Phase retrieval of widefield microscopy point spread functions

The three-dimensional imaging properties of a light microscope are traditionally described through an intensity point spread function (PSF) or its Fourier transform, the optical transfer function (OTF). However, the imaging properties can be more compactly described by a generalized two-dimensional pupil function. Use of the pupil function allows easy modification of an observed PSF to introduce known aberrations, a much more difficult task when using a PSF or OTF. Unfortunately, it is not straightforward to determine the complex-valued pupil function from the measured intensity PSF, because of the lack of phase information. This is the problem of phase retrieval. Several phase retrieval algorithms have been developed for two-dimensional imaging in astronomy. We have modified one such algorithm to be appropriate for the high-aperture, non-paraxial case of high resolution light microscopy. PSFs reconstructed from phase-retrieved pupil functions, modified by calculated aberrations closely reproduce the features of measured, aberrated PSFs.