In this research, a fast method to calculate the color rainbow holographic stereogram (CRHS) by taking full advantage of the sparsity of the frequency domain is demonstrated. The CRHS is a novel color rainbow hologram containing a large number of elemental CRHSs, where each elemental CRHS only reproduces the color light field information of local 3D color object. The color of the reconstructed color 3D image perceived by the human eye is determined by the spectrum of the reproduced dispersion of different elemental CRHSs that enter the human eye. The calculation of the CRHS is implemented with parallel computing by inversely Fourier transforming the frequency of each elemental CRHS. With the proposed method, the computation time for a resolution of 200k × 200k pixels and size of 64 × 64 mm CRHS is only 15.4 min for a color 3D model with 406k object points. The optical reconstruction with a white LED light illumination proves the effectiveness of our proposed method, which can be applied to the field of color holographic 3D display, advertising or holographic packaging.
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