To: ulhas{at}nagpur.dot.net.in, atm{at}shore.net
From: mdholm{at}telerama.com
Reply-To: mdholm{at}telerama.com


Hi Ulhas.

First, do a reality check.  Do Sixtests and FigureXP give the same P-V and
RMS values?  Sixtests doesn't put P-V in a box for you, but it is easy to
figure out.  Look carefully at the graph of residual error for the parabola
(the first of the graphs).  Read off the y value of the highest point and
the lowest.  The lowest will be negative, so the equation is High - Low. 
This is the P-V value in nanometers.  To convert to waves do 550 / P-V(nM).
 This actually gives the denominator of the wave rating.  In other words,
if the wave rating is 1/x, this equation gives you x.

Usually Sixtests and FigureXP should give pretty nearly the same result.  I
don't use FigureXP regularly, so I have forgotten if it produces an RMS
value.  I know it does produce a graph.  The graphs from the two programs
should be rather closely similar.

It is quite possible for the P-V error of a mirror to be fairly large, and
the RMS (thus the Strehl also) be fairly good.  This has been a much
debated topic, but the mathematical answer is that there can be fairly
large differences in RMS and Strehl compared to P-V.  Also, the
mathematical answer is that RMS (and Strehl) is the better number to base
decisions on.

It depends a bit on where the greatest error is at.  If a large part of the
P- V number is coming from near the middle of the mirror, it is safer to
ignore than if it is near the edge.

An edge going off wildly either up or down is a concern both because it
represents more area (and contributes more to the RMS calculation) and
because the extreme edge of a mirror is essentially impossible to measure
accurately with the Foucault test.  Using the quantitative Foucault test,
one always has to extrapolate a bit to estimate what the edge is doing. 
(The programs do this extrapolation automatically.)  If there is
significantly rapid change of curvature near the edge (a strongly tuned
edge, either up or down) the extrapolation can miss estimate the real
curvature.


My Strehl ratio calculator (using the formulas from Jim Burrows web site)
is at http://pong.telerama.com/~mdholm/atm/cells/rmscalc.html It gives a
Strehl ratio of 0.8804 for and RMS of 14.2 nM. Mark Holm
mdholm{at}telerama.com

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