Re: [ATM] [atm_free] RE: data and musings on thin mirror

[Nils Olof Carlin <nilsolof.carlin@telia.com>]

I wrote:
>
> You need to know the distance grating to mirror vertex of course but
> not to extreme precision. Then, like any other zonal test, you know 
the
> zonal location on the mirror, and you know the relative position of 
the
> normal at a point near the COC - as you do with e.g the Gaviola 
test,
> and from that information you can do some integration
> and come up with a best fit curve of some kind (parabola,
> ellipse/hyperble) without knowing the ecact location of the paraxial
> COC - if any.

Vladimir asked:

Well, Nils, which is it: (1) you need to know the COC (grating) 
location
"but not to extreme precision", or (2) you don't need to know it at 
all?

I reply:  I repeat my original statement that what you need to know is 
the distance grating - mirror (as well as the line separation of 
course). The position of the best-fit (paraxial) COC (relative to the 
position of the grating) is computed from the subsequent measurement 
data.

Vladimir again: 

Gaviola test is different, because it's based on direct measuerement 
of
zonal foci, from which the local (zonal) radius is derived. In other 
words,
it gives you two reference points - zonal ceneter and focus - 
determining 
the radius. Then you use the zonal data to piece together a surface 
profile approximation.

I disagree: in all these tests (the poor man's caustic is an 
exception) you know the zonal position and measure the normal to this 
zone with high precision at some point near the COC. In Foucault, you 
measure it on the axis, with Gaviola, near the computed focus (or COC) 
of the particular zone, for somewhat greater precision, and with a 
grating or moving wire, at some arbitrary plane near the COC. In 
traditional Hartmann, I believe, you use measurements at two separate 
planes, both near the COC, but what you get is still the coordinates of 
lines.

Once you know the coordinates for the zonal normals, the math 
evaluation is identical - see SIXTESTS for Caustic.

Vladimir: With Ronchi pattern alone, you only have a zone at the 
mirror
and corresponding zonal deformation at the grating pattern. If you 
don't
know grating  location (or aberration), you can't do any meaningful 
projection
to determine zonal radius/focus- you simply do not have a fixed second
reference point to connect with the zone at the mirror.

 If we don't know the location, the only way to determine the 
aberration is 
to
compare - mathematically or visually (measurement) - actual pattern to 
a
model pattern obtained from *known* location/aberration figures.
When they nearly coincide, we simply attribute the model pattern 
aberration
to the actual pattern. In fact, determining surface properties this 
way does
require known both pattern location and aberration.

I: I guess if visual pattern matching is what you want to do, you need 
to do this at at least two grating positions with known separation - at 
least I recall so from earlier threads. 

But that is something else than what I have discussed above.

Nils Olof
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