Re: [ATM] RE: [atm_free] The zonal Foucault test is freeofinherentcorrection bias - some supporting graphs

["vladimir sacek" <vlad@copper.net>]

Ken Lowther wrote:

> The shade of gray is not the only thing that I judge.  Nudging the tester 
> you can determine if the two sides 'wink' the same.  <

Certainly have similarities with a little trick that helps see better very 
faint nebulas and stars. Image movement can sharpen eye perception, as long 
as rodes are concerned, and they likely have a say in informing the brain 
about Foucault zonal openings. Maybe it should be incorporated as a technic 
enhancement to the test?

I read and re-read Linfoot's article that Mike posted  (link) to the list. 
While its mathematical description of the "diffraction Foucault" should be 
appropriate, and is definitely necessary for precise calculations, I find it 
somewhat abstract. Thinking about a simple verbal description helped me to 
overcome my long fixation to physical properties of the intensity 
distribution within the focusing zone at mirror's r.o.c. (no wonder Mark 
felt I was talking "geometry").

I think that what we really see during Foucault testing can
be described with a simple expansion of the classical geometric "picture", 
by incorporating in it the simplest
diffraction model, based on Huygens-Fresnel principle.
The principle says, basically, that every point on the wavefront emits 
secondary wavelets; alternatively, every point on any "main" ray (those 
converging towards focal point) emits secondary "raylets" in all directions. 
It is interference of these secondary wavelets (or raylets) in the focal 
zone that actually causes formation of diffraction pattern.

The pinhole, or a slit, sending light to the mirror, fills the two zonal 
openings with point sources of light. A pair of zonal opening act pretty 
much as a double slit at a converging beam, producing diffraction pattern at 
the r.o.c. This pattern consists of a bright vertical diffraction core 
(orientation identical to that of zonal openings) and successively fainter 
bright lines on its sides (the shape of which is likely somewhat curved, due 
to the shape of zonal openings).

However, the eye placed closely behind the focusing zone at r.o.c. doesn't 
see this pattern: it is too close for the eye to focus on it, and it 
probably wouldn't see it anyway w/o some sort of projection screen. What the 
eye sees are directly zonal openings, that is, point sources of light at 
mirror's surface. Every such point emits raylets in all directions. A tiny 
fraction of them reaches the eye lens after passing through the focusing 
zone at the r.o.c., and gets focused onto the retina. The only diffraction 
that matters takes place in this image of a zonal point source at the 
retina.

A pair of zones is nulled when the KE intercepts light at the middle of 
zonal focus range. The nulled zones are gray, and not dark, because some 
wavelets from them are still making it aside the KE and to the eye. The 
inverse shading results from the KE being blocking the wavelents from the 
two opposing zones in a different manner. Moving the KE out of this balanced 
position results in it blocking more of the wavelets from one zonal opening, 
and letting more through from the other one, resulting in brightness 
difference. The greater longitudinal aberration, the more of the KE movement 
it takes to produce perceptible zonal imbalance.

This may be where the significance of longitudinal aberration comes in. It 
is greatest for the central and edge zones, and increases with mirror 
diameter and F#. It would make it harder to pinpoint zonal radius for both, 
innermost and outermost zones, and the larger/faster mirror, the more so. 
However, I don't see, at this point,
what could cause reading bias toward either over- or under-correction.

Vlad



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