Fan Junliu, Wu Quanying, Lu Zhiyi, Li Xunwu, Chen Baohua
Appl Opt. 2017 Mar 20;56(9):2563-2567. doi: 10.1364/AO.56.002563.
Aberration detection of subapertures is critical to the resolution of a sparse aperture optical system. In this work, the Cramér-Rao lower bound (CRLB) expression of aberrations was first derived for the subapertures of a sparse aperture optical system. The aberrations were estimated by phase diversity, assuming that the photons follow the Poisson distribution. The derived formula has been applied to the Golay3 sparse aperture system to calculate the CRLB of the subapertures' aberrations with different defocus distances, fill factors, and ratios of photon numbers between the focal and defocal images. According to the CRLB criterion, the results indicate that the accuracy of aberration estimation increases as the fill factor of the sparse aperture system increases. The results also demonstrate that the optimal defocus distance of phase diversity is achieved when the CRLB reaches its minimum. The optimal ratio of photon numbers between the focal and defocal images is around 3∶7. However, for the piston error, more photons in the defocal image yield more accurate estimation results. This method can also be applied to the sparse aperture optical systems with other different configurations.
子孔径像差检测对于稀疏孔径光学系统的分辨率至关重要。在这项工作中，首先推导了稀疏孔径光学系统子孔径像差的克拉美 - 罗下界（CRLB）表达式。假设光子服从泊松分布，通过相位差技术估计像差。所推导的公式已应用于Golay3稀疏孔径系统，以计算不同离焦距离、填充因子以及焦面和离焦面图像之间光子数比情况下子孔径像差的CRLB。根据CRLB准则，结果表明随着稀疏孔径系统填充因子的增加，像差估计精度提高。结果还表明，当CRLB达到最小值时，可实现相位差技术的最佳离焦距离。焦面和离焦面图像之间光子数的最佳比例约为3∶7。然而，对于活塞误差，离焦面图像中更多的光子会产生更准确的估计结果。该方法也可应用于其他不同配置的稀疏孔径光学系统。
