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

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

Vladimir,

one last attempt from me to clarify the issues I see here:

The distance grating - center of mirror must be known (to some 
moderate precision - millimeters, not microns). Also, of course the 
Ronchi line spacing must be known (to one or at most a few microns). 
The location of the COC (of a best fit sphere, or the paraxial COC of a 
best fit parabola or other conic of your choice, etc) is the result of 
data reduction after the measurements. Thus, when you suggest as an 
alternative "you need to know the COC (grating) location", it seems 
that you are not aware of this distinction.

>>>It is another subject that the pattern itself, being blurred by 
diffraction, doesn't allow for high measurement precision, the higher 
line density (sensitivity) the more so.

Yes, a point I have repeatedly made, too, is that there is a limit to 
the number of lines/zones on the mirror you can read, and fewer the 
finer spacing of the grid lines. This is no limit to the otherwise 
similar lateral wire test. 

NO> 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,

>>>I don't see where do we disagree. What you call "measuring the 
normal" to a zone, comes directly from determining the zonal focus 
(combined axial focus for a pair of zones with Foucault, single zonal 
focus on the caustic with Gaviola), which is the term I've used. It is 
one same thing.

Again: your previous statement was:
"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. "

I claim there is no difference. In all cases, you decide the normal to 
the zone in question, in order to integrate the zones into an estimate 
of the profile (or deviation from the ideal conic desired).
The position of the zonal center is one point to decide the location 
of the line, so one other point is needed.

In Foucault, a point on the axis is chosen. In Gaviola, another point 
more or less close to the zonal COC is chosen. In the quantitative 
Ronchi method discussed here, the point is the position of the relevant 
line corresponding to the zone seen at the mirror.  The choices of 
points are different, the evaluation is not.

N O


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