光子学报, 2014, 43 (12): 1212003, 网络出版: 2014-12-26
二维调制传递函数及其在波前差检测方面的应用
Two Dimensional Modulation Transfer Function and Its Application in Wavefront Aberration Detection
几何光学 像质分析 波前差 调制传递函数 随机图像 功率谱密度 数值积分 Geometric optics Image quality evaluation Wavefront aberration Modulation transfer function Random image Power spectral density Numerical integration
摘要
光学系统像质分析在光学系统设计、加工和装调过程中具有重要意义.像质分析常用的方法有调制传递函数法和波前差法.对于高分辨率光学系统, 传统的一维调制传递函数由于只提供了一维空间频率信息, 因此在像质检测时有一定的局限性.本文基于随机数图像的傅里叶功率谱密度理论, 提出了一种利用随机数图像作为目标物来测量成像光学系统二维调制传递函数的方法;通过利用Newton-Cotes求积公式, 对有像差系统的光学传递函数计算公式做进一步推导, 提出了利用实际成像光学系统的二维调制传递函数值直接计算系统波前差的算法.实验结果表明, 二维调制传递函数较之一维调制传递函数更能真实地反应成像光学系统的成像性能;利用二维调制传递函数计算得到的波前差与理论波前差在轮廓上有较好的一致性, 可以作为实际系统波前差分析的一条新途径.
Abstract
Image quality evaluation is an important work to optical system design and manufacture. Generally, modulation transfer function and wavefront aberration are two common evaluation ways. For high resolution optical systems, the traditional one-dimensional modulation transfer function has some shortcomings when evaluating their image quality because it only provide one dimensional spatial frequency information. Based on the Fourier power spectrum density theory of random images, a method to measure the two-dimensional modulation transfer function of optical systems was proposed by setting random images as the target. An algorithm of using two-dimensional modulation transfer function to calculate the wavefront aberration directly was developed through simplifying the formula of optical transfer function. In this part, the Newton-Cotes integral formula was used. The experimental results show that the two-dimensional modulation transfer function is better than the one-dimensional modulation transfer function in revealing the true characteristics of imaging optical systems, and that the wavefront aberration calculated with the algorithm have the same contour with the theoretical wavefront aberration. It can be a potential way to measure wavefront aberration of optical systems.
康吉强, 程雪岷, 郝群. 二维调制传递函数及其在波前差检测方面的应用[J]. 光子学报, 2014, 43(12): 1212003. KANG Ji-qiang, CHENG Xue-min, HAO Qun. Two Dimensional Modulation Transfer Function and Its Application in Wavefront Aberration Detection[J]. ACTA PHOTONICA SINICA, 2014, 43(12): 1212003.