def plot_wollaston(stokes):
data = np.empty(shape=[0, 2])
sys_mm = MuellerMat.SystemMuellerMatrix([cmm.WollastonPrism(), cmm.HWP()])
# Find data points from 0 to 2 * pi
for angle in np.arange(0, 2 * math.pi, 0.001):
sys_mm.master_property_dict['HalfwaveRetarder'][
'theta'] = math.degrees(angle)
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'o'
I1 = sys_mm.evaluate() @ stokes
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'e'
I2 = sys_mm.evaluate() @ stokes
data = np.append(data, [[math.degrees(angle), (I1[0] - I2[0])]],
axis=0)
# Plot the data points
plt.scatter(*data.T, s=1)
plt.title('Difference between Wollaston prism beams over HWP angle')
plt.ylabel(
'Difference between $\mathdefault{I^+}$ and $\mathdefault{I^-}$')
plt.xlabel('HWP angle (deg)')
ax = plt.gca()
ax.set_xlim(0, 360)
ax.set_xticks([0, 90, 180, 270, 360])
plt.show()
def wollaston(stokes):
sys_mm = MuellerMat.SystemMuellerMatrix([cmm.WollastonPrism(), cmm.HWP()])
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'o'
pos = sys_mm.evaluate() @ stokes
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'e'
neg = sys_mm.evaluate() @ stokes
return [pos, neg]
def on_sky(values):
i = np.empty(shape=[0, 1])
m_system = np.empty(shape=[0, 4])
sys_mm = MuellerMat.SystemMuellerMatrix([cmm.WollastonPrism(), cmm.HWP(), cmm.Rotator()])
# Calculate the Mueller matrices
for j in range(len(values)):
sys_mm.master_property_dict['HalfwaveRetarder']['theta'] = values[j][2]
sys_mm.master_property_dict['Rotator']['pa'] = values[j][3]
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'o'
row1 = sys_mm.evaluate()
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'e'
row2 = sys_mm.evaluate()
i = np.append(i, [[values[j][0]]], axis=0)
m_system = np.append(m_system, [row1[0]], axis=0)
i = np.append(i, [[values[j][1]]], axis=0)
m_system = np.append(m_system, [row2[0]], axis=0)
# Return a least-squares solution
return inv(np.transpose(m_system) @ m_system) @ np.transpose(m_system) @ i
def track_plot(targets):
# Initialize the start time, the targets, and the initial stokes vector
time = Time("2015-09-13")
step = np.arange(0, 1, 1 / 86400)
stokes = [[0], [1], [0], [0]]
hwp_angles = [0, 22.5]
derotator = cmm.DiattenuatorRetarder()
m3 = cmm.DiattenuatorRetarder()
sys_mm = MuellerMat.SystemMuellerMatrix(
[cmm.WollastonPrism(), derotator,
cmm.HWP(), m3,
cmm.Rotator()])
# Put in M3 - use astropy for altitude - diattenuating rotator - as a perfect mirror with an angle
# "perfect" - no retardance and no diattenuation
# Derotator - diattenuating retarder at a given parallactic angle
# Check diattenuating retarder form with goldstein and witzel
# Can calculate coefficients from material parameters - Fresnel reflection - index of refraction
# Fresnel coefficients - how to get the r values and possibly retardance
# use hour angle and dec to find the parallactic angle
# find the altitude given an hour angle and a target
for hwp in hwp_angles:
angle_plot = []
time_plot = []
sys_mm.master_property_dict['HalfwaveRetarder']['theta'] = hwp
for j in range(len(targets)):
wollaston_data = []
target = FixedTarget.from_name(targets[j])
# Calculate the parallactic angles and the altitudes
angles = np.degrees((keck.parallactic_angle(time + step,
target)).to_value())
altitudes = (keck.altaz(time + step, target)).alt.to_value()
# Calculate the Wollaston beams and parallactic angle as time passes
for pa, alt in zip(angles, altitudes):
sys_mm.master_property_dict['Rotator']['pa'] = pa
m3.properties['theta'] = alt
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'o'
I1 = sys_mm.evaluate() @ stokes
sys_mm.master_property_dict['WollastonPrism']['beam'] = 'e'
I2 = sys_mm.evaluate() @ stokes
wollaston_data.append(np.asscalar(I1[0] - I2[0]))
angle_plot.append(np.array([angles, wollaston_data]).T)
time_plot.append(
np.array([((time + step).to_datetime()), wollaston_data]).T)
# Plot the angle data points
for k in range(len(targets)):
x, y = angle_plot[k].T
plt.scatter(x, y, s=1, label=targets[k])
plt.title(
'Difference between Wollaston prism beams over parallactic angle with HWP at %.1f degrees'
% hwp)
plt.ylabel(
'Difference between $\mathdefault{I^+}$ and $\mathdefault{I^-}$')
plt.xlabel('Parallactic angle (deg)')
plt.legend(loc="upper left")
plt.show()
# Plot the time data points
for k in range(len(targets)):
x, y = time_plot[k].T
plt.scatter(x, y, s=1, label=targets[k])
plt.title(
'Difference between Wollaston prism beams over time with HWP at %.1f degrees'
% hwp)
plt.ylabel(
'Difference between $\mathdefault{I^+}$ and $\mathdefault{I^-}$')
plt.xlabel('Time (hour of day)')
plt.legend(loc="upper left")
ax = plt.gca()
ax.xaxis_date()
ax.xaxis.set_major_formatter(mdates.DateFormatter('%H:%M'))
ax.set_xlim(datetime.date(2015, 9, 13), datetime.date(2015, 9, 14))
plt.show()
from pyMuellerMat import MuellerMat import numpy as np from numpy.linalg import inv import matplotlib.pyplot as plt from scipy.optimize import curve_fit # Initialize the telescope's latitude keck = np.radians(19.8260) # Initialize the finalized system Mueller Matrix derotator = cmm.DiattenuatorRetarder() derotator.name = 'derotator' m3 = cmm.DiattenuatorRetarder() m3.name = 'm3' master_sys_mm = MuellerMat.SystemMuellerMatrix([cmm.WollastonPrism(), derotator, cmm.HWP(), m3, cmm.Rotator()]) # Initialize the standards and convert to degrees # http://www.ukirt.hawaii.edu/instruments/irpol/irpol_stds.html # HDE 279652: RA 04 14 50.2, dec +37 35 54, P = 0.61 # HDE 279658: RA 04 13 47.3, dec +37 09 32, P = 1.42 # HDE 283637: RA 04 22 53.3, dec +27 30 18, P = 1.57 ra = np.array([[4, 14, 50.2], [4, 13, 47.3], [4, 22, 53.3]]) dec = np.array([[37, 35, 54], [37, 9, 32], [27, 30, 18]]) rad = np.radians(15 * (ra[:, 0] + ra[:, 1] / 60 + ra[:, 2] / 3600)) decd = np.radians(dec[:, 0] + dec[:, 1] / 60 + dec[:, 2] / 3600) p = np.array([0.0061, 0.0142, 0.0157]) # matplotlib formatting plt.rcParams['font.family'] = 'Times New Roman' plt.rcParams['font.size'] = 22