Rotating point spread function (PSF) microscopy via spiral phase engineering can localize point sources over large focal depths in a snapshot mode. The present work gives an approximate vector-field analysis of an improved rotating PSF design that encodes both the 3D location and polarization state of a monochromatic point dipole emitter for high-numerical-aperture microscopy. By examining the angle of rotation and the spatial form of the PSF, one can jointly localize point sources and determine the polarization state of light emitted by them over a 3D field in a single snapshot. Results of numerical simulations of noisy data frames under Poisson shot noise conditions and the errors in the recovery of 3D location and dipole orientation for a single point source are discussed.
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