Zernike coefficients for astigmatism obtained from Bath interferometry
contain astigmatism on the glass, stand induced astigmatism
Bath interferometer induced instrumental astigmatism.
method to separate them was suggested by Dale Eason and is known
as derotation method. His analysis program incorporates this method.
I will here describe variation of this method as I am using it with PSI-Bath
interferometer (Phase Shifting Interferometry). I have already posted first results on two small mirrors
one of 83 mm diameter f/5, 1:3.3 thickness to diameter ratio, and another
one 115 mm diameter f/4.5, 1:6.2 ratio.
The mirrors are small and thick and tested with optical axis vertical so not
much stand deformation was expected.
In the meantime another mirror was obtained, 200 mm, f/4, 1: 8 ratio and
the method was tested on this one.
Mirror was resting on Plop designed 6 point cell. 4 rotations were used.
0, 45, 90 and 135 degrees (approximately, exact values are not required
by the method). Since angular part of astigmatism polynomials is sin(2 theta)
and cos( 2 theta), mirror astigmatism from rotations was oriented 0, 90, 180 and 270 degrees.
For each rotation 10 interferograms phase shifted by 72 degrees, were made.
By using Stephen’s running method and Michael’s 5 phase cycle PSI analysis
program, it was possible to make 6 cycles from 10 shifted interferograms. interferograms 1 to 5, 2 to 6, 3 to 7, 4 to 8, 5 to 9 and 6 to 10
So I have 6 results for each rotation (24 in total).
Analysis program provided Z4 (x-ast) and Z5 (y-ast) components which were
plotted y-ast versus x-ast . Resulting plot is here, and in my Photos folder of
Photos, Vladimir Galogaza.
How did you determine this uncertainty of +- .003 waves?
I have made 6 interferometric measurements for each of four rotations.
That brings total of 24 pairs of Zernike astigmatism coefficients.
Fitting circle to measurements points is kind of averaging and circle
center is averaged results for all 24 points.
Circle radius is averaged mirror astigmatism. Distance from circle
center to each of measurement points is individual result.
The error is maximal deviation of all individual results from mean value
of all individual results.
Michael Peck told me that modified rotation method can also determine higher
order astigmatism . I have tried it with previous measurements and quality of
data was low enough to spoil such determination.
With my latest measurements, secondary astigmatism determination could
be estimated while tertiary failed, as demonstrated in the following three graphs.
(If the graphs are stripped in archives they can be found in my Photos album
Interferometry@yahoogroups.). This is one more demonstration of the superiority of the PSI-Bath (Phase Shift Bath Interferometry) data quality (IMO).
Recent upgrade as of March 2015.
Michael Peck upgraded his PSI analysis programs with option for elimination of instrumental aberrations like stand induced astigmatism, trefoil and higher. Mirror rotation angles should be known and used as input data together with interferograms and maximum order of aberrations to be handled.