利用Slanted-edge方法以及相位回復演算法量測光學系統的成像像差

To measure the aberrations of optical system by Slanted-edge method and Phase retrieval algorithm

李鴻儒(Hong-ru Li)

指導教授 ： 梁肇文

國立中央大學/理學院/光電科學與工程學系/碩士(2014年)

摘要

本論文從傅氏光學來分析光學系統的相位函數，也就是成像像差。首先利用Slanted edge量測方法，並加以改進量測方法使得所獲取的量測資訊能夠更不受雜訊的影響。因為量測方法所得到的資訊就是線擴散函數(Line Spread Function,以下簡稱LSF)或者是點擴散函數(Point Spread Function,以下簡稱PSF)，此兩函數在傅氏光學中對於透鏡的成像分析扮演著很重要的角色。在傅氏光學中光瞳函數(Pupil function)與剛剛所提到的LSF與PSF為傅立葉轉換的關係，因為存在著傅立葉轉換的關係，所以可以藉由相位回復演算法進行迭代運算出LSF和PSF所代表的相位函數，而此相位函數也代表著光學系統的成像像差。因此藉由改進後的Slanted edge量測方法以及相位回復演算法可以得到光學系統的成像像差。

關鍵字

相位回復演算法 ； 成像像差

並列摘要

This thesis discusses the analysis of phase function of optical system in the field of Fourier optics and this phase function is also called the imaging aberrations. Firstly, the experiment is by means of the Slanted-edge method and then improved the method so that the measured information can be obtained free from the impact of noise. The information which is obtained from the experiment is the Line spread function or the Point spread function. These two functions play the important role in the analysis of lens in the Fourier optics. In the Fourier optics, the Fourier transform of the pupil function are the Point spread function. Because there are the Fourier transform between the pupil function and Point spread function, we can utilize the phase retrieval algorithm to carry out the phase function of the Point spread function or the Line spread function. At the beginning, the phase function is the imaging aberrations of the optical system. Therefore, the thesis can discusses the imaging aberration of the optical system by the improved Slanted edge method and the phase retrieval algorithm.

並列關鍵字

Phase retrieval algorithm ； Slanted-edge method ； LSF ； PSF ； MTF

參考文獻

[1] D. Gabor, “A New Microscopic Principle”, Nature 161(4098), pp. 777-778, 1948.

[2] W. Hoppe, “Principles of electron structure research at atomic resolution using conventional electron microscope for the measurement of amplitudes and phases”, Acta Cryst, A26, pp, 414-429, 1970.

[5] J. R. Fienup, “Phase retrieval algorithm: a comparison”, Applied O　ptics, 21(15), 1982.

[6] J. R. Fienup, “Phase retrieval with continuous version of hybrid input-output”, OSA, 2003.

[7] J. W, Goodman, Introduction to Fourier Optics, 2nded, Mc Graw-Hill.