Xie Xufen, Fan Hongda, Wang Anding, Zou Nianyu, Zhang Yuncui
Appl Opt. 2018 Aug 1;57(22):6552-6558. doi: 10.1364/AO.57.006552.
The slanted-edge method for modulation transfer function (MTF) measurement uses edge target images whose gray values are often affected by noise and other factors, decreasing its accuracy. We first analyze the ill-posedness in the edge spread function (ESF) regression caused by noise. Second, we propose a regularized slanted-edge method to solve this problem by incorporating a Tikhonov regularization term. Combined with varying precision weights, the ESF is solved using the variational principle, and the MTF is estimated using the regularized ESF. The regularized slanted-edge method is verified for Gaussian, gamma, and Rayleigh noise. The results show that our method improves the accuracy by 0.01-9.02% and 4.33% on average. The proposed method is more robust to noise and accurate than the slanted-edge method.
用于调制传递函数（MTF）测量的斜边法使用边缘目标图像，其灰度值常受噪声等因素影响，从而降低了其准确性。我们首先分析了由噪声引起的边缘扩展函数（ESF）回归中的不适定性。其次，我们提出一种正则化斜边法，通过纳入蒂霍诺夫正则化项来解决此问题。结合不同精度权重，利用变分原理求解ESF，并使用正则化后的ESF估计MTF。针对高斯噪声、伽马噪声和瑞利噪声对正则化斜边法进行了验证。结果表明，我们的方法平均提高了0.01 - 9.02%的精度，平均提高了4.33%。所提出的方法比斜边法对噪声更具鲁棒性且更准确。
