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Subject: Re: 3d surface fitting
Date: Fri, 25 Apr 2008 00:25:05 +0000 (UTC)
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> If the curve has the wrong fundamental shape,
> then insisting that it take on the shape you
> want will not help.
> 
> Effectively, this is all you are doing when you
> tighten the tolerance. You are demanding
> more and more fervently that the curve takes
> on a different shape. Your demands will fall
> on deaf ears I'm afraid.
> 
> You might want to take a read through this
> document. It talks about the idea of a
> fundamental shape of a curve, and what
> you can do.

Thanks! That was indeed an interesting read on data
modelling... cleared up a few concepts better! :-)

However, from my theoretical predictions the intensity
profile must be the square of a bessel function (of the
first kind). That is the model I'm applying... 

... and the fit does find a bessel, but not centered at the
same spot as my empirical curve, and neither the same
'thickness' of the central core. 

Thus: a huge resnorm (of 1e7 or 1e8 order), and a residual
with bumps and humps from the zero plane.


While I realize I'm trying to coerce the minimization to
render a bessel form, there ARE some problems with my data:

1. In some of the frames, the central core has saturated the
ccd, and so the "heads" of the bessel are chopped off at the
ends.

2. Due to a slight amount of astigmatism, the annular rings
are not perfectly symmetrical but have a higher intensity in
one direction, or so.


I thought these limitations would not change severly affect
the fit, because the smallest residual should be the one
with the bessel's "head" filled out, with the annular rings
matching up. 

But that doesn't seem to be the case. Is there an
intelligent way to edit my model to incorporate the planar
top of the bessel into the fit? 

This has been a journey into modelling for me. Thanks for
the guidance! :)

Arjun