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Re: [ATM] Faucault testing questions
Mark,
I was talking in general terms. Spherical aberration (conic form) increases
exponentially with the zonal height: with the square longitudinally, with
the cube transversely, and with the fourth power on the wavefront. The
wavefront error is the one that matters in the context of my post.
I was probably more commenting on the "Foucault controversy" with large/fast
mirrors, than implying structural asymmetry of the two opposite side of
defocus
being probable factor in having this particular mirror (neither large nor
fast) significantly under-corrected.
However, I was assuming that Ken's measurements are
averages from both directions. Since he seems to be relying mostly on the
outside-in direction, another structural property of the focusing zone - as
well as a systemic error coming from the setup/procedure, as you imply - may
cause the undercorrection bias.
The structural property of the focusing zone I have in mind is a significant
axial extention of the central bright section with the increase of zonal
hight. This is directly related to the effective c.obstruction of the
aperture that a pair of zonal openings belongs to. As a result, the
extention of the central focused core rises exponentially
according to (1-c^2)^2 for an aberration-free aperture, and approximatelly
as much for an actual overcorrected mirror ("c" is the ratio of the inner
and outer zonal height).
On a typical 5-zone mask, "c" for the most inner zone is
0 (if open to the center) and 0.9 for the outer-most zone. Assuming 0.5a
("a" being the aperture radius) center zone hight, its regular focus depth
will be about four times longer than that of the outer-most zone w/o
obstruction effect. But with c.obstruction effect expanding focus depth of
the most outer zone by a factor of (1-0.9^)^2, or nearly 28 times, the
actual focus depth (i.e. length of the bright central core) for the
most-outer zone will be nearly 14 times greater. The extention factor
diminishes exponentially towards inner zones.
The mean zonal radius in the "geometrical" Foucault nearly coincides with
the middle of this extended bright core. I can't tell for sure - and haven't
heard or read that anyone did - at what point the transverse KE move
produces null effect. To me, it appears logical that zones will null as soon
as the KE begins to block this extended bright central core, which is of
nearly identical width along its entire length. There are speculations that
the null is most convincing when the KE intersects the middle of the core
(location of diffraction focus), but it doesn't seem to be really
substantiated; even if it is so, the difference in null appearance along the
entire core length is likely to be subtle.
Depending on the measurement method, this focus depth extention towards
outer zones may and may not cause systemic measurement error. If the
measurement is done in both directions, and averaged, it will be
effectivelly cancelled. But if the measurement is done in a single
direction, and the radius marked as soon as there was a null appearance, it
would likely induce systemic error towards overcorrection (in the resulting
apparent mirror shape) when measuring only from outside in, and towards
undercorrection when measured only from inside out.
Of course, this all is only a speculation, as long as it remains unknown how
specifically the location of the KE within the actual (diffraction) focal
zone determines
the null appearance. From little that I know, simulation softwares use
significantly thicker KE "model" than what an actual KE is, to
counter-effect diffraction focus extention. Obviuosly, this directly
defeats the purpose of
finding out how an actual null behaves for different KE positions along the
bright focused core. I'd expect that it could be properly simulated, and if
so, it would place this subject out of speculation. It would be good to know
what it really is, and isn't.
Vlad
> vladimir sacek wrote:
>
>>It raises exponentially towards the edge
>>
>
> Don't you mean quadratically?
>
> --
> Mark Holm
> mdholm@telerama.com
>
>
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