Wirtinger-derivative-based tilted plane diffraction propagation for holographic near-eye displays

In holographic near-eye displays, the generation of computational holograms requires using various free-space propagation numerical methods. Traditional free-space propagation is mainly focused on the propagation calculation between parallel planes, which is widely utilized in on-axis holographic displays. But for practical usage of the wearable holographic near-eye displays, the propagation between non-parallel planes is crucial for the hologram generation of off-axis projection to the holographic-optical-element (HOE) based combiner. However, at current few methods are reported for generating holograms with non-parallel-plane propagation. This paper proposes a novel method with Wirtinger derivatives to solve the problem of phase hologram retrieval between non-parallel planes. Using the Wirtinger derivatives can transfer the hologram phase retrieval to a quadratic problem. With different loss functions and stochastic optimization methods, this quadratic problem can be minimized by first-order optimization, resulting in a phase-only hologram of the tilted plane. The proposed method using the Wirtinger derivatives to calculate the tilted plane phase hologram can improve image quality significantly. The proposed method can achieve better PSNR and lower computational cost in the simulation than the traditional GS algorithm. The diffraction calculation of the tilted plane can further extend the propagation from two-dimensional(2D) to three-dimensional(3D), which will provide a new way for the hologram generation of 3D scenes.