The deconvolution of widefield fluorescence images provides only guesses of spatial frequency information along the optical axis due to the so called missing cone in the optical transfer function. Retaining the single-shot imaging speed of deconvolution microscopy while gaining access to missing cone information is thus highly desirable for microscopy of volumetric samples. Here, we present a concept that superimposes two orthogonally polarized excitation lattices with a phase-shift of p between them. In conjunction with a non-iterative image reconstruction algorithm this permits the restoration of missing cone information. We show how fluorescence anisotropy could be used as a method to encode and decode the patterns simultaneously and develop a rigorous theoretical framework for the method. Through in-silico experiments and imaging of fixed biological cells on a structured illumination microscope that emulates the proposed setup we validate the feasibility of the method.
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