Python实现矩形孔的夫朗和费衍射图样输出

以下是 Python 实现矩形孔的夫朗和费衍射图样输出的示例代码：

import numpy as np
import matplotlib.pyplot as plt

def rect(x, y, w, h):
    return np.logical_and(np.logical_and(x >= -w/2, x <= w/2), np.logical_and(y >= -h/2, y <= h/2))

def fraunhofer_rect(wavelength, a, L, N):
    x = np.linspace(-a/2, a/2, N)
    y = np.linspace(-a/2, a/2, N)
    X, Y = np.meshgrid(x, y)
    aperture = rect(X, Y, L, L)
    aperture_ft = np.fft.fftshift(np.fft.fft2(aperture))
    pattern = np.abs(aperture_ft)**2
    dx = x[1] - x[0]
    dy = y[1] - y[0]
    kx = 2*np.pi*np.fft.fftshift(np.fft.fftfreq(N, dx))
    ky = 2*np.pi*np.fft.fftshift(np.fft.fftfreq(N, dy))
    KX, KY = np.meshgrid(kx, ky)
    scaling = 1.0/(wavelength*L)
    pattern = np.fft.fftshift(pattern)
    pattern = pattern/scaling**2
    return pattern, kx, ky

def fresnel_rect(wavelength, a, L, N, z):
    x = np.linspace(-a/2, a/2, N)
    y = np.linspace(-a/2, a/2, N)
    X, Y = np.meshgrid(x, y)
    aperture = rect(X, Y, L, L)
    aperture_ft = np.fft.fftshift(np.fft.fft2(aperture))
    dx = x[1] - x[0]
    dy = y[1] - y[0]
    kx = 2*np.pi*np.fft.fftshift(np.fft.fftfreq(N, dx))
    ky = 2*np.pi*np.fft.fftshift(np.fft.fftfreq(N, dy))
    KX, KY = np.meshgrid(kx, ky)
    scaling = np.exp(1j*np.pi*wavelength*z*(KX**2 + KY**2))
    pattern_ft = aperture_ft*scaling
    pattern = np.abs(np.fft.ifft2(np.fft.ifftshift(pattern_ft)))**2
    dxp = wavelength*z/(L*N*dx)
    dyp = wavelength*z/(L*N*dy)
    xp = np.linspace(-wavelength*z/L, wavelength*z/L, N)
    yp = np.linspace(-wavelength*z/L, wavelength*z/L, N)
    return pattern, xp, yp

# Fraunhofer diffraction
pattern, kx, ky = fraunhofer_rect(633e-9, 0.1, 2e-3, 1024)
plt.imshow(pattern, extent=[kx.min(), kx.max(), ky.min(), ky.max()], cmap='gray')
plt.xlabel('kx (1/m)')
plt.ylabel('ky (1/m)')
plt.title('Fraunhofer diffraction pattern')
plt.show()

# Fresnel diffraction
pattern, xp, yp = fresnel_rect(633e-9, 0.1, 2e-3, 1024, 1.0)
plt.imshow(pattern, extent=[xp.min(), xp.max(), yp.min(), yp.max()], cmap='gray')
plt.xlabel('x (m)')
plt.ylabel('y (m)')
plt.title('Fresnel diffraction pattern (z = 1 m)')
plt.show()

这段代码中，`rect` 函数用于生成矩形孔的孔径函数，`fraunhofer_rect` 函数用于计算矩形孔的 Fraunhofer 衍射图样，`fresnel_rect` 函数用于计算矩形孔的 Fresnel 衍射图样。在主程序中，我们先输出 Fraunhofer 衍射图样，然后输出 Fresnel 衍射图样。你可以根据自己的需要修改函数的输入参数来生成不同的图像。