Fast calculation of computer-generated spherical hologram by spherical harmonic transform

This paper presents a fast calculation method for spherical computer-generated hologram by using a spherical harmonic transform. A three-dimensional (3D) object defined in the 3D Cartesian coordinate system is numerically Fourier transformed with fast Fourier transforms (FFTs). Fourier components on the spherical surface of the radius 1/lambda are extracted. The wavefronts on the spherical surface can be calculated from the single spherical Fourier components. This paper reveals the analytical diffraction integral between the spherical Fourier components and the wavefront on the spherical surface. This diffraction integral is expressed in the form of convolution integral on the sphere and can be calculated very fast based on the spherical harmonic transform. By the numerical simulation, the validity and the effectiveness of our proposal has been verified.