以光学中圆孔的弗朗禾费衍射为例

matlab

N = 256; % grid numberD = 1; % diameter of aperture pupil [m]L = 5.0*D/1.22; % Airy disk occupies 5 pixels/grids [m]x = linspace(-L/2.0, L/2.0, N);y = linspace(-L/2.0, L/2.0, N);[xm, ym] = meshgrid(x, y);r = sqrt(xm.^2 + ym.^2); % 注意加.AP = double((r <= D/2.0)); psf = abs(fftshift(fft2(AP))).^2;subplot(121);imagesc(AP);title('Pupil');axis square; colorbar;subplot(122);imagesc(psf);title('Point Spread Function');axis square; colorbar;

python

先生成孔径函数

import tensorflow as tfimport numpy as npimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3Dfrom scipy.io import savematprint(tf.__version__) # 2.1.0# 生成Pupil函数N = 256D = 1L = 10.0*D/1.22x = np.linspace(-L/2.0, L/2.0, N) y = np.linspace(-L/2.0, L/2.0, N)[xm, ym] = np.meshgrid(x, y)r = (xm**2.0 + ym**2.0)**0.5AP = np.double((r <= D/2.0)) print(AP.dtype) # float64hf = plt.figure()ax = Axes3D(hf)ax.plot_surface(xm, ym, AP, cmap='jet')ax.view_init(90, 0)savemat('pupil.mat', mdict={'AP': AP}) # 保存数据到matlab中验证

输出

2.1.0

float64

numpy ===> np.fft.fft2

psf = np.fft.fftshift(np.fft.fft2(AP))psf = (np.abs(psf))**2print(psf.dtype)print(np.max(psf))hf2 = plt.figure()ax2 = Axes3D(hf2)ax2.plot_surface(xm, ym, psf, cmap='jet')ax2.view_init(90, 0)savemat('psf.mat', mdict={'psf': psf})

输出

float64

571536.0与matlab的输出结果是对的上的

tensorflow ====>tf.fft2d(v1.) 或tf.signal.fft2d(v2.)

AP_t = plex(AP,tf.zeros_like(AP)) # 必须转化为复数print(AP_t.dtype)psf_t = tf.signal.fftshift(tf.signal.fft2d(AP_t)) psf_t = tf.square(tf.abs(psf_t))print(psf_t.dtype)psf_t = psf_t.numpy()print(psf_t.dtype)print(np.max(psf_t))hf3 = plt.figure()ax3 = Axes3D(hf3)ax3.plot_surface(xm, ym, psf_t, cmap='jet')ax3.view_init(90, 0)savemat('psf_t.mat', mdict={'psf_t': psf_t})

输出

<dtype: ‘complex128’>

<dtype: ‘float64’>tensorflow输出的数据类型

float64numpy输出的数据类型

571536.0与matlab的输出结果是对的上的

python的绘图效果不太好，但经与matlab的数值结果对比验证，两者是一致。matlab的绘图比较好看是进行了插值运算