Rigorous Diffraction Theory for 360° Computer‐Generated Holograms

Most algorithms for a computer-generated hologram using FFT are effective only under the condition that both the input and observation surfaces are finite planes that are parallel to each other. To synthesize a 360 degree hologram in a computer, a numerical simulation of the diffraction on the non planar observation surfaces is required. At first, we propose a simple but rigorous equation which describes the relation between the diffracted wavefront of a 3-D object and its 3-D Fourier spectrum. In this method, an exact solution of the diffraction integral is given by the Green function. This principle gives us an intuitive understanding of calculation processes for various diffraction situation. Alternatively, fast computation solutions for spherical computer generated hologram employing PSF (convolution method) is proposed. We start with Helmholtz equation, with considering a boundary value problem in spherical co-ordinates. The solution define the transfer function and the spectral decomposition of the wave field in the spherical surface. Using the transfer function and the wave spectrum we can develop a spectral propagation formula (for spherical surfaces in spherical coordinates) analogous to the angular spectrum formula. Some computer simulation and experimental results are presented.