得到37项zernike系数后如何复现波前图

如何通过37项系数计算波前图，python或者matlab有代码吗

直接在ZEMAX里面加载一个面型就可以了，选择泽妮可系数就好了

如果用代码呢，比如用python如何通过这37项系数复现波前

# Python代码实现Zernike 37项系数重建波前图
import numpy as np
import matplotlib.pyplot as plt
from scipy.special import factorial

def zernike_radial(n, m, rho):
    R = np.zeros_like(rho)
    for k in range((n - abs(m)) // 2 + 1):
        R += rho**(n - 2 * k) * ((-1)**k * factorial(n - k)) /
              (factorial(k) * factorial((n + abs(m)) // 2 - k) * factorial((n - abs(m)) // 2 - k))
    return R

def zernike_polynomial(n, m, rho, theta):
    if m > 0:
        return zernike_radial(n, m, rho) * np.cos(m * theta)
    elif m < 0:
        return zernike_radial(n, -m, rho) * np.sin(-m * theta)
    else:
        return zernike_radial(n, m, rho)

def wavefront_from_zernike(coefficients, grid_size=100):
    x = np.linspace(-1, 1, grid_size)
    y = np.linspace(-1, 1, grid_size)
    X, Y = np.meshgrid(x, y)
    rho = np.sqrt(X**2 + Y**2)
    theta = np.arctan2(Y, X)
   
    wavefront = np.zeros_like(X)
    zernike_map = [
        (0, 0), (1, -1), (1, 1), (2, 0), (2, -2), (2, 2), (3, -1), (3, 1), (3, -3), (3, 3),
        (4, 0), (4, -2), (4, 2), (4, -4), (4, 4), (5, -1), (5, 1), (5, -3), (5, 3), (5, -5),
        (5, 5), (6, 0), (6, -2), (6, 2), (6, -4), (6, 4), (6, -6), (6, 6), (7, -1), (7, 1),
        (7, -3), (7, 3), (7, -5), (7, 5), (7, -7), (7, 7)
    ]
    for i, (n, m) in enumerate(zernike_map[:len(coefficients)]):
        wavefront += coefficients[i] * zernike_polynomial(n, m, rho, theta)
   
    wavefront[rho > 1] = np.nan
    return wavefront

coefficients = np.random.randn(37)  # 随机生成37项Zernike系数
wavefront = wavefront_from_zernike(coefficients)

plt.imshow(wavefront, extent=[-1, 1, -1, 1], cmap='jet')
plt.colorbar()
plt.title('Wavefront Reconstruction from Zernike Coefficients')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()

您好，我用了你这个代码，为什么我复现出的和zemax画的有差别，大约图像旋转了90度

应是坐标问题，旋转一下应该就可以