1 import cv2
 2 import numpy as np
 3 import math
 4 
 5 # 讀取圖片
 6 img = cv2.imread('lena.pgm', cv2.IMREAD_GRAYSCALE) / 255  # 歸一化
 7 cv2.namedWindow("lena", cv2.WINDOW_AUTOSIZE)
 8 cv2.imshow("lena", img)
 9 print("原圖:", img)
10 # cv2.waitKey(0)
11 # cv2.destroyAllWindows()
12 
13 N = 512
14 m, n = img.shape[0], img.shape[1]
 
15 lamd = 623*10**(-9)
16 d0 = 0.1
17 d = 0.01
18 f = 0.025
19 di = f * d0 / (d0 - f)  # 透鏡成像原理 1/d0 + 1/di = 1/f
20 
21 # 進行N*N取樣,根據Shannon取樣定理
22 dx0 = N / m
23 dy0 = N / n
24 dks = lamd * d0 / (N * dx0)
25 dep = lamd * d0 / (N * dy0)
26 dfx = 1 / (N * dx0)
27 dfy = 1 / (N * dy0)
28 
29 # 相位因子
30 yinzi_1 = np.zeros((m, n), dtype=complex)
 
31 for k in range(m):
32     for l in range(n):
33         yinzi_1[k][l] = np.exp(1j * math.pi * ((k * dx0)**2 + (l * dy0)**2) / (lamd * d0))
34 # 明文資訊進行離散菲涅爾變換
35 U0 = np.fft.fft2(img * yinzi_1)
36 # print("U0:", U0)
37 
38 # 透鏡透過率函式
39 t = np.zeros((m, n), dtype=complex)
40 for i in range(m):
41     for j in
 
 range(n):
42         t[i][j] = np.exp((-1j) * math.pi * ((i * dks)**2 + (j * dep)**2) / (lamd * f))
43 
44 # 透鏡前表面轉換到透鏡後表明經過透鏡透過率函式的調製
45 UL2 = U0 * t
46 
47 # 相位因子
48 yinzi_3 = np.zeros((m, n), dtype=complex)
49 for i in range(m):
50     for j in range(n):
51         yinzi_3[i][j] = np.exp(1j * math.pi * ((i * dks)**2 + (j * dep)**2) / (lamd * di))
52 # 透鏡後表明資訊進行離散菲涅爾變換
53 U0_ = np.fft.fft2(UL2 * yinzi_3)
54 # 結果是複數形式，取絕對值提取振幅並且進行歸一化處理
55 U0_s = np.abs(U0_) / np.max(np.abs(U0_))
56 # print("原圖:", U0_)
57 
58 # 顯示影象，凸透鏡成像的結果是倒立的影象
59 cv2.namedWindow("origin", cv2.WINDOW_AUTOSIZE)
60 cv2.imshow("origin", U0_s)
61 cv2.waitKey(0)
62 cv2.destroyAllWindows()

結果顯示 圖片用的是512*512的lena灰度影象