利用反摺積求得點擴散函數進行光學顯微鏡影像還原術

Abstract

本研究探討在不改變光學顯微鏡系統下，求得更接近樣品訊號，且突破繞射極限的反摺積顯微術。原理為將光學顯微鏡量測之影像視為點擴散函數(PSF)與樣品訊號之摺積，在已知樣品訊號的情況下，可透過反摺積運算求得PSF。本論文使用兩種方式定義光學顯微鏡系統的PSF，其一如前述以反摺積運算解得PSF，相異於多數文獻使用樣品尺度小於繞射極限的顯微鏡影像作為PSF。經過將定義之PSF代入詳細推導並修正之最大期望演算法與最大似然估計(EM-MLE)後可求得樣品實際訊號。比較此訊號可知，以我們的方法解得之PSF代入EM-MLE後，在形貌與演算速度上都較多數文獻使用的方法優異。最後以模擬確認其差異確實來自於取得PSF方法的不同。另外本研究亦指出系統雜訊為帕松雜訊，並進一步討論雜訊對於反摺積顯微術的影響。

In our research, we use deconvolution microscopy system to obtain sample signal which is closer to the original sample morphology and non-diffraction limited in the maintenance of microscope optical system. The principle of deconvolution microscopy is consider microscopy image as a convolution result of point spread function (PSF) and sample signal. In the case of known sample signals, PSF can be obtained by deconvolution algorithm. In this experiment, we used two method to define PSF of microscope optical system. First we bring PSF into expectation–maximization algorithm and maximum-likelihood estimation(EM-MLE) after derivation the actual sample signal can be obtained. The second method is directly use the microscope image of the sample which is less than the diffraction limit as PSF. Result shows that not only morphology but also algorithmic speed used in the first method are both superior to the second method. Finally, we use computer simulation to confirm the result of the difference really dependent on two method we use to obtain the sample signal. In addition, in our research also find out the noise in our system can be describe as Poisson noise and further discuss the influence to the deconvolution microscopy.