def H(self, pol=None):
if pol is None: # For normalization
cc = sh.SHCoeffs([1, 0, 0, -1 / np.sqrt(5), 0, 0]) / np.sqrt(
4 * np.pi)
if self.optical_axis == [1, 0, 0]: # x-illumination
cc = cc.rotate()
return cc
out = []
for j in range(6):
l, m = util.j2lm(j)
theta, phi = util.xyz2tp(*pol)
if l == 0:
cc = 1.0
else:
cc = 0.4
out.append(cc * util.spZnm(l, m, theta, phi))
return sh.SHCoeffs(out)
def h(self):
if self.illuminate_all:
return tf.TFCoeffs([[1.0, 0, 0, 0, 0, 0], 6 * [0], 6 * [0]])
n0 = [
1 + (self.alpha**2) / 4, 0, 0,
(-1 + (self.alpha**2) / 2) / np.sqrt(5), 0, 0
]
n_2 = 6 * [0]
n2 = 6 * [0]
if self.polarizer is not None:
n_2 = [0, np.sqrt(3 / 5), 0, 0, 0, 0]
n2 = [0, 0, 0, 0, 0, np.sqrt(3 / 5)]
if self.optical_axis == [1, 0, 0]: # x-illumination
n0 = sh.SHCoeffs(n0).rotate().coeffs
n_2 = sh.SHCoeffs(n_2).rotate().coeffs
n2 = sh.SHCoeffs(n2).rotate().coeffs
return tf.TFCoeffs([n0, n_2, n2])
def H(self, x, y, z):
if self.detect_all:
return tf.TFCoeffs([[1.0, 0, 0, 0, 0, 0], 6 * [0], 6 * [0]])
# Find cylindrical coordinates based on view
if self.optical_axis == [0, 0, 1]: # z-detection
nu = np.sqrt(x**2 + y**2)
phi_nu = np.arctan2(y, x)
z_ax = z
elif self.optical_axis == [1, 0, 0]: # x-detection
nu = np.sqrt(y**2 + z**2)
phi_nu = np.arctan2(z, y)
z_ax = x
A1 = self.A1
A2 = self.A2
n0 = [
A1(nu) + (self.alpha**2 / 4) * A2(nu), 0, 0,
(-A1(nu) + (self.alpha**2 / 2) * A2(nu)) / np.sqrt(5), 0, 0
]
n_2 = 6 * [0]
n2 = 6 * [0]
if self.polarizer:
# TODO: Update these (unused for now)
n_2 = [
2 * C(nu) * np.sin(2 * phi_nu), -np.sqrt(0.6) * A(nu), 0,
(4.0 / np.sqrt(5)) * C(nu) * np.sin(2 * phi_nu), 0, 0
]
n2 = [
2 * C(nu) * np.cos(2 * phi_nu), 0, 0,
(4.0 / np.sqrt(5)) * C(nu) * np.cos(2 * phi_nu), 0,
np.sqrt(0.6) * A(nu)
]
if self.optical_axis == [1, 0, 0]: # x-detection
n0 = sh.SHCoeffs(n0).rotate().coeffs
n_2 = sh.SHCoeffs(n_2).rotate().coeffs
n2 = sh.SHCoeffs(n2).rotate().coeffs
ax_weight = np.exp(-(z_ax**2) / (2 * (self.sigma_ax**2)))
return sh.SHCoeffs(n0) * ax_weight
def h(self, x, y, z):
if self.detect_all:
return tf.TFCoeffs([[1.0, 0, 0, 0, 0, 0], 6 * [0], 6 * [0]])
# Find cylindrical coordinates based on view
if self.optical_axis == [0, 0, 1]: # z-detection
r = np.sqrt(x**2 + y**2)
phi = np.arctan2(y, x)
z_ax = z
elif self.optical_axis == [1, 0, 0]: # x-detection
r = np.sqrt(y**2 + z**2)
phi = np.arctan2(z, y)
z_ax = x
a1 = self.a1
a2 = self.a2
n0 = [
a1(r) + (self.alpha**2 / 4) * a2(r), 0, 0,
(-a1(r) + (self.alpha**2 / 2) * a2(r)) / np.sqrt(5), 0, 0
]
n_2 = 6 * [0]
n2 = 6 * [0]
if self.polarizer:
n_2 = [
2 * a2(r) * np.sin(2 * phi), -np.sqrt(0.6) * a1(r), 0,
(4.0 / np.sqrt(5)) * a2(r) * np.sin(2 * phi), 0, 0
]
n2 = [
2 * a2(r) * np.cos(2 * phi), 0, 0,
(4.0 / np.sqrt(5)) * a2(r) * np.cos(2 * phi), 0,
np.sqrt(0.6) * a1(r)
]
if self.optical_axis == [1, 0, 0]: # x-detection
n0 = sh.SHCoeffs(n0).rotate().coeffs
n_2 = sh.SHCoeffs(n_2).rotate().coeffs
n2 = sh.SHCoeffs(n2).rotate().coeffs
return tf.TFCoeffs([n0, n_2, n2])
def plot_SVS(self,
filename='svs.pdf',
n_px=2**6,
marks=[[1e-5, 0], [0.5, 0], [1.0, 0], [1.5, 0]]):
print('Plotting: ' + filename)
# Layout windows
inches = 1.5
rows = self.sigma.shape[-1] + 1
