To: atm{at}shore.net
From: Jim Burrows 
Reply-To: Jim Burrows 


At 12:11 2003-04-01 +0200, Vladimir Galogaza wrote:

>Reading this and subsequent discussion I wonder if, taking into account
>statistical nature of surface error  numbers ( Strehl, RMS, PV)
>these are linearly additive for two or more subsequent mirrors or some other
>relationship has to be used to determine  final   error resulting from
>individual errors.

If x and y are uncorrelated random errors, then statistics says variance(x
+ y)= variance(x)+variance(y).  So if the errors are uncorrelated,
RMSı(system) = RMSı(primary)+RMSı(secondary).  BTW, PV isn't statistical
and would be nearly impossible to evaluate for multiple-mirror systems. 
The RMS result is for straight-on systems like casses.  For diagonals,
hmm...

At 09:37 2003-04-01 -0800, Tim Rickard wrote:

>Also, multiply diagonal error by a coefficient of 1.41 if at a 45 degree
>angle.

I think you should divide by 1.41!  Draw a square with side s and diagonal
d, d=sqrt(2)s, and suppose d represents the (perpendicular) surface error,
then, as usual, the wavefront error straight in and out is 2d, but the
wavefront error in and out at 45 deg would be 2s (smaller!).

         -- Jim Burrows
         -- mailto://burrjaw{at}earthlink.net
         -- http://home.earthlink.net/~burrjaw
         -- Seattle N47.4723 W122.3662 (WGS84)

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