Study On Co-phase Error Correction Of Optical Multi-aperture Imaging System Based On Stochastic Parallel Gradient Decent Algorithm

The spatial angle resolution of optical telescope imaging system is mainly affected by the observation wavelength and the system's aperture.When the wavelength is constant,the spatial angle resolution depends on the diameter of aperture of optical telescope imaging system.The optical multi-aperture imaging system is an effective way to increase the aperture and the resolution of the optical imaging system,the difficulty of which is lied in detecting and correcting of co-phase error.This paper presents a method based on stochastic parallel gradient decent algorithm(SPGD)to correct the co-phase error.Compared with the current method,SPGD method can avoid detecting the co-phase error and simplify the process of the co-phase error's correction.First,this paper deduced the mathematical expression of PSF and MTF of the multi-aperture imaging system based on the basic principle of the single aperture imaging system,revealed the reason why the multi-aperture imaging system can raise the spatial angle resolution of the imaging system by comparing with the single aperture's PSF and the multi-aperture's PSF,introduced three kinds of multi-aperture array structures——Ring type,Golay-3 type,Y type and simulated the MTF of them,discussed three performance evaluation methods of the multi-aperture array structures.Second,introduced two kinds co-phase error of the multi-aperture imaging system——piston error and tilt error and explained the cause of them,given the mathematical expression of PSF and MTF of the multi-aperture imaging system with piston error and tilt error and simulated of the PSF and the MTF,analysed the influence of co-phase error on the imaging quality of the multi-aperture imaging system.Third,introduced the basic principle and procedure of the stochastic parallel gradient decent algorithm,presented three evaluation methods of the image's definition,analysed the influence of the co-phase error on the performance evaluation methods under monochromatic light and multi wavelength and proposed a co-phase error correction method based on stochastic parallel gradient decent algorithm.In the case of single wavelength and multi wavelength,simulated the process of the correction of the co-phase error based on stochastic parallel gradient decent algorithm.Introduced the influence of the gain coefficient and disturbance amplitude on the stochastic parallel gradient decent algorithm and given a method adaptive updated the gain coefficient to balance the convergence speed and the stability of the algorithm.Finally,based on the double aperture imaging platform,the closed loop correction system was built.This system based on SPGD algorithm corrected the co-phase error of the double aperture imaging system in the case of single wavelength and multi wavelength.The experimental results proved the correctness of the analysis of the theoretical and the simulation results.