环五孔稀疏孔径系统成像性能研究

Research on Imaging Performance of Annular-5 Sparse Aperture System

稀疏孔径系统作为高分辨率成像解决方案,其成像性能却受子孔径之间活塞误差和各独立子孔径波前残差强烈影响。以均匀环五孔构型为研究对象,通过对点扩散函数和调制传递函数的表征,数值模拟得到了该构型的成像相关误差指标。从频域覆盖无截断的角度分析了环五孔构型的填充因子,选择范围为27.8%至68.5%。以斯特列尔比(大于0.80)为评价准则,填充因子为43.2%时的子孔径之间的活塞误差最大容忍度约为λ/6,含有独立自适应光学系统的各子孔径的波前残差均方根最大容忍度约为λ/14。填充因子的选择范围从根本上受到子孔径波前残差的限制,而子孔径之间的共相则需以一定的自适应光学校正水平为前提。

High-resolution imaging plays a crucial role in various fields such as astronomical observations,earth sciences,and national defense.Traditionally,the main approach to improve angular resolution is via increasing the aperture of optical system.However,manufacturing and maintaining large aperture telescopes often come with high costs,and space-based optical systems are particularly constrained by payload limitations.Sparse aperture systems have emerged as a solution that can simultaneously reduce cost budgets and process requirements,garnering widespread attention since their inception.The high-resolution imaging capability of sparse aperture systems is essentially achieved through the interference between sub-apertures,resulting in a reduction of the half-width of the sub-aperture′s Airy disk.To achieve effective interference between subapertures,the control of optical path difference,or the co-phasing of sub-apertures is of great importance and therefore can largely determine the imaging performance of the sparse aperture system.Although adaptive optics systems can provide a relatively flat wavefront,the correction process is performed independently for each subaperture,and the relative optical path of the sub-paths used for coherent interference can not be simultaneously controlled.In this study,a annular-5 configuration is firstly discussed based on the constraints imposed by the frequency domain.The annular-5 configuration exhibits a five-fold symmetry,with non-redundant baseline directions between sub-apertures.The resulting modulation transfer function possesses a ten-fold symmetry,providing certain advantages on an equivalent single-aperture telescope.The analytical expression for the point spread function of the annular-5 configuration has been derived based on the theory of Fourier optics.Theoretically,the peak of the point spread function for the annular-5 configuration is 25 times larger than the peak of the point spread function for an individual sub-aperture.This is because the annular-5 configuration collects 5 times more light flux at the entrance pupil compared to a single sub-aperture,and the interference effect causes the energy to shift from dark fringes to bright fringes,enhancing the main peak by 20 times.Therefore,the interference between sub-apertures is crucial for improving the resolution of sparse aperture systems.Considering the constraint of frequency domain coverage without zero frequency,the maximum range for the achievable fill factor of the annular-5 configuration is 27.8%to 68.5%.The discussion on the equivalent aperture highlights the trade-off optimization of fill factor in sparse aperture systems.Based on the analysis under the ideal condition of no aberrations,the influences of piston errors and adaptive optics residual wavefront errors on the annular-5 configuration are investigated numerically by characterizing the point spread function and modulation transfer function.The results demonstrate that the tip/tilt errors in adaptive optics residuals have the most notable impact on the imaging quality.Specifically,tip/tilt errors cause the diffraction patterns of the subapertures to be misaligned,resulting in the diffraction envelopes not overlapping with each other,which leads to incomplete coherent interference of the beams.Using a Strehl ratio greater than 0.80 as the evaluation criterion,separate discussions are conducted on the tolerance of piston errors and adaptive optics errors of the annular-5 configuration.Assuming a fill factor of 43.2%,numerical calculations indicate that the piston errors between sub-apertures need to be controlled withinλ/6 at a minimum,while the root mean square of wavefront residuals for each sub-aperture,which includes independent adaptive optics systems,needs to be controlled approximately withinλ/14.Thus,the co-phasing between sub-apertures relies on the prerequisite of a certain level of adaptive optics correction.The research results on the annular-5 configuration have a certain degree of universality and can provide valuable references for future imaging research on sparse aperture systems.