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Add error propagation from uncertainties on the polarizer axis

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Thibault Barnouin
2021-06-23 13:37:54 +02:00
parent 5493120a56
commit 65aa4e2b2e
22 changed files with 125 additions and 268 deletions
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src/lib/reduction.py
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@@ -26,19 +26,15 @@ prototypes :
- polarizer_avg(data_array, error_array, headers, FWHM, scale, smoothing) -> polarizer_array, pol_error_array
Average images in data_array on each used polarizer filter.
- compute_Stokes(data_array, error_array, headers, FWHM, scale, smoothing) -> I_stokes, Q_stokes, U_stokes, Stokes_cov
- compute_Stokes(data_array, error_array, headers, FWHM, scale, smoothing) -> I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux
Compute Stokes parameters I, Q and U and their respective errors from data_array.
- compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers) -> P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P
- compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux, headers) -> P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P
Compute polarization degree (in %) and angle (in degree) and their
respective errors
- rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers, ang) -> I_stokes, Q_stokes, U_stokes, Stokes_cov, headers
- rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux, headers, ang) -> I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux, headers
Rotate I, Q, U given an angle in degrees using scipy functions.
- rotate2_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers, ang) -> I_stokes, Q_stokes, U_stokes, Stokes_cov, P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P, headers
Rotate I, Q, U, P, PA and associated errors given an angle in degrees
using scipy functions.
"""
import copy
@@ -56,6 +52,14 @@ from lib.plots import plot_obs
from lib.cross_correlation import phase_cross_correlation
# Useful tabulated values
#FOC instrument
globals()['trans2'] = {'f140w' : 0.21, 'f175w' : 0.24, 'f220w' : 0.39, 'f275w' : 0.40, 'f320w' : 0.89, 'f342w' : 0.81, 'f430w' : 0.74, 'f370lp' : 0.83, 'f486n' : 0.63, 'f501n' : 0.68, 'f480lp' : 0.82, 'clear2' : 1.0}
globals()['trans3'] = {'f120m' : 0.10, 'f130m' : 0.10, 'f140m' : 0.08, 'f152m' : 0.08, 'f165w' : 0.28, 'f170m' : 0.18, 'f195w' : 0.42, 'f190m' : 0.15, 'f210m' : 0.18, 'f231m' : 0.18, 'clear3' : 1.0}
globals()['trans4'] = {'f253m' : 0.18, 'f278m' : 0.26, 'f307m' : 0.26, 'f130lp' : 0.92, 'f346m' : 0.58, 'f372m' : 0.73, 'f410m' : 0.58, 'f437m' : 0.71, 'f470m' : 0.79, 'f502m' : 0.82, 'f550m' : 0.77, 'clear4' : 1.0}
globals()['pol_efficiency'] = {'pol0' : 0.92, 'pol60' : 0.92, 'pol120' : 0.91}
def get_row_compressor(old_dimension, new_dimension, operation='sum'):
"""
Return the matrix that allows to compress an array from an old dimension of
@@ -438,6 +442,19 @@ def get_error(data_array, sub_shape=(15,15), display=False, headers=None,
#error = np.std(sub_image) # Previously computed using standard deviation over the background
error = np.sqrt(np.sum(sub_image**2)/sub_image.size)
error_array[i] *= error
# Quadratically add uncertainties in the "correction factors" (see Kishimoto 1999)
#wavelength dependence of the polariser filters
#estimated to less than 1%
err_wav = data_array[i]*0.01
#difference in PSFs through each polarizers
#estimated to less than 3%
err_psf = data_array[i]*0.03
#flatfielding uncertainties
#estimated to less than 3%
err_flat = data_array[i]*0.03
error_array[i] = np.sqrt(error_array[i]**2 + err_wav**2 + err_psf**2 + err_flat**2)
background[i] = sub_image.sum()
data_array[i] = data_array[i] - sub_image.mean()
data_array[i][data_array[i] < 0.] = 0.
@@ -727,6 +744,13 @@ def align_data(data_array, headers, error_array=None, upsample_factor=1.,
rescaled_image[i][rescaled_image[i] < 0.] = 0.
# Uncertainties from shifting
prec_shift = np.array([1.,1.])/upsample_factor
shifted_image = sc_shift(rescaled_image[i], prec_shift, cval=0.)
error_shift = np.abs(rescaled_image[i] - shifted_image)/2.
