Wirtinger holography for near-eye displays

Near-eye displays using holographic projection are emerging as an exciting display approach for virtual and augmented reality at high-resolution without complex optical setups --- shifting optical complexity to computation. While precise phase modulation hardware is becoming available, phase retrieval algorithms are still in their infancy, and holographic display approaches resort to heuristic encoding methods or iterative methods relying on various relaxations. In this work, we depart from such existing approximations and solve the phase retrieval problem for a hologram of a scene at a single depth at a given time by revisiting complex Wirtinger derivatives, also extending our framework to render 3D volumetric scenes. Using Wirtinger derivatives allows us to pose the phase retrieval problem as a quadratic problem which can be minimized with first-order optimization methods. The proposed Wirtinger Holography is flexible and facilitates the use of different loss functions, including learned perceptual losses parametrized by deep neural networks, as well as stochastic optimization methods. We validate this framework by demonstrating holographic reconstructions with an order of magnitude lower error, both in simulation and on an experimental hardware prototype.