Analytical phase optical transfer function for Gaussian illumination and the optimized illumination profiles

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