Re: [ATM] Re: [atm_free] The zonal Foucault test is free ofinherent correction bias - some supporting graphs

[Michael Peck <mpeck1@ix.netcom.com>]

At 03:08 AM 3/13/2005, Nils Olof Carlin wrote:

>I think that the actual kind of test should be better defined in the
>discussion. "Foucault" has been sometimes used to mean just about any test
>with KE on axis (not by you!). "Couder" can mean masked testing with
>apertures of unspecified width - with the apertures not under test open or
>closed.

Nils:

What would you propose as definitions?

I'd say the two defining attributes of a Foucault test are a) the use of a 
knife edge as a spatial filter; and b) the measurement of longitudinal 
aberration. I wouldn't consider details of mask construction or even the 
use of a mask to be critical to the definition. I also wouldn't consider 
direct (fix zone radius, measure f) or inverse (fix f, measure zone radius) 
measurement of longitudinal aberration to be critical to the definition.

I'd call a Couder mask one in which the zone widths are chosen to represent 
more or less equal areas on the mirror. Again, number of zones and details 
of mask construction aren't critical to the definition.


>Linfoot, it seems to me, gives little consideration to the optimum width of
>the zone (WRT the dimensions of a near-paraboloid mirror). with a zonal
>illumination like fig.8, it should be relatively easy to compare
>illuminations - fig. 9 shows a very much less favorable light distribution,
>due to a too wide zone (this is the situation I try to avoid in my zone
>calculator).

I got up early enough to do one more round of simulations this morning. The 
only changes I made were to use virtual "Couder" masks, still with a single 
pair of openings for each mask. I also calculated effective zone radii 
using all three formulas in common use, namely median, rms, and Nils' formula.

Real quick summary: the results were the same as before, with only trivial 
estimated departures from the input perfect mirror. Nils' formula worked 
the best overall, with an estimated RMS of only 0.4nm on the surface and a 
tiny amount of overcorrection. For the other two estimated RMS increased to 
about 1nm. This is all basically consistent with Jim Burrows' simulation of 
a "Tex standard" mirror.

One interesting difference from the equal zone width simulation: the "2 
sigma" limits on zonal readings were essentially constant with zone radius, 
insteading of declining monotonically.

Again, this simulation was of a 500mm f/4 mirror tested on 15 zones, with 
the inner 1/16 of the mirror diameter masked off.

I'll post some graphs later -- maybe much later. I'm getting on a plane in 
a few hours and there won't be time today. I can't comment on differences 
with Steve's results right now.

Mike Peck


Michael Peck
mpeck1@ix.netcom.com

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