Re: [ATM] Calculate Astigmatism

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

At 16:37 23-03-04 -0800, Jim Burrows wrote:
>At 2004-03-23 17:11 -0500, Douglas S Angle wrote:
>
>>I thought my question in 2000 was essentially the same as Robert's last
>>week.  But "0.1mm" is a far cry from "almost to the nanometer".  I still
>
>Geeze, 2000 was very early in my term of office, it's all the fault of the 
>last guy <g>.  I ignored Mike Peck saying primary astigmatism was the real 
>threat <another g>.  Anyway, the required

I don't think I deserve any credit for that insight. What I remember having 
some conversations about was this part:

>accuracy dR in the radii of curvature on two diameters to achieve the 
>accuracy dRMS from primary astigmatism is 2*sqrt(6)*(R/r)²*dRMS, with r 
>the mirror semi-diameter.  To get dRMS to 5 nm (20 nm is a passing mirror) 
>for Texereau's standard 8"f/6, dR = 2*sqrt(6)*24²*5E-6 = .014 mm.  Oh 
>well, R to the micron instead of nanometer - you still can't turn the 
>mirror to that

Let's cut ourselves some slack and multiply that by a factor of 4. So to 
measure primary astigmatism to even maximal tolerance we'd have to measure 
radius of curvature differences to ~0.05mm. That might not be so difficult 
*if* you measure two or more diameters without disturbing your apparatus. 
But when you do a zonal test on a single diameter, rotate your mirror, then 
fiddle the tester to relocate the light cone you're almost certainly 
throwing away the ability to make differential measurements to the required 
accuracy.

I think Dave Rowe made a couple of pretty good posts on precisely this 
subject on the Yahoo group ATM_Free last week. Alas for the innumerate 
among us, he used pretty much the same scary math as Jim.

This seems to be an ongoing source of confusion for ATM's and even some 
pros. I suspect it's because people don't (or can't) work through the 
arithmetic, and don't quite understand the distinction between primary and 
higher order astigmatism.

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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