RE: [ATM] I Hate Fudge (was Backup Thoughts)

["Richard Schwartz" <richas@earthlink.net>]

These guys are doing optimization by gradient descent, and that works only
for a narrow class of problems.   I, on the other hand, am using a crude
monte carlo procedure that takes forever to converge, but has no
differentiability requirements on the function to be minimized.

. . . Richard

-----Original Message-----
From: atm-bounces@atmlist.net [mailto:atm-bounces@atmlist.net] On Behalf Of
Richard F.L.R. Snashall
Sent: Tuesday, January 18, 2005 5:25 PM
To: ATM list
Subject: Re: [ATM] I Hate Fudge (was Backup Thoughts)



Richard F.L.R. Snashall wrote:

> I've been trying to determine the reason for the poor performance in 
> an estimator
> procedure.  I'd appreciate any thoughts on the math for the procedure, 
> given in:
>
>    http://users.rcn.com/rflrs/minim.htm

What has all this got to do with optics, you ask?

Well... in honor of having just received "Opticheskoe Steklo Katalog" (if my
transliteration is correct) from LZOS, I revisited the dispersion formula
calculator:

    http://users.rcn.com/rflrs/glasgen.htm

(warning, that script is 150 Kb!), and added wavelengths to match the
entire two sets of wavelengths of that catalog.  I had to double the
width, as the length without would be quite sizeable.

The failures I mentioned... I have used a little trick that I saw somewhere
that adds a damping factor to the diagonal of the matrix (damped least
squares curve fitting).  It may take a few iterations to fully settle down,
but I tried it on a few glasses  LZOS K8 using Schott BK7 as a model,
LZOS KF6 using Schott KF3 as a model, and LZOS OK4 using
Ohara S-FPL53 as a model.  In each case, the tool converged to a
solution close to the original glass; this is mildly surprising for OK4,
as there are only eleven indices given.

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