Optimization Of The Optical Sparse Array Configuration

Sparse aperture optical systems are synthesized by several space distributed and"coherent small sub-apertures. In order to properly combine the coherent image on focusplane of the optical system, the location of each sub-aperture must be phased andcontrolled precisely to provide the difffraction-limited resolution as that of thecorresponding single aperture system. It can successfully avoid the difficulty of processingvery large aperture optical elements, and it is one of the most challenging approaches forthe realization of space-borne optical systems with large apertures and high resolutions.The array configuration of a sparse aperture system has a direct effect on themodulation transfer function (MTF) of the optical system and it will influence the imagingquality of the system consequently. Based on the principle of Fourier Optics and OptimumTheory, the optimization of the sparse array configuration was analyzed and calculated inthis dissertation. The main contents are as follows:The signification of research on the sparse aperture system and the research progressof the optimization of the sparse array configuration is introduced firstly.The basic principle of imaging and the basic array configurations of sparse aperturesare studied. Imaging simulations have illuminated that array configuration has an importanteffect on imaging quality. Based on the principle of Fourier Optics, we analyze thecharacteristic of the coverage of the spatial frequency plane and get the analyticalexpression of MTF of the sparse systems.Then, the general processes of optimization of the sparse array configuration, the ruleof the optimization problem and the thought of establishing the objective function havebeen analyzed in detail. We establish the objective function from three aspects—based ongiven region of frequencies of interest, uniform frequency coverage of MTF plane, and themaximal average MTF coverage of the systems. According to the characteristic of this problem, the simulated annealing algorithm has been chosen for optimum calculation andthe particular processes of optimization are obtained.Finally, programs are compiled by using Mathematica software and some examples ofoptimization of the sparse array configuration are given with regard to the three aspects.The analysis and evaluation of the optimum results show that the above optimizingalgorithm can give reasonable configuration, which the characteristics are coincident to theexpected ones.