Re: ATM Laser Beam Test Spherical Aberration

[Bratislav Curcic <epabcc@epa.ericsson.se>]

Steve,

> ...an in-line Barlow will double the spherical aberration

>  What was I thinking of!! Of course, an f/12 sphere has *less* spherical
> aberration (s.a.) than a f/6 sphere. So much less that a lot of people
> wouldn't even parabolize an f/12 sphere. The results that I get from my
> equations of s.a. = 0.03" for a 12" f/12 sphere and s.a. = 0.06" for a
> 12" f/6 sphere and s.a. = 0.12" for a 12" f/3 sphere are all entirely
> correct. So, if you want to purposefully *increase* the s.a. in some
> test that's trying to measure it, so that the test is more sensitive,
> you put a positive, focal length *reducing* lens in-line, not a
> negative, focal length *extending* Barlow lens.

Uh-oh ... I think you're mixing apples and oranges here. Having
reduced or increased final f-ratio doesn't necessarily mean that
your system will behave as if it was outright faster or slower.
It would take too much to make a proper proof, but those who want
can trust me when I say that reducing final f/ratio (using
positive lens) will **DECREASE** sensitivity of the test. It will
NOT directly double spherical aberration (nor negative - Barlow) 
will reduce it. Have some ray trace program (or do it even on paper)
and you will see that final longitudinal aberration gets SMALLER
when you place positive lens into the incoming beam. But this will
not affect the SPHERICAL aberration of the whole system in simple
predictable manner. 
12" f/6 spherical mirror does NOT have twice the spherical aberration
of the same mirror with focal reducer halving it to f/3. We can
purposefully make a combination of lenses that will reduce final
f/ratio and CANCEL the spherical aberration of spherical primary at the
same time. We can also extend the final f-ratio and again cancel
the spherical aberration altogether (Jones, Bird etc.). Or we can
leave the final f-ratio more or less untouched and (yes you've guessed 
it) again cancel the spherical (Maksutov subaperture corrector).

While here, I'll admit that I finally looked closer into Steve's
proposal for 'null test'. Practical problems aside (as how to get
absolutely parallel movement of lasers and how to reliably measure
longitudinal aberration at focus, and how to test any significant
portion of the mirror), it IS basically 'just another Foucault done at
focus', and it OUGHT to work. Having two beams should aid _greatly_ in
finding the 'focus' of the zone, especially when edge zones are tested.
Whether this makes it sensitive enough to make any meaningful
conclusions about the mirror's quality remains to be seen. I'm guessing
that longitudinal aberration will have be measured reliably about
10 or 20 microns in order to catch surface slope errors that are
measurable using good ol' COC Foucault. "Reliably" means not just being
able to _measure_ this (any better micrometer or dial indicator can do
that), "reliably" means that ALL cumulative errors of the setup are
small enough not to influence this. And this includes beam parallelism
and focusing (un)certainty.  I guess the starting point would be trying
to distinguish between a half wave and 'good' (presumably better that a
quarter wf) mirrors using this test. If they are easily distinguishable
(a casual look thru these two scopes would instantly tell them apart),
you may be onto something.

Good luck,
Bratislav