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How to accurately measure a 200-mm primary
mirror in an assembled Cassegrain telescope
(Left) The data as measured. (Center) The data following island leveling. (Right)
The data with Zernike terms removed to reveal the underlying shape, including the
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algorithm fills in missing data by carrying the local slopes across the obscured
structure, such as spider legs:
The slope is determined by calculating
the derivative of the surface figure in
both X and Y directions.
Slope data are filled in across the
masked region to achieve continuous
The X and Y slope data are integrated
to recover the corrected surface.
From the corrected surface data, the
software determines the piston difference between islands.
These height differences are rounded
to the nearest one-half wave.
The piston of each island is adjusted
to create a continuous surface.
Piston, tilt, power and other aberrations can be removed from the
entire dataset. In some cases, removing these terms before leveling the
islands improves the process. In other
situations, particularly when the test
mirror has large aberrations, islands
are leveled first and then higher-order
aberration terms are removed.
The figure above shows the results
of following these steps when measuring a 200-mm primary mirror in an
assembled Cassegrain telescope. The
left image shows the data as measured,
with ambiguous half-wave steps. The
center image shows the result of using
the bridging method to level the islands.
In the image on the right, the first
35 annular Zernike terms have been
removed from the data, revealing the
residual surface shape. In this example,
polishing marks are clearly visible in
the final data, producing a result that is
useful for the engineering and manufacturing team.
When one is taking averaged measurements, an additional processing step is
required. In each measurement to be
averaged, the unwrapping algorithms
will attempt to force the data islands
up or down to half-wave multiples. For
one measurement, island A might be
higher than island B, but in the next,
island B may be higher than A. This can
result in phase differences between the
Although this ambiguity cannot be
resolved, the height of each island can be
made consistent across all measurements
within the average. Therefore, the island
height in the final average may be offset
by one-half wave due to this fundamental ambiguity. However, there will be
no fractional steps between islands, so
processing can continue.
Mike Zecchino (Mike.Zecchino@4DTechnology.
com) is an applications engineer with 4D Technology.