Piston Error Correction Of Multi Aperture Systems Using Meta-heuristic Stochastic Parallel Gradient Descent Algorithm

The aperture size of optical system is the key factor to limit its imaging resolution.The synthetic aperture imaging system effectively solves the problem that the large aperture primary mirror is difficult to process by separating the mirror,which is the inevitable development trend of the next generation optical telescope.Due to the system alignment error and platform jitter and other factors,there are common phase errors among sub apertures.The correction of common phase error is the key to highresolution imaging of synthetic aperture imaging system.Therefore,the research of common phase problem has important practical significance and theoretical value for the key scientific fields such as deep space exploration and ground remote sensing in the future.Aiming at the translation error in the common phase error,this paper proposes a translation error correction method based on sub heuristic SPGD algorithm,which can effectively solve the 2 π ambiguity problem existing in the traditional optimization of the common phase method,realize the translation error correction of large range and high precision,and provide an effective solution for the key technical problems of optical multi aperture imaging.Firstly,based on the basic model of incoherent imaging,the imaging principles of traditional large aperture system and optical multi aperture imaging system are derived respectively,and the essential reasons for the improvement of imaging resolution of multi aperture system are revealed from the perspectives of spatial domain and frequency domain.The source of the common phase error among the subapertures is described and its influence on imaging is analyzed.Taking the translation error as the research object,the nonlinear functional relationship between the translation error and the image clarity evaluation index under different lighting conditions is fitted.Finally,the translation error correction is transformed into the objective function optimization problem.Then,combined with the advantages and disadvantages of the existing cophase optimization algorithm,a method of multi-spectral detection is proposed to eliminate the 2 π ambiguity in the cophase process,so as to increase the detection range and simplify the cophase problem to a non convex function optimization process.Aiming at the problem that the existing algorithms can not meet the requirements of high precision and high real-time co phase detection at the same time,a sub heuristic SPGD algorithm combining heuristic global search and local gradient descent is proposed.The algorithm introduces the imaging principle into the iterative process,and solves the problem that the traditional SPGD algorithm is easy to fall into local extremum through the constraints and incentives of heuristic function.The strong global convergence of the algorithm is verified by the optimization test of non convex function.Finally,the simulation platform of multi aperture imaging is built,and the sub heuristic SPGD algorithm is used to detect the point target and the area target in the three aperture and seven aperture arrangement,respectively;the influence of different noise and high-order aberrations of each sub aperture on the detection effect of the algorithm is analyzed.The simulation results show that the sub heuristic SPGD algorithm can keep the cophase accuracy of 0.05 λ in different target scenarios,and can be applied to complex structures with large number of sub apertures,and the algorithm has high stability and strong robustness.