Zernike

Python code to handle complex- and real-valued Zernike polynomials. This module was part of enzpy but will be further developed here instead.

Installation

You can install zernike using pip

pip install --user zernike

Example: plot the Zernike pyramid

python -m zernike.pyramid

Example: plot the first 9 Zernike polynomials

import numpy as np
import matplotlib.pyplot as plt
from zernike import RZern

cart = RZern(6)
L, K = 200, 250
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)

c = np.zeros(cart.nk)
plt.figure(1)
for i in range(1, 10):
    plt.subplot(3, 3, i)
    c *= 0.0
    c[i] = 1.0
    Phi = cart.eval_grid(c, matrix=True)
    plt.imshow(Phi, origin='lower', extent=(-1, 1, -1, 1))
    plt.axis('off')

plt.show()

Example: fit Zernike polynomials in Cartesian coordinates

import numpy as np
import matplotlib.pyplot as plt
from zernike import RZern

cart = RZern(6)
L, K = 200, 250
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
cart.make_cart_grid(xv, yv)

c0 = np.random.normal(size=cart.nk)
Phi = cart.eval_grid(c0, matrix=True)
c1 = cart.fit_cart_grid(Phi)[0]
plt.figure(1)
plt.subplot(1, 2, 1)
plt.imshow(Phi, origin='lower', extent=(-1, 1, -1, 1))
plt.axis('off')
plt.subplot(1, 2, 2)
plt.plot(range(1, cart.nk + 1), c0, marker='.')
plt.plot(range(1, cart.nk + 1), c1, marker='.')

plt.show()

Example: fit Zernike polynomials in polar coordinates

import numpy as np
from zernike import RZern, FitZern

pol = RZern(6)
L, K = 200, 250
ip = FitZern(pol, L, K)

pol.make_pol_grid(ip.rho_j, ip.theta_i)
c_true = np.random.normal(size=pol.nk)
Phi = pol.eval_grid(c_true)
c_hat = ip.fit(Phi)
R = np.zeros((pol.nk, 3))
R[:, 0] = c_true
R[:, 1] = c_hat
R[:, 2] = np.abs(c_true - c_hat)
print(R)
np.linalg.norm(c_true - c_hat)/np.linalg.norm(c_true)

Installation from the GitHub repository

• You should first install the following requirements:
  • Anaconda for Python 3. This includes Python as well as some necessary scientific libraries.
  • Git. This is necessary for the automatic version numbering of this package. Also, make sure you choose Git from the command line and also 3rd-party software in Adjusting your PATH environment.
• Clone this repository using Git. From any folder in File Explorer, right-click and hit Git Bash here. Paste git clone https://github.com/jacopoantonello/zernike and hit enter. Do not use GitHub's Download ZIP button above, as the installation script will not work in that case.
• Finally, double-click on install.bat.

Tests

python -m zernike.test