Optical phase-space functions describe spatial and angular information simultaneously; examples include light fields in ray optics and Wigner functions in wave optics. Measurement of phase-space enables digital refocusing, aberration removal and 3D reconstruction. High-resolution capture of 4D phase-space datasets is, however, challenging. Previous scanning approaches are slow, light inefficient and do not achieve diffraction-limited resolution. Here, we propose a multiplexed method that solves

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... these problems. We use a spatial light modulator (SLM) in the pupil plane of a microscope in order to sequentially pattern multiplexed coded apertures while capturing images in real space. Then, we reconstruct the 3D fluorescence distribution of our sample by solving an inverse problem via regularized least squares with a proximal accelerated gradient descent solver. We experimentally reconstruct a 101-Megavoxel 3D volume (1010×510×500μm with NA 0.4), demonstrating improved acquisition time, light throughput and resolution compared to scanning aperture methods. Our flexible patterning scheme further allows sparsity in the sample to be exploited for reduced data capture.