Non-uniform Fourier Domain Stretching method for ultra-wide-angle wave propagation

TL;DR

The paper introduces the NU-FDS method, a novel Fourier domain approach that significantly accelerates and improves the accuracy of ultra-wide-angle hologram reconstruction, enabling detailed 3D object visualization.

Contribution

It presents the NU-FDS algorithm, combining phase-space analysis with non-uniform Fourier magnification for fast, precise WA-CGH reconstruction, surpassing previous computational limitations.

Findings

Accurately reconstructs large, detailed 3D objects from WA and UWA CGH.

Supports high field of view (up to 120°) and high resolution (up to 16K).

Reduces computation time while maintaining reconstruction quality.

Abstract

Numerical inspection of wide-angle (WA) or ultra-wide-angle (UWA) computer-generated holograms (CGH) is a computationally demanding task. To surpass this limitation, we propose a novel computational approach for fast and accurate WA-CGH reconstruction based on Fast Fourier transform Fresnel diffraction (FrT) and non-uniform frequency hologram magnification. This novel algorithm, referred to as the non-uniform Fourier Domain Stretching (NU-FDS) method, is based on approximating a spherical wave coming from any object point with a parabolic wave, with the points of convergence of the two waves being different. It is supported by a mathematical solution developed using phase-space to determine the frequency distribution needed to find the distribution of non-uniform magnification. It corrects the axial distance of a parabolic wave so the FrT solution can be applied for WA-CGH reconstruction. The NU-FDS algorithm also allows the reconstruction of a partial view with freedom of position and size selection, reducing computation time. In this way, the NU-FDS method enables fast and accurate quantitative assessment of the 3D information coded into the CGH. The presented evidence shows that the NU-FDS algorithm can accurately and efficiently reconstruct large and highly detailed 3D objects from WA and UWA CGH of FoV and resolution up to 120{\deg} and 16K, respectively.