#sum quadratically the errors
rescaled_error[i] = np.sqrt(rescaled_error[i]**2 + error_shift**2)
shifts.append(shift)
errors.append(error)
@@ -937,10 +961,6 @@ def polarizer_avg(data_array, error_array, data_mask, headers, FWHM=None,
FWHM=FWHM, scale=scale, smoothing=smoothing)
else:
# Average on each polarization filter.
#pol0 = pol0_array.mean(axis=0)
#pol60 = pol60_array.mean(axis=0)
#pol120 = pol120_array.mean(axis=0)
# Sum on each polarization filter.
print("Exposure time for polarizer 0°/60°/120° : ",
np.sum([header['exptime'] for header in headers0]),
@@ -953,9 +973,6 @@ def polarizer_avg(data_array, error_array, data_mask, headers, FWHM=None,
# Propagate uncertainties quadratically
#err0 = np.mean(err0_array,axis=0)/np.sqrt(err0_array.shape[0])
#err60 = np.mean(err60_array,axis=0)/np.sqrt(err60_array.shape[0])
#err120 = np.mean(err120_array,axis=0)/np.sqrt(err120_array.shape[0])
err0 = np.sum(err0_array,axis=0)*np.sqrt(err0_array.shape[0])
err60 = np.sum(err60_array,axis=0)*np.sqrt(err60_array.shape[0])
err120 = np.sum(err120_array,axis=0)*np.sqrt(err120_array.shape[0])
@@ -1042,6 +1059,9 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
+45/-45deg linear polarization intensity
Stokes_cov : numpy.ndarray
Covariance matrix of the Stokes parameters I, Q, U.
pol_flux : numpy.ndarray
Array containing the transmittance corrected fluxes from the multiple
polarizer plates
"""
# Check that all images are from the same instrument
instr = headers[0]['instrume']
@@ -1064,15 +1084,7 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
print("WARNING : Negative value in polarizer array.")
# Stokes parameters
#default
#I_stokes = (2./3.)*(pol0 + pol60 + pol120)
#Q_stokes = (2./3.)*(2*pol0 - pol60 - pol120)
#U_stokes = (2./np.sqrt(3.))*(pol60 - pol120)
#transmittance corrected
trans2 = {'f140w' : 0.21, 'f175w' : 0.24, 'f220w' : 0.39, 'f275w' : 0.40, 'f320w' : 0.89, 'f342w' : 0.81, 'f430w' : 0.74, 'f370lp' : 0.83, 'f486n' : 0.63, 'f501n' : 0.68, 'f480lp' : 0.82, 'clear2' : 1.0}
trans3 = {'f120m' : 0.10, 'f130m' : 0.10, 'f140m' : 0.08, 'f152m' : 0.08, 'f165w' : 0.28, 'f170m' : 0.18, 'f195w' : 0.42, 'f190m' : 0.15, 'f210m' : 0.18, 'f231m' : 0.18, 'clear3' : 1.0}
trans4 = {'f253m' : 0.18, 'f278m' : 0.26, 'f307m' : 0.26, 'f130lp' : 0.92, 'f346m' : 0.58, 'f372m' : 0.73, 'f410m' : 0.58, 'f437m' : 0.71, 'f470m' : 0.79, 'f502m' : 0.82, 'f550m' : 0.77, 'clear4' : 1.0}
transmit = np.ones((3,)) #will be filter dependant
filt2 = headers[0]['filtnam2']
filt3 = headers[0]['filtnam3']
@@ -1092,27 +1104,26 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
transmit4 = trans4[filt4.lower()]
transmit *= transmit2*transmit3*transmit4
pol_efficiency = {'pol0' : 0.92, 'pol60' : 0.92, 'pol120' : 0.91}
pol_eff = np.ones((3,))
pol_eff[0] = pol_efficiency['pol0']
pol_eff[1] = pol_efficiency['pol60']
pol_eff[2] = pol_efficiency['pol120']
theta = np.array([np.pi, np.pi/3., 2.*np.pi/3.])
