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


Oops, I clicked Send before I was finished.  Here it is again (quoted),
with the rest appended.

Quoting 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 an RMS of 14.2 nM.

It also gives a Strehl ratio of 0.8385 for an RMS of 16.7 nM.

I think I would push to get those Strehl values comfortably over 0.9,
especially if you plan to use this scope at fairly high magnification.  It
is highly unlikely that anything after the primary will improve its image
forming performance.

One of the things my Strehl ratio calculator does is let you estimate the
Strehl ratio for a two mirror system.  A primary RMS of 12.9 nM gives a
Strehl ratio of very nearly 0.90.  If we assume a Cassegrain secondary
(angle = 0) that has the same RMS error, 12.9 nM, (and assume the errors
are uncorrelated) the resultant Strehl is a decent, but not great, 0.86. 
If you take the Primary RMS down to 8 nm, assuming the same secondary RMS
of 12.9 nM, the Strehl climbs to a respectable 0.92.


Mark Holm
mdholm{at}telerama.com

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