Fw: [ATM] Another automated Foucault success

["Vladimir Galogaza" <vladimir.galogaza@zg.htnet.hr>]

In his post Michael Peck compares Foucault test with interferometric
on the same mirror
http://home.netcom.com/~mpeck1/astro/temppix/sacoeff.png

 He wrote:
"I was going to offer a long winded explanation of what the coefficient values
and
error bars mean, but I'll pass for now. If you care feel free to ask."

I felt free, asked and got the answer as follows ( with permission of author).

> Anyway, the Foucault results are from a "modal"
> (http://home.netcom.com/~mpeck1/astro/modal/modal.pdf) fit to the raw test
> data. I fit 4th through 12th order spherical aberration terms to the data
> -- that corresponds to Z8, Z15, Z24, Z35 and Z36 in the "Quickfringe" set
> of Zernikes. The error bars are +- 1 sigma as reported by the lm() output in
R.
>
> The points plotted for the interferometric results were averages of 10
> interferograms, with the error bars being the calculated standard
> deviations of the mean values (aka "standard errors"). The interferometry
> output was scaled to rms contributions to surface errors, measured in
> nanometers.
>
> It looks like three out of 5 of the plotted pairs of error bars overlap at
> the 1 sigma level. Since +- 1 sigma is approximately a 68% confidence limit
> that's about what you'd expect from normal statistical variation.
>
> Physically the test results say this mirror is significantly
> undercorrected, with a measurable but optically not too significant amount
> of what Suiter calls "higher-order spherical aberration." Both Foucault and
> interferometry agree that there are no higher order zonal defects of any
> significance.
>
> The things I found interesting about this exercise were:
>
> 1) I wrote up the Foucault results 4 years ago and expanded on the analysis
> a couple years later, so the Foucault results constitute a genuine -
> successful - prediction.
>
> 2) My analysis of how to extract statistical uncertainties from test
> results actually appears to give meaningful results.
>
> 3) Foucault was too optimistic about the quality of the mirror because
> asymmetric aberrations weren't measured. This is more or less consistent
> with conventional wisdom. It still did a good job measuring what it should
> measure, namely the average radial surface error profile.
> Michael Peck
> mpeck1@ix.netcom.com




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