Ray Optics Approach to Holography

TL;DR

This paper introduces an efficient optimal transport-based algorithm for phase retrieval in holography, overcoming vortex formation issues and connecting ray optics with quantum learning for improved laser beam shaping.

Contribution

The work presents a novel optimization method that avoids vortex formation, establishes a theoretical link between optimal transport and ray optics, and applies quantum learning concepts to phase retrieval.

Findings

Algorithm achieves state-of-the-art accuracy and efficiency.

Bypasses vortex formation in phase retrieval.

Connects optimal transport with ray-optics limit.

Abstract

Retrieving the phase of a complex-valued field from the measurements of its amplitude is a crucial problem with a wide range of applications in microscopy and ultracold atomic physics. In particular, obtaining an accurate and efficient solution to this problem is a key step in shaping laser beams for trapping atoms in optical tweezer arrays and applying high-fidelity entangling gates on a neutral atom quantum computer. Current approaches to this problem fail to converge on the optimal solution due to a phenomenon known as vortex formation. In this work, we present an efficient optimization algorithm using Optimal Transport. Our approach completely bypasses the creation of phase vortices and allows for a state-of-the-art solution both in terms of accuracy and efficiency. Furthermore, we show a deep theoretical connection between the Optimal Transport plan and the ray-optics limit of the Wigner distribution of the unknown complex-valued field, and show that our method can be used to retrieve the phase-space transformation of any unknown quadratic phase system. Finally, we reinterpret this problem in the modern quantum learning framework. The techniques we develop provide both useful intuition and practical tools for advancing the frontiers of phase retrieval and laser beam shaping.