[ATM] Re: Weird Foucault readings

[Vladimir Sacek <vladis.2@juno.com>]

Even putting aside thermal/setup differences, it is still hard to have
Foucault zonal readings confirmed in follow-up tests for larger fast
mirrors. The reason for this is that parabolic mirror has significant
spherical aberration at c.o.c. (same as a sphere of identical
diameter/radius would have at infinity focus, only of opposite sign). As
a consequence, no Couder zone has rays forming a common focus; rays from
the top of the zone focus farther away than rays from the zone bottom.
Best focus is at the midway between the two, because the ray
concentration there is highest. 

A 16" f/4.5 mirror at c.o.c is 3.9 waves over-corrected. Its longitudinal
aberration is 11.1mm, which means that longitudinal aberration of, say,
90-100% zone is 2.11mm. In order to determine mean radius for that zone,
one needs to find the best focus - which is exactly in the middle of this
2.11mm section - just by looking at the change in illumination of the
zonal openings as  the KE intercepts light along this section. Some form
of zonal null will show at nearly half of the 2.11mm section, around and
in between the circle of least confusion and the best focus. But at what
location the zone null becomes most obvious? It should be at the location
of best focus, since the most intense, central part of the blur here is
about 2/3 the size of the circle of least confusion, but the visual
difference is rather subtle. The question is, how accurately location of
the best focus can be determined, or what level of error is inevitable
due to eye/brain limitations?

Suppose the parabola is perfect, but the null for 90-100% zone is
measured not at the best focus - where it is supposed to be - but at the
midway between best focus and circle of least confusion. In this case,
that would result in 0.26mm reading error. Let's assume, for the sake of
illustration, that all other zonal readings are correct; after reduction
it would indicate worse than 1/4 wave wavefront error for this zone.

One thing that might work better is having a light-meter instead of KE.
It would be used to determine location of peak intensity for each zone.
This location would coincide with the zone's best focus.  A perfect
parabola has determined best  zonal foci location, just as it has
determined zonal radii, and the rest of procedure would be similar to
Foucault's. Main difference would be that reading precision would depend
on meter's precision, not a subjective individual interpretation.

Accuracy in determining best foci locations would directly determine
accuracy of determining appropriate "zonal" conics and surface error.
Assuming that the intensity drop in the focal area of each zone is
similar to that for a "standard" (full aperture) spherical aberration, a
1/4 wave p-v wavefront accuracy with 16" f/4.5 mirror would require about
0.3% light-meter sensitivity, while 1/8 wave p-v accuracy would reguire
about 0.07% meter sensitivity. For an 8" f/6 mirror, same meter
sensitivity levels should allow for nearly five times better accuracy:
1/20 wave and 1/40 wave wavefront, respectively.

Of course, this is only on paper. In practice, it is to expect problems,
as usual. Still, at the first sight, it appears worth consideration.

Vlad


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