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针对点衍射干涉仪(PDI)的小孔衍射波前,提出了一种基于扩展奈波尔-泽尼克(Nijboer-Zernike)(ENZ)理论进行超高精度检测的方法。描述了点衍射干涉仪的工作原理和基于扩展Nijboer-Zernike多项式的相位恢复算法。分析了对光瞳函数利用Zernike多项式展开的方法。仿真实验中,当信噪比(SNR)为55 dB,采用10 bit模数转换时,得到的Zernike系数中代表波像差的虚部的恢复误差不大于3×10-5。从噪声和模数转换的角度通过模拟实验显示这种方法对实现小孔衍射波前超高精度的光学检测具有可行性。
Aiming at the small aperture diffraction before PDI, a method based on the extended Niebohr-Zernike (ENZ) theory for ultra-high precision detection is proposed. The operating principle of the point diffraction interferometer and the phase recovery algorithm based on the extended Nijboer-Zernike polynomial are described. The method of expanding the pupil function using Zernike polynomials is analyzed. In the simulation experiment, when the SNR is 55 dB, the recovery error of the imaginary part of the Zernike coefficient which represents the wave aberration is not more than 3 × 10-5 when 10-bit analog-digital conversion is used. Simulation results show that this method is feasible to realize the ultra-high precision optical detection of pinhole diffraction wavefronts from the perspective of noise and analog-to-digital conversion.