To: atm{at}shore.net, lsayre{at}apk.net
From: mdholm{at}telerama.com
Reply-To: mdholm{at}telerama.com


>Should I be concentrating on lowering the RMS error and ignoring the rise in
>P/V error?  Overall the RMS error did not come down as much each time as
>the P/V error went up.

If the P/V error goes really wacko, it might indicate something is wrong,
but it is very possible for small to moderate changes to have the two going
in opposite directions.  Concentrate on the RMS and use the PV as a sanity
check. What you should see in the case of RMS going down as PV goes up is
that the area affected by the highest peaks and lowest valleys is
decreasing faster than the height of those peaks and valleys.  Not an easy
thing to see off of the deformation plots unless it is a really big effect.
 It really requires an integration to measure.

As several others have pointed out, with good math and physics to back them
up, the PV and RMS measures are only rather loosely linked.  Often they
move in the same direction, but not always.  For big changes they are
likely to move in the same direction, but not always for smaller changes.

David Lewis suggests that a good cell should produce not more than 1/120
wave (approx 4x10^-6 mm) RMS deformation.  If you have an excellent mirror,
you may want to hold the cell induced deformation to a tighter standard,
but there really isn't much point pushing for less than about 1/200 wave. 
These values are very roughly equivalent to 1/20 and 1/40 wave P-V.

With 1/120 wave RMS, is is pretty likely that something else in the optical
system, other than the cell, will introduce a larger error.  With 1/200, it
is a dead certaintly.

Plop tends to locate it's deepest "valley" at the center of the
mirror.  This is especially true when a secondary obstruction is specified,
but then the center of the mirror doesn't enter into the P-V or RMS
calculations.  Even when the mirror is unobstructed, the center is still
likely to end up as the lowest point, partly because of the way mirrors
bend, and partly because the center has less area and thus contributes less
to the RMS error, than zones farther out.  Putting either the max or min
point in the center is probably a "natural" result of minimizing
RMS.  The fact that it is usually the minimun is probably a result of the
way mirrors bend.


Mark Holm
mdholm{at}telerama.com

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