cols = len(marks) + 1
f, axs = plt.subplots(rows,
cols,
figsize=(inches * cols, inches * (rows - 0.75)),
gridspec_kw={
'hspace': 0.05,
'wspace': 0.10,
'height_ratios': [1, 1, 1, 0.05]
})
# Label top row with arrow
axs[0, 0].annotate(
'',
xy=(-0.03, 1.1),
xytext=(0.55, 1.1),
textcoords='axes fraction',
xycoords='axes fraction',
ha='center',
va='center',
arrowprops=dict(arrowstyle='<->, head_width=0.05, head_length=0.1',
connectionstyle="arc3",
linewidth=0.5),
)
axs[0, 0].annotate(r'$2\textrm{NA}/\lambda$',
xy=(0, 0),
xytext=(0.25, 1.2),
textcoords='axes fraction',
xycoords='axes fraction',
ha='center',
va='center',
fontsize=7)
# Top row singular values
for j, ax in enumerate(axs[:-1, 0]):
ax.axis('off')
ax.annotate('$j=' + str(j) + '$',
xy=(1, 1),
xytext=(-0.15, 0.5),
textcoords='axes fraction',
ha='center',
va='center',
rotation=90)
extent = [-2, 2, -2, 2]
origin = 'lower'
ax.imshow(self.sigma[:, :, j] / self.sigma_max,
cmap="bwr",
vmin=-1,
vmax=1,
interpolation='none',
extent=extent,
origin=origin)
ax.set_xlim([-2.05, 2.05])
ax.set_ylim([-2.05, 2.05])
levels = [-0.1, -1e-5, 1e-5, 0.1]
ct = ax.contour(self.sigma[:, :, j] / self.sigma_max,
levels,
colors='k',
linewidths=0.5,
extent=extent,
origin=origin)
for mark in marks:
ax.plot(mark[0] * np.cos(mark[1]),
mark[0] * np.sin(mark[1]),
'xk',
ms=2.5,
mew=0.5)
# Colorbars
X, Y = np.meshgrid(np.linspace(0, 1, 100), np.linspace(0, 1, 100))
axs[-1, 0].imshow(X,
cmap="bwr",
vmin=-1,
vmax=1,
interpolation='none',
extent=[0, 1, 0, 1],
origin='lower',
aspect='auto')
axs[-1, 0].contour(
X,
levels,
colors='k',
linewidths=0.5,
extent=[0, 1, 0, 1],
origin='lower',
)
axs[-1, 0].set_xlim([0, 1])
axs[-1, 0].set_ylim([0, 1])
axs[-1, 0].tick_params(direction='out', bottom=True, top=False)
axs[-1, 0].xaxis.set_ticks([0, 0.5, 1.0])
axs[-1, 0].yaxis.set_ticks([])
for j, ax in enumerate(axs[-1, 1:]):
ax.axis('off')
# For saving singular function pngs
folder = 'singular'
if not os.path.exists(folder):
os.makedirs(folder)
# Object space singular functions
for j, ax in np.ndenumerate(axs[:-1, 1:]):
if self.det.optical_axis == [0, 0, 1]: # z-detection
u, s, v = self.calc_point_SVD(marks[j[1]][0], marks[j[1]][1],
0)
elif self.det.optical_axis == [1, 0, 0]: # x-detection
u, s, v = self.calc_point_SVD(0, marks[j[1]][0],
marks[j[1]][1])
# Labels
if j[0] == 0:
rho_label = str(marks[j[1]][0])
if marks[j[1]][0] < 1e-3:
rho_label = '0'
ax.annotate(r'$\rho = ' + rho_label + '$',
xy=(1, 1),
xytext=(0.5, 1.15),
textcoords='axes fraction',
ha='center',
va='center')
ax.annotate(r'$\phi_{\rho} = ' + str(marks[j[1]][1]) + '$',
xy=(1, 1),
xytext=(0.5, 0.95),
textcoords='axes fraction',
ha='center',
va='center')
ax.axis('off')
ax.annotate('$\sigma=' +
'{:.2f}'.format(s[j[0]] / self.sigma_max) + '$',
xy=(1, 1),
xytext=(0.5, 0),
textcoords='axes fraction',
ha='center',
va='center')
# Create singular function plots
sh = shcoeffs.SHCoeffs(u[:, j[0]])
shfilename = folder + '/' + str(j[0]) + str(j[1]) + '.png'
sh.plot_dist(filename=folder + '/' + str(j[0]) + str(j[1]) +
'.png',
r=1.1)
from PIL import Image
im1 = np.asarray(Image.open(shfilename))
ax.imshow(im1, interpolation='none')
f.savefig(filename, bbox_inches='tight')