      < 1/4
     WRMS     0.2   1/1692.3     < 1/13.4
Strehl ratio     -  1.000        > 0.8

Plot file:  MIRROR.GGP.

Hit <Enter> for mirror deviation plot>
-----------------------------------------

REMARKS

Input data:
(1)  The choice between fixed and moving source measurements is
indicated in the fourth input line:  zero source distance for moving
source measurements or the actual mirror vertex to source distance (mm)
for fixed source.  Although it is usual to place the fixed source at the
paraxial radius of curvature, that is not required for this program,
only that the actual distance be indicated, perhaps obtained by a tape
measurement.  The program will output the computed focal length of the
best-fit parabola.
(2)  For each zone, the X measurement is the distance from the mirror
vertex to the source/KE (moving source) or KE (fixed source) along-axis
position.  In the classical caustic test [Ref. 5], the X distance for a
zone is set to a specified distance (to the x-coordinate of the evolute
for the Gaviola moving source test or to the Schroader or Banerjee [Ref.
4] distance for the fixed source).  Again, this is not required for this
data reduction program, the X value can be chosen or measured at will.
(3)  The cross-axis Y measurements are negative if they are on the
opposite side of the optical axis from the zone, as is usual for the
classical caustic test.  If non-standard X values are chosen, the
measured Y values could be plus, minus, or zero.
(4)  The program will complain and halt if the zone radii are not in
order from smallest to largest or if any zone radii are repeated.  If
multiple measurements are made, the data must be preprocessed to present
a single pair of X,Y values for a each zone.
(5)  Measurement interpolation methods used in this program differ from
test to test:  linear interpolation used for the Foucault test, while
quadratic X-interpolation and cubic Y-interpolation is used for the
other two tests.  Essentially, quadratic/cubic interpolation assumes
that the mirror surface between two measurements is parabolic, rather
than whatever results from linear measurement interpolation for
Foucault.  This may explain why results for two tests may differ for
theoretical measurements when they should be the same.  In general, the
Foucault test will be somewhat pessimistic, and the other two tests
optimistic.  For any of the tests, the results are reliable if a
reasonable number of zones are used; in the extreme, any mirror with
only measurements of two zones would be declared excellent using the
caustic or poor-man's without regard to the surface between the zones.
(6)  Also a general caution:  for the same measurement accuracy, caustic
testing is inherently less accurate than Foucault testing; the cross-
axis measurements (Y) should be read to significantly higher precision
than the along-axis Xs.  Since the caustic measurements are easier to
make - no shadow matching - multiple readings, averaging, and more zones
are called for.
(7)  Plot file output (bracketed data for caustic tests):
     (CAP_X[, CAP_Y]):  readings,
     (FIT_X[, FIT_Y]):  interpolated readings,
     (P_CAP_X[, P_CAP_Y]):  corresponding readings for best-fit
      parabola.
     The remainder of the plot file outputs is described in Ref. [2].

REFERENCES
[1] http://www.halcyon.com/burrjaw/atm/atm_math.htm
[2] README.TXT for the FOUCAULT.EXE program, in
ftp://ftp.halcyon.com/pub/users/burrjaw/foucault.zip
[3] README.TXT for the CAUSTIC.EXE program, in
ftp://ftp.halcyon.com/pub/users/burrjaw/caustic.zip
[4] Banerjee et al, "Improving the accuracy of the caustic test", App.
Optics, 37(7), March 1998, p. 1227.
[5] J. Strong, "Concepts of Classical Optics", W.H. Freeman, San
Francisco, 1958, p. 298.

-- Jim Burrows
-- Phone:  206-244-2933
-- Email:  burrjaw@halcyon.com
-- JD2451063 = 1998-09-06