flux = 2.*np.array([pol0/transmit[0], pol60/transmit[1], pol120/transmit[2]])
pol_flux = 2.*np.array([pol0/transmit[0], pol60/transmit[1], pol120/transmit[2]])
norm = pol_eff[1]*pol_eff[2]*np.sin(-2.*theta[1]+2.*theta[2]) \
+ pol_eff[2]*pol_eff[0]*np.sin(-2.*theta[2]+2.*theta[0]) \
+ pol_eff[0]*pol_eff[1]*np.sin(-2.*theta[0]+2.*theta[1])
coeff = np.zeros((3,3))
globals()['a_stokes'] = np.zeros((3,3))
for i in range(3):
coeff[0,i] = pol_eff[(i+1)%3]*pol_eff[(i+2)%3]*np.sin(-2.*theta[(i+1)%3]+2.*theta[(i+2)%3])/norm
coeff[1,i] = (-pol_eff[(i+1)%3]*np.sin(2.*theta[(i+1)%3]) + pol_eff[(i+2)%3]*np.sin(2.*theta[(i+2)%3]))/norm
coeff[2,i] = (pol_eff[(i+1)%3]*np.cos(2.*theta[(i+1)%3]) - pol_eff[(i+2)%3]*np.cos(2.*theta[(i+2)%3]))/norm
a_stokes[0,i] = pol_eff[(i+1)%3]*pol_eff[(i+2)%3]*np.sin(-2.*theta[(i+1)%3]+2.*theta[(i+2)%3])/norm
a_stokes[1,i] = (-pol_eff[(i+1)%3]*np.sin(2.*theta[(i+1)%3]) + pol_eff[(i+2)%3]*np.sin(2.*theta[(i+2)%3]))/norm
a_stokes[2,i] = (pol_eff[(i+1)%3]*np.cos(2.*theta[(i+1)%3]) - pol_eff[(i+2)%3]*np.cos(2.*theta[(i+2)%3]))/norm
I_stokes = np.sum([coeff[0,i]*flux[i] for i in range(3)], axis=0)
Q_stokes = np.sum([coeff[1,i]*flux[i] for i in range(3)], axis=0)
U_stokes = np.sum([coeff[2,i]*flux[i] for i in range(3)], axis=0)
I_stokes = np.sum([a_stokes[0,i]*pol_flux[i] for i in range(3)], axis=0)
Q_stokes = np.sum([a_stokes[1,i]*pol_flux[i] for i in range(3)], axis=0)
U_stokes = np.sum([a_stokes[2,i]*pol_flux[i] for i in range(3)], axis=0)
# Remove nan
I_stokes[np.isnan(I_stokes)]=0.
@@ -1125,15 +1136,6 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
if mask.any():
print("WARNING : I_pol > I_stokes : ", I_stokes[mask].size)
#plt.imshow(np.sqrt(Q_stokes**2+U_stokes**2)/I_stokes*mask, origin='lower')
#plt.colorbar()
#plt.title(r"$I_{pol}/I_{tot}$")
#plt.show()
#I_stokes[mask]=0.
#Q_stokes[mask]=0.
#U_stokes[mask]=0.
#Stokes covariance matrix
Stokes_cov = np.zeros((3,3,I_stokes.shape[0],I_stokes.shape[1]))
Stokes_cov[0,0] = (4./9.)*(pol_cov[0,0]+pol_cov[1,1]+pol_cov[2,2]) + (8./9.)*(pol_cov[0,1]+pol_cov[0,2]+pol_cov[1,2])
@@ -1154,10 +1156,10 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
I_stokes, Q_stokes, U_stokes = Stokes_array
Stokes_cov[0,0], Stokes_cov[1,1], Stokes_cov[2,2] = Stokes_error**2
return I_stokes, Q_stokes, U_stokes, Stokes_cov
return I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux
def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers):
def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux, headers):
"""
Compute the polarization degree (in %) and angle (in deg) and their
respective errors from given Stokes parameters.
@@ -1174,6 +1176,9 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers):
+45/-45deg linear polarization intensity
Stokes_cov : numpy.ndarray
Covariance matrix of the Stokes parameters I, Q, U.
pol_flux : numpy.ndarray
Array containing the transmittance corrected fluxes from the multiple
polarizer plates
headers : header list
List of headers corresponding to the images in data_array.
----------
@@ -1202,15 +1207,32 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers):
I_pol = np.sqrt(Q_stokes**2 + U_stokes**2)
P = I_pol/I_stokes*100.
