Fast polygon-based method for calculating computer-generated holograms in three-dimensional display

In the holographic three-dimensional (3D) display, the numerical synthesis of the computer-generated holograms needs tremendous calculation. To solve the problem, a fast polygon-based method based on two-dimensional Fourier analysis of 3D affine transformation is proposed. From one primitive polygon, the proposed method calculates the diffracted optical field of each arbitrary polygon in the 3D model, where the pseudo-inverse matrix, the interpolation, and the compensation of the power spectral density are employed. The proposed method could save the computation time in the hologram synthesis since it does not need the fast Fourier transform for each polygonal surface and the additional diffusion computation. The numerical simulation and the optical experimental results are presented to demonstrate the effectiveness of the method. The results reveal the proposed method could reconstruct the 3D scene with the solid effect and without the depth limitation. The factors that influence the image quality are discussed, and the thresholds are proposed to ensure the reconstruction quality.