Wirtinger Holography for Near-Eye Displays
Wirtinger Holography on a Display Prototype. To compute phase-only modulation patterns, we depart from existing iterative projection algorithms, such as error-reduction Gerchberg-Saxton methods [Gerchberg 1972; Peng et al. 2017], and heuristic encoding approximations, such as the double phase encoding method [Hsueh and Sawchuk 1978]. Instead, we revisit the use of formal optimization using complex Wirtinger derivatives for the underlying phase retrieval problem. We built a near-eye display prototype using a phase-only spatial light modulator (SLM) and off-the-shelf optics (left). Compared to holographic reconstructions at a set focal distance from the existing methods [Peng et al. 2017] (center left) and [Maimone et al. 2017] (center right), the proposed Wirtinger holography substantially reduces reconstruction artefacts on our prototype, while achieving an order of magnitude reduced error in simulation. Mouse embryo image by Miltenyi Biotec.
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..
Holographic Phase Retrieval Methods on Proposed Prototype Display.
We show monochrome reconstructions for the green and red wavelength channels of our system. The phase-only holograms used in this prototype are provided in the supplemental material. The images in each row are captured with same camera settings, using ISO 100 and same exposure time 10 ms.
RGB Holographic Display on Proposed Prototype Setup.
We present RGB color images with each color channel captured sequentially. The phase-only holograms used in this prototype are provided in the supplemental material. The images in each row are captured with same camera settings, using ISO 100 and exposure time 10 ms. We have tuned the output power of three lasers before acquisition to approximately white-balance the illumination. Please zoom into the electronic version of this document for better viewing. Actin cell image by Jan Schmoranzer.