P[I_stokes <= 0.] = 0.
PA = (90./np.pi)*np.arctan2(U_stokes,Q_stokes)+90.*2.
PA = (90./np.pi)*np.arctan2(U_stokes,Q_stokes)
if (P>100.).any():
print("WARNING : found pixels for which P > 100%", P[P>100.].size)
#Associated errors
s_P = (100./I_stokes)*np.sqrt((Q_stokes**2*Stokes_cov[1,1] + U_stokes**2*Stokes_cov[2,2] + 2.*Q_stokes*U_stokes*Stokes_cov[1,2])/(Q_stokes**2 + U_stokes**2) + ((Q_stokes/I_stokes)**2 + (U_stokes/I_stokes)**2)*Stokes_cov[0,0] - 2.*(Q_stokes/I_stokes)*Stokes_cov[0,1] - 2.*(U_stokes/I_stokes)*Stokes_cov[0,2])
s_PA = (90./(np.pi*(Q_stokes**2 + U_stokes**2)))*np.sqrt(U_stokes**2*Stokes_cov[1,1] + Q_stokes**2*Stokes_cov[2,2] - 2.*Q_stokes*U_stokes*Stokes_cov[1,2])
#Error propagated from uncertainties in the direction of polarizers' axis
#uncertainty estimated to 3° (see Nota et al 1996)
k1, k2, k3 = pol_efficiency['pol0'], pol_efficiency['pol60'], pol_efficiency['pol120']
f1, f2, f3 = pol_flux
theta1, theta2, theta3 = np.pi, np.pi/3., 2.*np.pi/3.
norm = k2*k3*np.sin(-2.*theta2+2.*theta3) + k3*k1*np.sin(-2.*theta3+2.*theta1) + k1*k2*np.sin(-2.*theta1+2.*theta2)
C1 = 1/(I_stokes**2*P/100.)
C2 = P/100./I_stokes
dP_dtheta1 = 2.*(k1*k2*k3/norm) * (np.cos(-2.*theta3+2.*theta1)/k2 - np.cos(-2.*theta1+2.*theta2)/k3) * (((a_stokes[1,0]+a_stokes[2,0]-1.)*C1 + a_stokes[0,0]*C2)*f1 + ((a_stokes[0,1]) * (C2-C1))*f2 + ((a_stokes[0,2]) * (C2-C1))*f3)
dP_dtheta2 = 2.*(k1*k2*k3/norm) * (np.cos(-2.*theta1+2.*theta2)/k3 - np.cos(-2.*theta2+2.*theta3)/k1) * (((a_stokes[1,0]+a_stokes[2,0]-1./(1.-k3/k1*np.cos(-2.*theta2+2.*theta1)/np.cos(-2*theta1+2.*theta2)))*C1 + (a_stokes[0,0]-1./(1.-k1/k3*np.cos(-2.*theta1+2.*theta2)/np.cos(-2*theta2+2.*theta3))*C2)*f1 + ((a_stokes[0,1]+np.cos(2.*theta2)/(a_stokes[1,2]*np.cos(2.*theta2)-a_stokes[1,1]*np.sin(2.*theta2))) * (C2-C1))*f2 + ((a_stokes[0,2]+np.sin(2.*theta2)/(a_stokes[1,2]*np.cos(2.*theta2)-a_stokes[1,1]*np.sin(2.*theta2))) * (C2-C1))*f3))
dP_dtheta3 = 2.*(k1*k2*k3/norm) * (np.cos(-2.*theta2+2.*theta3)/k1 - np.cos(-2.*theta3+2.*theta1)/k2) * (((a_stokes[1,0]+a_stokes[2,0]+1./(1.-k1/k2*np.cos(-2.*theta3+2.*theta1)/np.cos(-2*theta2+2.*theta3)))*C1 + (a_stokes[0,0]+1./(1.-k2/k1*np.cos(-2.*theta2+2.*theta3)/np.cos(-2*theta3+2.*theta1))*C2)*f1 + ((a_stokes[0,1]+np.cos(2.*theta3)/(a_stokes[2,2]*np.cos(2.*theta3)-a_stokes[2,1]*np.sin(2.*theta3))) * (C2-C1))*f2 + ((a_stokes[0,2]+np.sin(2.*theta3)/(a_stokes[2,2]*np.cos(2.*theta3)-a_stokes[2,1]*np.sin(2.*theta3))) * (C2-C1))*f3))
s_P_ax = np.sqrt(dP_dtheta1**2+dP_dtheta2**2+dP_dtheta3**2)*3.
s_PA_ax = np.ones(s_PA.shape)/np.sqrt(2)*3.
