###### Abstract  
The synthesis of the spherical hologram has been widely investigated in recent years as it enables a large field of view both horizontally and vertically. However, there is an important issue of long time consumption in spherical computer-generated holograms (SCGHs). To address this issue, a fast diffraction calculation method is proposed for SCGH based on phase compensation (PC). In our method, a wavefront recording plane (WRP) near the SCGH is used to record the diffraction distribution from the object plane, and the phase difference is compensated point-to-point from the WRP to generate the SCGH, during which a nonuniform sampling method is proposed to greatly decrease the sampling rate and significantly accelerate the generation speed of SCGH. In this paper, there are three main contributions: (1) SCGHs with the resolution of full high-definition can be synthesized in visible range with reducing the sampling rate. (2) Due to the current difficulty of realizing holographic display with curved surfaces, our PC method provides an alternative approach to implement optical experiments of SCGH, which takes it closer to the practical applications of spherical holography. (3) The problem of time-consuming calculation of the propagation model between plane and sphere is solved firstly to our best knowledge. spherical computer-generated hologram; phase compensation; fast diffraction calculation 2020 10 5784 10.3390/app1075784 10.3390/app1075784 10.3390/app1075784 10.3390/app1075784 10.3390/app1075784 10.390/app1075784 10. There are a number of achievements in the field of spherical holography [16; 17; 18; 19; 20; 21]. However, the huge amount of data limits the computational time for the process of SCGH generation, which is one of the major obstacles to the practical application of spherical holography. To address this issue, several pieces of research associated with the speed enhancement of spherical hologram synthesis have been reported [17; 18; 19; 20; 21]. [PERSON] et al. proposed a method for fast calculating the spherical hologram distribution using convolution algorithm based on fast Fourier transform (FFT) [17]. It approximated the diffracted optical field as the calculation result of a convolution integral, which enables FFT to shorten the total computing time. [PERSON] and [PERSON] explored a fast calculation method of SCGH using spherical wave spectrum [18], which is based on wave propagation defined in spectral domain and in spherical coordinates. It uses only \(N(logN)^{2}\) operations for calculations on \(N\) sampling points and can accelerate the computing process effectively. [PERSON] et al. proposed an acceleration method for SCGH calculation of real objects using graphics processing unit(GPU) [19]. It improved the calculation efficiency compared with the computation speed of central processing unit(CPU). Additionally, [PERSON] et al. introduced a spherical harmonic transform-based fast calculation algorithm for SCGH considering occlusion culling [20]. In this method, the diffraction integral is expressed in the form of the convolution integral, which can be calculated rapidly by performing spherical harmonic transform instead of FFT. It cuts down the computing time and removes occlusion as well. Besides, [PERSON] and [PERSON] applied SCGH to holographic video and proposed a faster generation method of holographic videos of objects moving in space using a spherical hologram-based 3D rotational motion compensation scheme [21], which provides another possible application of SCGH. The methods above are basically devoted to the study of fast calculation methods of SCGH generated by concentric spherical surfaces. However, extremely high pixel resolution is required to satisfy the sampling theorem for the visible range of light wavelengths. For example, it is nearly 200,000 \(\times\) 200,000 for wavelength \(\lambda\) = 632.8 nm when the radii of the inner and outer sphere are 1 cm and 10 cm, respectively, when calculated by convolution method [17].