Re: [ATM] Quantifying visual seeing error

[Michael Peck <mpeck1@ix.netcom.com>]

At 13:29 10/2/05, vladimir wrote:

>w~0.1(D/r0)^(5/6)
>
>However, according to Mahajan, this (random aberration)
>RMS error has different relation to the (random aberration)
>Strehl. For instance, while the conventional relationship
>implies 0.37 Strehl for (D/r0)=1 (w/0.16 long exposure RMS error),
>the exact Strehl value is 0.445. The random

I think this relates to something I posted about a few months ago, 
namely that Mahajan's approximation to the Strehl ratio errs on the 
pessimistic side for moderate RMS wavefront errors (the post is 
archived at <http://astro.umsystem.edu/atm/ARCHIVES/AUG05/msg00158.html>).

This has to be a statistical relationship too, since wavefronts are 
varying randomly with randomly varying total RMS error. I just tried 
generating 100 random wavefronts according to a Kolmogorov turbulence 
model with D/r0 = 1 and in fact the mean Strehl ratio was 0.442, but 
with standard deviation of 0.26. Most of that variance is due to the 
total RMS wavefront error's variance.

Anyway, I don't see how this theoretical statistical relationship 
helps visual observers, since we don't have any direct way to 
estimate Fried parameters, RMS wavefront errors, or Strehl ratios. 
Now if you could measure one of those quantities, an interesting 
experiment would be to relate those to an empirical seeing scale like 
Pickering's. I suppose for those of us who lack the means or 
motivation to go out and collect actual data simulations a la Suiter 
could be a useful substitute. Suiter didn't have the computational 
power to do accurate simulations of Kolmogorov turbulence, which is 
probably why his results differed from Mahajan's. That's not a 
problem today, although it still takes a lot of CPU cycles to produce 
a convincing looking movie of a simulated turbulent atmosphere.

Mike



_________________

Michael Peck
email mpeck1@ix.netcom.com
Wildlife photoblog! http://wildlife-pix.com
Amateur telescope making http://home.earthlink.net/~mlpeck54/astro/astro.html 

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