Re: [ATM] Astigmatism need fixing? And how to do so?

["vladimir sacek" <vlad@copper.net>]

J Killea wrote:

> Along the better axis, I am at 21nm PV (surface), and along the other 
> axis, PV= 45nm.  Also of concern is that along the poorer axis, b 
> = -0.761, versus -0.941 on the better axis. ...  Do these measurements 
> indicate significant astigmatism?
> y, mm X, mm
> 18.263 6.1271
> 50.698 6.7615
> 74.790 7.3565
> 86.512 7.5660
> 94.759 7.8562

> y, mm X, mm
> 18.263 6.5881
> 50.698 6.9412
> 74.790 7.3254
> 86.512 7.6416
> 94.759 7.8829

> y, mm X, mm
> 18.263 6.3576
> 50.698 6.8513
> 74.790 7.3409
> 86.512 7.6038
> 94.759 7.8696

It may be superficial, but it appears as if reading differences increase 
towards inner zones. In othet words, that surface accuracy of the outer 
portion of the mirror is better than that of the inner portion. Interesting 
question is what causes different zonal readings. Since they are determined 
by -Kh^2/R (moving source), with K being the conic along the radius, "h" the 
zonal height and R the paraxial r.o.c., it can be either from the radial 
variation of  r.o.c. or conic constant, or both combined. If it is r.o.c. 
variation alone, it is astigmatism; if it is conic variation alone, it is 
spherical aberration that varies radially; if it is both, it is combined 
effect of both aberrations.

The difference would be that in the case of astigmatism the rms surface 
error doubles in the wavefront, while in the case of pure spherical 
aberration surface rms halves in the wavefront. In other words, tolerable 
RMS surface error should be smaller for astigmatism (radial r.o.c. 
variation) than spherical aberration (radial conic variation), as long as 
the latter would benefit from refocusing. It would be more complicated for 
two of them combined, and likely beyond the reach of Foucault test 
procedures.

Vlad


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