Re: SCT Primary Mirror and Wavefront Aberrations

From: Vladimir Sacek (vladis.2_at_juno.com)
Date: 07/10/04 

Date: 10 Jul 2004 06:45:39 -0700

"matt" <mariusrf@bellsouth.net> wrote in message news:<ysxHc.31109$9t6.28370@bignews3.bellsouth.net>...

>I don't see how the corrector plate could in any way
> influence the primary mirror wavefront errors other than SA . My original
> question, regarding overall errors, was referring to the OTHER
> manufacturing errors , not to SA which in theory is compensated for by the
> corrector and aspheric secondary . Say the primary is not that spheric , due
> to its manufacturing , deviating from spheric by x . Say the primary also
> has a certain amount of peaks and valleys with a certain RMS or P-V value .
> How does the scope overall aberrations change , in a quantitative way , that
> was the sense of my question .

Surface roughness on any optical surface will cause corrresponding
wavefront deformation. If it only originates from a single surface,
surface(s) that follow it will simply transmit it as it is to the
final wavefront. If more than one surface contribute roughness of
unknown interferometric profile, the resulting statistical (probable)
error is found as the square root of the sum of RMS roughness errors
on each surface squared.

With aperture stop at the corrector, its only aberration contribution
is spherical aberration. However, if corrector's surfaces are not
rotationally symmetrical, or if it is decentered/tilted, it also will
induce astigmatism and/or coma.

If the primary has a figure error, it will introduce spherical
aberration, coma and astigmatism, because different figure has
appropriate different aberration coefficients, and the sum of the
coefficients for the system also changes. Primary's aberration for
spherical aberration is S=(K+1)/4R^3, with K=primary conic, and
R=primary's r.o.c.

Assuming that the SCT design calls for, say, 8" f/2 spherical primary
(K=0, R=32"), and it is actually a mild ellipsoid with K=-0.05, all
the aberration coefficients for the primary will change to some
degree. Both astigmatism and coma coefficients will be only slightly
affected. The s.a. aberration coefficient will change from 1/4R^3 to
0.95/4R^3, which will result in the system s.a. coefficient going from
zero to S=0.05/4R^3, or 0.00000038 for R in inches. This determines
system's transverse spherical aberration (blur diameter at the
paraxial focus) as SFD^4 (F=system's F#), which comes to 0.0156", or
0.4mm.

With the paraxial blur being nearly 30 times the Airy disc diameter
(F/745 in mm for 550nm wavelength), the s.a. induced by this figure
deviation is 1.1 wave
(paraxial blur for 1/4 wave s.a. is 6.6 times the Airy disc diameter,
and changes in proportion to the aberration). This is still only a
half of the surface error at the edge of primary (given by
KD/1024F^3), which is characteristic for spherical aberration induced
by conic deviations (pure figure error).

>From the primary mirror coefficient, it is obvious that even a system
with perfectly spherical primary can have primary-originated s.a. if
primary's r.o.c. differes from the design.

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