  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 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 ($1010\times510\times500\mu$m 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.
