Phase retrieval for high-numerical-aperture optical systems

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functionsreproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.