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I have been using a new phase retrieval iteration that
is derived from the maximum likelihood equation for Poisson statistics
in the data. The joint likelihood 
of getting the
observed counts 
in
each pixel given the expected counts 
is
Here the continuous variables 
and 
have been replaced
by discrete variables, and the equations are written as one-dimensional
for simplicity of notation.
The image 
is equal to the PSF times a constant. If we allow
the amplitude of the complex pupil function 
to vary, then
the maximum likelihood solution occurs where all partial derivatives of
with respect to 
are zero:
The iteration is simply
This is a ``gradient step'' for updating the complex pupil amplitude
. If one wants only the phase 
to to vary during the
iteration, holding the pupil illumination function 
fixed, it is
possible to renormalize to a constant amplitude after each
iteration.