
2007.09.25

  The PSF model has parameters which vary across the image.  This 2D
  is can be represented as either a polynomial (ordinary or chebychev)
  or as an image map.  The user requests the maximum X & Y scale
  (PSF.TREND.NX & PSF.TREND.NY) for the variations, and
  psphotChoosePSF / pmPSFtry attempt to find the best choice for the
  scale.  For the polynomial representations, NX and NY are the order
  of the variation.  For the image map, NX and NY are the size of the
  image map.

2007.09.21

  there are three places where we can choose to use errors in the fits or not:

  * non-linear fitting of the models to the pixel flux distribution (poissonErrorsPhotLMM)
  * linear fitting of the models to the pixel flux distribution (poissonErrorsPhotLin)
  * fitting of the 2D variations in the psf parameters (poissonErrorsParams)
  * fitting of the 2D variations in the aperture residuals

2007.09.20

  I am upgrading the PSF model to allow the parameter variation to be
  modeled with pmTrend2D instead of just polynomials.  I am making a
  list of places to modify the code:

pmPSFAlloc : need a method beyong psfTrendMask to carry in the psf
options

pmPSF_ModelToFit : no need to change these

update pmPSFBuildSimple to set the parameters of the pmTrend, which
ever is used.

pmPSFtry.c: some significant re-work!



pmPSF_IO : need new functions to save / load the trend (psImages)

2006.10.27

  I have been working to fix the PSF modeling in psphot.  The PSF
  model consists of a flux model for an individual object using an
  analytical model with a number of parameters.  For a collection of
  PSF objects, the variation of the parameters as a function of
  position are then themselves fitted with a model.  The PSF model for
  a single object consists of a radial profile with a functional form
  f(z) where a given value of z defines an elliptical coutour of the
  form z = \frac{x^2}{2\sigma_x^2} + \frac{y^2}{2\sigma_y^2} +
  \sigma_{xy}xy.



  The term \sigma_{xy} is difficult to model as a simple function of x
  and y (eg, a low-order polynomial).  

  A better model can be constructed for
  \frac{\sigma_{xy}}{(\sigma_x^{-2} + \sigma_y^{-2})^2}, which varies
  like a^2 \sin 2\theta 

