Re: [ATM] Quantifying visual seeing error

["vladimir" <svla@isp.com>]

Michael Peck wrote:

> 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 

According to Mahajan (Aberation theory made simple,
p80, or Optical imaging and aberrations 2, p103) this
approximation underestimates Strehl for (unbalanced)
coma and astigmatism, and overestimates it for the
rest of them (spherical, balanced spherical, balanced
coma and balanced astigmatism; term "balanced" means
shifted - either axially or radially from paraxial focus - to the point of 
best focus). For the 0.16 RMS error level, the exact Stehl (reading off 
the graph) is 0.39 for astigmatism, slightly less for coma, 0.36 for 
balanced astigmatism, 0.34 for spherical and balanced spherical, 
and slightly less for balanced coma. The approximation puts it at 0.38. 
This doesn't seem to be explaining the 
0.445 "seeing" Strehl for the same nominal RMS error.

> 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. 

Don't know how close Suiter is, but wouldn't expect him
to be far from the exact values. Still think that Pickering's 
scale could be related - very approximately, but that's still
better than nothing - to the Fried parameter (r0). The 
instantaneous blur radius is approximated by Lambda/r0,
and that is close to what the eye sees size-wise. If (1)
on the scale has blur diameter 6 times the Airy disc's,
that implies (D/r0)~6. For (3) on the scale, the blur is
half as large, and so is the approx. r0. It is less obvious 
what the dinamics is for the upper part of the scale, but
some resonable path can be followed. I went through
it again, and came up with somewhat better visual seeing
error approximation of w~0.08(D/r0)^(5/6). That would
put (D/r0)~1 as a level of both "diffraction limited resolution" 
(Lambda/D) and "diffraction limited" visual (0.80 Strehl).

Still, the theory seems to make seeing harsher on optical quality 
than what it appears to me. With r0~2.2 inch in a
typical 2 arcsec seeing, everything bigger than 60mm
in aperture would be - on average - less than diffraction
limited due to seeing alone (low 8 and worse on the scale). 
Maybe I just need to straighten out some (mis)conceptions.

Vlad

I 
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