#Sum quadratically
s_P = np.sqrt(s_P**2 + s_P_ax**2)
s_PA = np.sqrt(s_PA**2 + s_PA_ax**2)
debiased_P = np.sqrt(P**2 - s_P**2)
@@ -1240,77 +1262,7 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers):
return P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P
def rotate_data(data_array, error_array, data_mask, headers, ang):
"""
Use scipy.ndimage.rotate to rotate I_stokes to an angle, and a rotation
matrix to rotate Q, U of a given angle in degrees and update header
orientation keyword.
----------
Inputs:
data_array : numpy.ndarray
Array of images (2D floats) to be rotated by angle ang.
error_array : numpy.ndarray
Array of error associated to images in data_array.
headers : header list
List of headers corresponding to the reduced images.
ang : float
Rotation angle (in degrees) that should be applied to the Stokes
parameters
----------
Returns:
new_data_array : numpy.ndarray
Updated array containing the rotated images.
new_error_array : numpy.ndarray
Updated array containing the rotated errors.
new_headers : header list
Updated list of headers corresponding to the reduced images accounting
for the new orientation angle.
"""
#Rotate I_stokes, Q_stokes, U_stokes using rotation matrix
alpha = ang*np.pi/180.
#Rotate original images using scipy.ndimage.rotate
new_data_array = []
new_error_array = []
for i in range(data_array.shape[0]):
new_data_array.append(sc_rotate(data_array[i], ang, reshape=False,
cval=0.))
new_error_array.append(sc_rotate(error_array[i], ang, reshape=False,
cval=error_array.mean()))
new_data_array = np.array(new_data_array)
new_data_mask = sc_rotate(data_mask, ang, reshape=False, cval=True)
new_error_array = np.array(new_error_array)
for i in range(new_data_array.shape[0]):
new_data_array[i][new_data_array[i] < 0.] = 0.
#Update headers to new angle
new_headers = []
mrot = np.array([[np.cos(-alpha), -np.sin(-alpha)],
[np.sin(-alpha), np.cos(-alpha)]])
for header in headers:
new_header = copy.deepcopy(header)
new_header['orientat'] = header['orientat'] + ang
new_wcs = WCS(header).deepcopy()
if new_wcs.wcs.has_cd(): # CD matrix
del new_wcs.wcs.cd
keys = ['CD1_1','CD1_2','CD2_1','CD2_2']
for key in keys:
new_header.remove(key, ignore_missing=True)
new_wcs.wcs.cdelt = 3600.*np.sqrt(np.sum(new_wcs.wcs.get_pc()**2,axis=1))
elif new_wcs.wcs.has_pc(): # PC matrix + CDELT
newpc = np.dot(mrot, new_wcs.wcs.get_pc())
new_wcs.wcs.pc = newpc
new_wcs.wcs.set()
new_header.update(new_wcs.to_header())
new_headers.append(new_header)
return new_data_array, new_error_array, new_data_mask, new_headers
def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers, ang, SNRi_cut=None):
def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, pol_flux, data_mask, headers, ang, SNRi_cut=None):
"""
Use scipy.ndimage.rotate to rotate I_stokes to an angle, and a rotation
matrix to rotate Q, U of a given angle in degrees and update header
@@ -1328,6 +1280,9 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers,
+45/-45deg linear polarization intensity
Stokes_cov : numpy.ndarray
Covariance matrix of the Stokes parameters I, Q, U.
pol_flux : numpy.ndarray
Array containing the transmittance corrected fluxes from the multiple
polarizer plates
headers : header list
List of headers corresponding to the reduced images.
ang : float
@@ -1350,6 +1305,8 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers,
accounting for +45/-45deg linear polarization intensity.
new_Stokes_cov : numpy.ndarray
Updated covariance matrix of the Stokes parameters I, Q, U.
new_pol_flux : numpy.ndarray
Rotated fluxes from the multiple polarizer plates
new_headers : header list
Updated list of headers corresponding to the reduced images accounting
for the new orientation angle.
