  The imaging performance of tomographic deconvolution phase microscopy can be
described in terms of the phase optical transfer function (POTF) which, in
turn, depends on the illumination profile. To facilitate the optimization of
the illumination profile, an analytical calculation method based on polynomial
fitting is developed to describe the POTF for general non-uniform
axially-symmetric illumination. This is then applied to Gaussian and related
profiles. Compared to numerical integration methods that integrate over a
series of annuli, the present analytical method is much faster and is equally
accurate. Further, a balanced distribution criterion for the POTF and a
least-squares minimization are presented to optimize the uniformity of the
POTF. An optimum general profile is found analytically by relaxed optimal
search and an optimum Gaussian profile is found through a tree search.
Numerical simulations confirm the performance of these optimum profiles and
support the balanced distribution criterion introduced.
