Design And Imaging Of Aspheric Sparse Aperture Optical System

The angular resolution of the telescope is proportional to the aperture size of the optical system,and a larger effective aperture can obtain a higher angular resolution.However,as the aperture size increases,the weight of the optical system and the cost of manufacture will increase.In addition,the mirror of large aperture is more susceptible to deformation because of stress and temperature.Sparse aperture can obtain the same angular resolution by replacing a single large aperture with a plurality of small apertures arranged in a specific way,while the manufacturing difficulty and cost of large-scale optical system can be effectively reduced.This paper mainly studies the sparse aperture optical system from three aspects:optimization and design of sparse aperture array,design of sparse aperture optical system and image restoration.First,given that the mid-frequency modulation transfer function(MTF)of the four-hole Tri-arm structure drops too fast,a new sparse aperture array—quasi-four mirror structure is therefore proposed with the MTF as the evaluation basis.Based on the four-hole Tri-arm structure,there is a special proportional relationship between the diameter of the central submirror and the diameter of the three surrounding sub-mirrors.When filling factors and lightpassing areas of the two structures are equal simultaneously,the quasi-four mirror structure has a larger actual cut-off frequency and better mid-frequency MTF characteristics than that of the four-hole Tri-arm structure.Second,in view of the problems that the current sparse-aperture optical system only has small field of view,the secondary mirror obstructs the sub-mirror,and the processing,measurement and adjustment of free-form surface are difficult.Based on paraxial imaging theory and aberration theory,this paper discusses the selection of parameters,the calculation of initial structure and the design of sparse aperture optical system.A quadric surface sparse aperture optical system with full field angle of 1° and wavelength range of visible light and an odd aspheric sparse aperture optical system with full field angle of 0.3° and wavelength range of 0.3-1.5 μm are designed respectively.Both F-numbers of the two systems are 5 and filling factors are 40.3%.What’s more,the secondary mirrors of them have no obstruction to the sub-mirrors and the structures are compact.In the designed quadric surface sparse aperture optical system,imaging quality close to the diffraction limit can be achieved under full field of view.The adopted corrective lens group is the positive and negative structure of H-ZK11 from CDGM.As for the odd aspheric sparse aperture optical system designed,the primary mirror is still a quadric surface and the secondary mirror only uses 3rd and 4th aspheric terms,so the processing,measurement and adjustment are less difficult.Finally,for the sparse aperture optical system,the mid-frequency MTF decreases rapidly due to pupil dispersion,which seriously affects the imaging quality for medium and high frequency objects.The paper analyzes the imaging process and the image degradation model of the sparse aperture optical system.In 0 field of view,0.7 field of view and 1 field of view,the image degradation caused by diffraction limit and aberration of sparse aperture optical system is restored by the inverse convolution algorithm.It is thus proved that high spatial resolution image can be obtained based on image restoration algorithm with the quadric surface sparse aperture optical system and the odd aspheric sparse aperture optical system designed in this paper.Besides,the influence of signal-to-noise ratio on sparse aperture optical system is studied by image average and deconvolution algorithm under Gaussian noise.It is very helpful to apply aspheric surface to sparse aperture optical system to improve the field of view and imaging quality of the system.