Spherical-harmonic-transform-based fast calculation algorithm for spherical computer-generated hologram considering occlusion culling

The diffraction integral onto a spherical surface is discussed in the three-dimensional (3D) Fourier domain of the 3D object used. The diffraction integral is expressed in the form of the convolution integral between the partial Fourier components of the 3D object and the kernel function defined on the sphere. This two-dimensional convolution on the sphere can be calculated rapidly based on the convolution theorem by performing spherical harmonic transform instead of Fourier transform. This paper presents a detailed derivation of this diffraction integral and analyzes the sampling pitch required for handing the data on the sphere. Our proposed method is verified using a simple simulation of Young’s interference experiment. Moreover, a numerical simulation with a more complicated 3D object is demonstrated. Our proposed method speeds up the calculation of the diffraction integral by more than 6,000 times compared with the direct calculation method.