Re: [ATM] (Long) How good is good enough? (was how much celldeformation is too much?)

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

At 17:27 25-07-04, Scott Milligan wrote:
>
>
>In the professional literature, the question has received both theoretical
>and empirical attention; however, since professional astronomers are by and
>large unconcerned with visual observation of the scene, the most useful
>results of their analyses have been directed at answering the question "how
>good does my telescope have to be given the fact that I am making a long
>exposure image through a randomly varying phase-amplitude screen? (i.e. the
>atmosphere).
>
>

Scott:

The standard theory of atmospheric turbulence developed by Fried and many 
others has been extended to the case of instantaneous exposures, which is 
more or less what's relevant to visual observers. In fact Fried himself 
wrote a paper titled "Probability of getting a lucky short-exposure image 
through turbulence" (1978, J.O.S.A., vol 68, p.1651-1658) [someone posted a 
copy online at 
<http://www.astrosurf.com/cavadore/optique/turbulence/Probability_of_getting_a_lucky_.pdf>].

Fried defined a "lucky exposure" as one for which the rms atmospheric 
wavefront phase error is less than 1 radian, which falls a bit short of 
what visual observers consider "diffraction limited" - a phase error of a 
radian corresponds to Strehl ~= 0.37. But the theory can be used to predict 
the probability of arbitrary amounts of atmospheric distortion.

I've done some simulations using Noll's (1976, JOSA, vol. 66, p. 207-211) 
calculation of the covariance matrix of Zernikes. Here's an example: the 
Fried parameter r0 in excellent seeing is supposed to be around 25 cm. At 
D/r0 =2 I got a probability rms<=1/(2pi) waves of .984, which agrees with 
Fried's estimate of .986+-.006. The probability rms<=0.075 waves was about 
0.11, which is still significantly greater than zero.

So, on purely theoretical grounds I would predict that in excellent seeing 
you should be able to distinguish excellent from mediocre optics in a 
largish telescope (if you know what you're looking for, etc.).



>
>
>I can start us off by recalling observations I have made through several
>scopes for which I have a pretty good data trail, at least as far as
>describing optical quality on the bench tests goes.  But it is dinner time
>now, and I will only do this if others on this list think it would be of
>value.  Thanks for taking the time to read this.

I for one would be interested in your experiences. I suspect few list 
members have both detailed quantitative information about the optical 
quality of their instruments and quantitative information about seeing 
conditions at their favored observing sites. That may be why you've had no 
responses so far.

Mike Peck


_________________

Michael Peck
email mpeck1@ix.netcom.com
Wildlife photography page http://home.netcom.com/~mpeck1/index.html
Amateur telescope making http://home.netcom.com/~mpeck1/astro/astro.html 

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