Non-uniform Fourier domain stretching method for ultra-wide-angle wave propagation

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 is referred to as the Non-Uniform Fourier Domain Stretching (NU-FDS) method. It 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. Finally, the NU-FDS method provides a fast and accurate quantitative assessment of WA or UWA CGH. The algorithm also allows the reconstruction of a partial view of any location, reducing computation time. 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° and 16 K, respectively.