Re: [ATM] The zonal Foucault test is free of inherent correction bias

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

Ken Lowther wrote:
>
> Quoting Michael Peck <mpeck1@ix.netcom.com>:
>
>> This is being crossposted to both the ATM list and ATM_FREE. For the 
>> benefit of those on the atm list who haven't followed recent threads on 
>> ATM_FREE, a hypothesis has been advanced that zonal Foucault tests are 
>> biased towards undercorrection, at least for relatively large, fast 
>> mirrors.
>
> Isn't this why we tried the 'round robin'?  I can see differences by f 
> ratio, but why would size matter?

Giveen f-ratio, the amount of spherical aberration of a paraboloid at r.o.c. 
increases with the diameter. It also increases with the cube of f-ratio. 
Consequently, fast large mirrors have highest "doze" of spherical 
aberration.

Presence of spherical aberration does affect form of the diffraction focal 
zone of the most outer zones. While zonal separation itself results in 
significant decrease in defocusing sensitivity (picturesquely, extends the 
central, bright core of the focused image axially), presence of spherical 
aberration results in asymmetry of the core intensity distribution within 
the defocused zones immediately adjoining  the extended central bright core.
The central bright core does extend - potentially significantly - into 
defocused zone away from mirror, while disintegrating almost immediately in 
the defocused zone toward a mirror. Since the amount of zonal spherical 
aberration increases with the fourth power of zonal height
(for constant zonal width), a purely logical implication is that this zonal 
defocus asymmetry could result in a radii measurement bias.

Mike's results indicate no bias, but it is only directly applicable to the 
simulation itself. The manner in which the radii are measured and averaged 
up can play a role and, also, axial thickness of the KE relative to the 
physical dimensions of the diffraction form in the focusing zone.
Speculation can only go so far. It would probably take a series of 
appropriate simulations, or actual measurementso to determine whether there 
is a bias, or not. Better yet, both combined.

If the bias is there, physical asymmetry of the diffraction form at the 
focal zone could be a factor.

Vlad





_______________________________________________
ATM mailing list http://www.atmlist.net/