Holographic phase retrieval via Wirtinger flow: Cartesian form with auxiliary amplitude.

We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex circle, and it can take a large gradient while diverging from the origin. This characteristic contributes to accelerating the gradient descent. Meanwhile, at the final stage of optimization, each element evolves along a complex circle, similar to previous state-of-the-art gradient methods. The experimental results demonstrate that our method outperforms previous methods, primarily due to the optimization of the amplitude.

Pixel-density enhanced integral three-dimensional display with two-dimensional image synthesis.

Integral three-dimensional (3D) displays can display naturally viewable 3D images. However, displaying 3D images with high pixel density is difficult because the maximum pixel number is restricted by the number of lenses of a lens array. Therefore, we propose a method for increasing the maximum pixel density of 3D images by optically synthesizing the displayed images of an integral 3D display and high-definition two-dimensional display using a half mirror. We evaluated the improvements in 3D image resolution characteristics through simulation analysis of the modulation transfer function. We developed a prototype display system that can display 3D images with a maximum resolution of 4K and demonstrated the effectiveness of the proposed method.