  Conventional stereo suffers from a fundamental trade-off between imaging
volume and signal-to-noise ratio (SNR) -- due to the conflicting impact of
aperture size on both these variables. Inspired by the extended depth of field
cameras, we propose a novel end-to-end learning-based technique to overcome
this limitation, by introducing a phase mask at the aperture plane of the
cameras in a stereo imaging system. The phase mask creates a depth-dependent
point spread function, allowing us to recover sharp image texture and stereo
correspondence over a significantly extended depth of field (EDOF) than
conventional stereo. The phase mask pattern, the EDOF image reconstruction, and
the stereo disparity estimation are all trained together using an end-to-end
learned deep neural network. We perform theoretical analysis and
characterization of the proposed approach and show a 6x increase in volume that
can be imaged in simulation. We also build an experimental prototype and
validate the approach using real-world results acquired using this prototype
system.
