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

[Jim Burrows <burrjaw@earthlink.net>]

At 2005-03-10 20:38 -0600, Michael Peck wrote:

>1) There is no systematic bias in the surface error profiles.
>
>Linfoot's work differs from common ATM practice in 4 ways:
>b) He uses rather more zones than is common for ATMs.
>
>In the meantime I've posted a subject header with an unambiguous assertion 
>in hopes that someone will feel motivated to try to prove me wrong.

I've done this before, maybe posted it to the ATM list, but let's do it 
again:  running Diffract (using wave optics) simulating a perfect Texereau 
standard mirror 200 mm f/6 with a standard Couder mask, 4 zones with 
outside radii: 50, 70.7, 86.6, 100 mm.  The program outputs the left-right 
contrast difference, as if one had a photometer comparing the total light 
reflecting from each zone.  Running fixed source, the longitudinal readings 
giving an exact contrast match are:

         zone    reading, mm
         1       .486
         2       1.510
         3       2.589
         4       3.662

Now there's 3 choices of representative zone radii:  Texereau's mean, 
Couder's rms, Nils Olof's ave(mean, rms).  Running these choices through 
Sixtests, assuming .001" reading S.D.:

choice  RMS     sigma   b
mean            3.2     0.5     -0.965
rms             1.3     0.2     -1.018
Nils            1.8     0.3     -0.986

So Couder wins the RMS contest, Nils Olof gets the conic constant prize; 
Texereau's mean loses both, and, most important for this discussion, that 
choice indeed says the perfect mirror is under-corrected.

         -- Jim Burrows
         -- mailto://burrjaw@earthlink.net
         -- http://home.earthlink.net/~burrjaw
         -- Seattle N47.4723 W122.3662 (WGS84)  

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