Research on Imaging Performance of Annular-5 Sparse Aperture System
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 sub-apertures,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 sub-aperture,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 sub-apertures 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 within λ/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 within λ/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.
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