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 molecular architecture of biological systems by mapping oriented fluorophores. However, existing PFM methods focus on retrieving the averaged orientation of fluorophore ensemble in voxel while struggling to uncover their comprehensive three-dimensional (3D) molecular orientation distributions, particularly in thick, densely labeled or structurally complex specimens. To overcome these limitations, we introduce the efficient generalized Richardson-Lucy (eGRL) algorithm, a robust, high fidelity computational framework for reconstructing complete 3D position and orientation (totally six dimensions, also termed spatio-angular) distributions of ensembles of fluorescent molecules from PFM data. We first statistically model the oriented fluorophores imaging process in spatio-angular hyperspace and propose an iterative maximum-likelihood based solution to the inverse problem. Then we integrate both dimensionality reduction and angular domain transformation techniques to address the computational bottleneck general in high-dimensional statistical algorithms and develop an effective processing pipeline to further mitigate the exponential memory increase required for large data. Collectively, these advances not only enhance accuracy but also the efficiency of spatio-angular image reconstruction, allowing eGRL to be deployed effectively on standard computational platforms. By applying eGRL to both simulated and experimental data, we demonstrate its versatility across different PFM implementations and improved accuracy for 3D reconstructions compared to existing methods. We use our methods to resolve biological spatio-angular structures and dynamics otherwise impossible to resolve, including the tangential alignment of actin filaments in U2OS cells, nanowire-guided cytoskeletal organization in NIH3T3 cells, rotational actin patterns in live HeLa protrusions, and membrane tension-induced anisotropy in live macrophages.