In order to obtain the phase distribution from the intensity distribution of the light field in low-light conditions, we investigate the Zernike phase retrieval based on the Gerchberg-Saxton algorithm using the fractional Fourier transform and the corresponding optical system. By studying the relationship between fractional Fourier transform and Fresnel diffraction, the Lohmann optical system is improved. How the Fresnel near-field and far-field outputs influence the high and low frequency parts of phase recovery is analyzed based on wavelet theory. The numerical results show that the algorithm has good convergence and recovery accuracy with root-mean-square error (RMSE) less than 0.15λ(λ is the wavelength). When the outputting planes are placed in the Fresnel near-field, the high-frequency part of the recovery phase is better, while when they are placed in the far-field, the low-frequency part is better.