Efficient spatio-angular reconstruction enables high-fidelity mapping of six-dimensional structures and dynamics with polarized fluorescence microscopy.

Understanding molecular orientation and density distributions is essential for unveiling biological structure and function. Polarized fluorescence microscopy (PFM) offers valuable insights into the structural orientation information, yet existing methods typically retrieve only ensemble-averaged orientations within each voxel and struggle to resolve comprehensive three-dimensional (3D) orientation distributions, particularly in thick or densely labeled complex specimens. Here we introduce the efficient generalized Richardson-Lucy (eGRL) algorithm, a computational framework that reconstructs complete 3D position and 3D orientation (spatio-angular) distributions of fluorescent molecules from PFM measurements. eGRL statistically models the oriented-fluorophore imaging process, solves the inverse problem with an iterative maximum-likelihood solution, and integrates dimensionality reduction with angular-domain transformation to achieve accurate and efficient reconstruction on standard computational platforms. Validated on simulated and experimental data across diverse PFM implementations, eGRL resolves previously inaccessible spatio-angular structures and dynamics, including actin filament alignment, nanowire-guided cytoskeletal organization, rotational actin patterns, and membrane tension-induced anisotropy in live cells.