为了实现大口径拼接薄膜镜失调误差在线校正,建立了由5块子镜组成的菲涅耳波带片拼接成像模型,分析了光学系统的点扩展函数(PSF)和调制传递函数(MTF)与失调误差的关系,并采用随机并行梯度下降算法(SPGD)对失调误差进行在线校正仿真。为了验证所提算法的性能,选取远场光强平方和、远场光斑等效半径、桶中功率、MTF积分和光强二阶矩5个性能评价函数作为优化指标,对失调误差进行盲优化校正,并比较了上述评价指标的收敛速度和精度。100组随机误差的校正结果表明上述指标均能收敛,优化后的波前残差方均根(RMS)均小于0.13λ,斯特列尔比(SR)均大于0.96,其中MTF积分和光强二阶矩指标的收敛速度最快,远场光斑等效半径指标的精度最优。

To achieve the online correction of the misaligned error of large aperture thin film splicing mirrors, an imaging model comprising five pieces of Fresnel lens was established herein. By analyzing the point spread function (PSF) and the modulation transfer function of the optical system in the presence (MTF) of the misaligned error, the relationships between the misaligned error and PSF as well as MTF were obtained. The stochastic parallel gradient descent (SPGD) algorithm was used to correct the misaligned error online. To verify the performance of the proposed algorithm, five performance evaluation functions, including sum of square of far-field light intensity, equivalent radius of far-field light spot, power in barrel, MTF integral, and second-order moment of light intensity, were selected as optimization indexes to correct the misalignment error, and the convergence speed and accuracy of evaluation indexes were compared. The correction results of 100 random errors show that the five indexes can convergence, and the root mean square values of the corrected wavefront are less than 0.13λ and the Strehl ratio is greater than 0.96. The MTF integral and the second-order moment of light intensity converge fastest, and the precision of the equivalent radius of far-field facula index is optimal.