以Gerchberg-Saxton方法和近遠場二階相關性質重建被毛玻璃遮蔽的物體影像之研究

Abstract

光的電場數學形式是√(I(x,y))×e^(i×∅(x,y))，我們只能使用量測光強度的攝影機或是偵測器來量物體的近場光強度I_N(x,y)和物體的遠場繞射光強度I_F(x,y)；但是藉由被稱為Gerchberg-Saxton Method的傅立葉疊代法，我們可產生一組各自帶有相位資訊之複數近場√(I_N (x,y))×e^(i×∅_N (x,y))、複數遠場√(I_F (x,y))×e^(i×∅_F (x,y))。這個方法一般都是應用在沒有擾動介質(毛玻璃)之簡單系統中，因此初始條件e^(i×Constant)可以被假設為空間均勻的。 然而，如果我們想要把傅立葉配對疊代法(Gerchberg-Saxton Method)應用在有擾動介質(毛玻璃)的系統之下，我們就需要猜一個適當的初始條件。在本論文中，我們將光學二階相關性質應用在找出近場影像、遠場影像之相關區域，並藉由近遠場相關區域找出毛玻璃相位。為了驗證其解的正確性，我們以毛玻璃干涉實驗來確認其計算結果，並得到很好的驗證。在論文的最後一個章節中，我們利用改良的Gerchberg-Saxton Method找出適當的近遠場電場，並且試著重建被毛玻璃所擋住的物體形狀。

The mathematical form of light field is known as √(I(x,y))×e^(i×∅(x,y)). We can only measure the near-field light intensity I_N(x,y) and far-field intensity I_F(x,y) of an object with a simple intensity camera or detector. With the so-called Gerchberg-Saxton Method, we could generate a pair of complex numbers of √(I_N (x,y))×e^(i×∅_N (x,y)) and √(I_F (x,y))×e^(i×∅_F (x,y)), each has its own phase information. This iterative method is generally being used in systems without disturbing medium_(such as ground glass), so the initial- guessed e^(i×Constant) could be assumed to be spatially uniform. However, if we want to use this method in system with disturbing medium_(such as ground glass), we need to guess an appropriate initial condition. In this thesis, we find the correlation between the region in the near-field and the region in the far-field using optical second order correlation. With this information, we obtain the phase introduced by the ground glass. To verify the validity of the result, we also perform an interference experiment and find very good agreement. In the last chapter of this thesis we use the improved Gerchberg-Saxton Method to match the near-field and far-field light field. We also try to reconstruct the image of the object blocked by a ground glass.