Re: ATM lies, damn lies, and mirror tests

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

Steve,

just to quickly point out few more things that I don't quite
understand about this test. 

> If you think we're talking about actually focusing one of the laser
> beams to an Airy disk, then you are not understanding the test.

Can you explain HOW do you avoid a section of paraboloidal 
mirror (no matter how small, it is still paraboloid!) to focus
incoming parallel light ? It is the same as stopping down your
scope to 1mm. It WILL form an image, believe me.

> I don't think you are seeing what we are talking about. I haven't done
> the math (maybe someone has?) but the difference in the location where
> light comes to a focus using only the central part of a sphere as
> compared to an outer zone of a sphere, given the incoming light is
> parallel and not divergent, ought to be about the same as that same
> difference in a Foucault test when looking at a parabolic surface using
> a diverging light source at the center of curvature.

No. It will be much smaller (the 'math' is BTW in Texerau). The
paraboloidal mirror tested at COC exhibits spherical aberration. A
great one as such. Easily measured by millimeters. Conversly, all
errors of the surface are magnified as well. In fact we can show that
transverse abberations of our mirror tested at COC are 4 times larger
than they are going to be when mirror generates image at focus.  See
Texerau and study the graphs again.

>  One laser
> shines its spot, say, 2" to the left of center. The other laser shines
> its spot 2" exactly diametrically located to the right of center. For
> now, assume the laser beams are 100% parallel and colinear with its
> optical axis when coming into the mirror.

You see, this is the very exact point where we can do some questioning.
'What if not' is the crucial one. And relatively easy to analyse to boot.
It is VERY easy to prove that twisting one laser pointed a microradian 
or two will deflect the beam FAR more than say 1/10 wave bump on the 
mirror.

> These small areas of the
> mirror, over such a small extent, work like little flat mirrors, and
> just reflect the laser beam back, essentially unmodified (ie, no
> "focussing")

The question #1 again. How do you PREVENT paraboloidal section from
focusing incoming parallel light ?

>  Due to the same tremendous optical lever effect
> that makes the Foucault test work, the location of the focal points of
> these two zones should be easily measurable.

I just _have_ to be rude here (I hope you will forgive me, Steve). It
just so plainly shows that you never made or tested a mirror with
Foucault test. Otherwise you'd KNOW how small dimensions we're talking
here. A half wave slope error on the front (enough to make mirror
junkable) will deflect your 'ray' couple of MICRONS at focus. Taking
reflection in account (doubles the error), and leverage (the laser
pointer is say 2 inches long, while 2*focal length is say about 100
inches), you will have to keep back and front of your laser pointer to
within HUNDRED TIMES less than transverse error at focus, while moving
it across.  Now we are talking nanometers. And that's SMALL. In fact so
small that with today's technology we have no means to directly measure
it.

> I can explain how simple techniques can probably be used to achieve the
> required alignment accuracy, if you wish.

But you don't KNOW what 'required alignment accuracy' is. This can only
be done through a careful error analysis (series of 'what if' and 'what
if not', OK it is a bit more complicated than that; in fact there is a
whole branch in Numerical Analysis devoted just to that). Point is,
having Foucault presented 'down to Earth' as it is in amateur
literature DOESN'T mean it hasn't been scrutinized to death by many
opticians and mathematicians in the past. Having it oversimplified and
devoid of math (as often 'presented' in ATM literature) makes it look
like something TOO simple. Well, it isn't. And cannot be. For something
with ambitions to be as exact as testion of optics to a fraction of
wavelength of light (the MOST precise measurement human kind could do
for quite a while !) it requires a MONUMENTAL homework. C'mon guys,
people do PHD thesis on this ! 

> Without a doubt, if I ever build such a devise, I'll report on its
> behaviour right here on this list. And I will quantify that behaviour in
> a scientifically rigorous manner by taking repeated measurements and
> doing statistical analyses.

A 'scientifically rigorous manner' doesn't just include statistical
analysis. It first includes a proof that test is doable, and then 
analizes all possible weakneses and error sources. 

I can't tell you what or what not to do, but a friendly advice is : 
don't waste your time. 

> I'm trying to defend it here. And if a proposed mirror testing scheme is
> not appropriate to be discussed on this list, then what is?

By all means, YES ! Of course that this _is_ the place for such
discussions.  That's what we're doing now, isn't it ? But there is a
big difference between discussion about a new TN tweak and proposing a
fundamentally new testing method. Former can be discussed over a beer
or two, later, as far as I'm concerned, has to be a bit more elaborated
and backed by some serious homework. 

Or maybe I'm just paranoically sensitive, having a bad childhood with
too much math ?

Cheers,
Bratislav