def plot_zernike_wfe(indices_coeffs):
'''
Quickly plots a sum of given Zernike polynomial terms.
Parameters:
indices_coeffs (list): List containing tuples of the kind (j, coeff), where j is the Zernike poylnomial index according to Noll's convention
Returns:
-
'''
x = np.arange(-1, 1, 0.05)
y = np.arange(-1, 1, 0.05)
wfe_img = np.zeros((len(x), len(y)))
for counterx, elx in enumerate(x):
for countery, ely in enumerate(y):
# perform transformation to polar coordinates
rho = np.sqrt(elx**2+ely**2)
theta = np.arctan2(ely, elx)
# calculate image
if rho <= 1:
wfe_img[counterx][countery] = float(wfe(indices_coeffs, rho, theta, 1))
# plot image
plt.imshow(wfe_img)
plt.colorbar()
plt.title("Aberrated Wavefront")
plt.xlabel("x")
plt.ylabel("y")
plt.xticks([0, len(x)/2, len(x)-1], [-1, 0, 1])
plt.yticks([0, len(y)/2, len(y)-1], [-1, 0, 1])
plt.show()
def aperture(D=1., lam=1, a0=1., list_wfe=None, n=100):
'''
Returns a numpy array containing a circular aperture, possibly including wavefront aberrations.
Parameters:
D (float): Aperture diameter in meters
lam (int): Wavelength in meters
a0 (float): Initial amplitude
list_wfe(list): List describing the wavefront error
n (int): Number to specify shape of array, i. e. n x n
Returns:
(array): Complex array containing a circular aperture of diameter D
'''
# create 1-dimensional x and y arrays
i = np.arange(1, n)
x = i - n / 2
y = n / 2 - i
# convert to 2-dimensional arrays
X = x[:, np.newaxis]
Y = y[np.newaxis, :]
# define radius
R = D / 2
# define ideal aperture
aperture = a0 * (X**2 + Y**2 < R**2).astype(complex)
# add wavefront error if a list of terms is given
if list_wfe is not None:
for counterx, elx in enumerate(x):
for countery, ely in enumerate(y):
aperture[countery, counterx] *= np.exp(-2 * np.pi * 1j * float(
wfe(list_wfe, np.sqrt(elx**2 + ely**2), np.arctan2(
ely, elx), R)) / lam)
return aperture
# # solve for roots, i. e. real part of amplitude a0
# a0_real = fsolve(func, 1)[0]
# # define full complex amplitude a0
# a0_ab = a0_real + a0_imag*1j
'''amplitude normalization common'''
for counterx, elx in enumerate(x):
for countery, ely in enumerate(y):
# perform transformation to polar coordinates
ra = np.sqrt(elx**2 + ely**2)
the = np.arctan2(ely, elx)
# specify wavefront error
wfe_gen = float(wfe(list_wfe, ra, the, D1_2))
# define aprture 1
aperture1_id_norm[counterx][countery] = 1 * np.heaviside(
D1_2 - ra, 1) * np.heaviside(ra, 1)
aperture1_ab_norm[counterx][countery] = 1 * np.heaviside(
D1_2 - ra, 1) * np.heaviside(ra, 1) * np.exp(
-2 * np.pi * 1j * wfe_gen / lam)
# normalize this amplitude to unit intensity
aperture1_common = aperture1_id_norm + aperture1_ab_norm
amplitude_temp = np.sum(aperture1_common)
# choose initial amplitude imaginary part because of degeneracy
a0_imag = amplitude_temp.imag
e_diff = np.zeros((len(x), len(y)), dtype=complex)
coeff = get_coeff_from_rms(rms, list_wfe)
for index in range(len(list_wfe)):
list_wfe[index] += (coeff, )
'''amplitude normalization common'''
for counterx, elx in enumerate(x):
for countery, ely in enumerate(y):
# perform transformation to polar coordinates
ra = np.sqrt(elx**2 + ely**2)
the = np.arctan2(ely, elx)
# specify wavefront error
wfe_gen = float(wfe(list_wfe, ra, the, D1_2))
# define aprture 1
aperture1_id_norm[counterx][countery] = 1 * np.heaviside(
D1_2 - ra, 1) * np.heaviside(ra, 1)
aperture1_ab_norm[counterx][countery] = 1 * np.heaviside(
D1_2 - ra, 1) * np.heaviside(ra, 1) * np.exp(
-2 * np.pi * 1j * wfe_gen / lam)
# normalize this amplitude to unit intensity
aperture1_common = aperture1_id_norm + aperture1_ab_norm
amplitude_temp = np.sum(aperture1_common)
# choose initial amplitude imaginary part because of degeneracy
a0_imag = amplitude_temp.imag