@@ -1372,6 +1329,8 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers,
new_Q_stokes = np.cos(2*alpha)*Q_stokes + np.sin(2*alpha)*U_stokes
new_U_stokes = -np.sin(2*alpha)*Q_stokes + np.cos(2*alpha)*U_stokes
new_pol_flux = copy.deepcopy(pol_flux)
#Compute new covariance matrix on rotated parameters
new_Stokes_cov = copy.deepcopy(Stokes_cov)
new_Stokes_cov[1,1] = np.cos(2.*alpha)**2*Stokes_cov[1,1] + np.sin(2.*alpha)**2*Stokes_cov[2,2] + 2.*np.cos(2.*alpha)*np.sin(2.*alpha)*Stokes_cov[1,2]
@@ -1386,6 +1345,7 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers,
new_U_stokes = sc_rotate(new_U_stokes, ang, reshape=False, cval=0.)
new_data_mask = sc_rotate(data_mask, ang, reshape=False, cval=True)
for i in range(3):
new_pol_flux[i] = sc_rotate(new_pol_flux[i], ang, reshape=False, cval=0.)
for j in range(3):
new_Stokes_cov[i,j] = sc_rotate(new_Stokes_cov[i,j], ang,
reshape=False, cval=0.)
@@ -1421,139 +1381,7 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers,
new_U_stokes[new_I_stokes == 0.] = 0.
new_Q_stokes[np.isnan(new_Q_stokes)] = 0.
new_U_stokes[np.isnan(new_U_stokes)] = 0.
new_pol_flux[np.isnan(new_pol_flux)] = 0.
new_Stokes_cov[np.isnan(new_Stokes_cov)] = fmax
return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_data_mask, new_headers
def rotate2_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers, ang):
"""
Use scipy.ndimage.rotate to rotate I_stokes to an angle, and a rotation
matrix to rotate Q, U of a given angle in degrees and update header
orientation keyword.
----------
Inputs:
I_stokes : numpy.ndarray
Image (2D floats) containing the Stokes parameters accounting for
total intensity
Q_stokes : numpy.ndarray
Image (2D floats) containing the Stokes parameters accounting for
vertical/horizontal linear polarization intensity
U_stokes : numpy.ndarray
Image (2D floats) containing the Stokes parameters accounting for
+45/-45deg linear polarization intensity
Stokes_cov : numpy.ndarray
Covariance matrix of the Stokes parameters I, Q, U.
headers : header list
List of headers corresponding to the reduced images.
ang : float
Rotation angle (in degrees) that should be applied to the Stokes
parameters
----------
Returns:
new_I_stokes : numpy.ndarray
Rotated mage (2D floats) containing the rotated Stokes parameters
accounting for total intensity
new_Q_stokes : numpy.ndarray
Rotated mage (2D floats) containing the rotated Stokes parameters
accounting for vertical/horizontal linear polarization intensity
new_U_stokes : numpy.ndarray
Rotated image (2D floats) containing the rotated Stokes parameters
accounting for +45/-45deg linear polarization intensity.
new_Stokes_cov : numpy.ndarray
Updated covariance matrix of the Stokes parameters I, Q, U.
P : numpy.ndarray
Image (2D floats) containing the polarization degree (in %).
s_P : numpy.ndarray
Image (2D floats) containing the error on the polarization degree.
PA : numpy.ndarray
Image (2D floats) containing the polarization angle.
s_PA : numpy.ndarray
Image (2D floats) containing the error on the polarization angle.
debiased_P : numpy.ndarray
Image (2D floats) containing the debiased polarization degree (in %).
s_P_P : numpy.ndarray
Image (2D floats) containing the Poisson noise error on the
polarization degree.
s_PA_P : numpy.ndarray
Image (2D floats) containing the Poisson noise error on the
polarization angle.
"""
# Rotate I_stokes, Q_stokes, U_stokes using rotation matrix
alpha = ang*np.pi/180.
new_I_stokes = 1.*I_stokes
new_Q_stokes = np.cos(2*alpha)*Q_stokes + np.sin(2*alpha)*U_stokes
new_U_stokes = -np.sin(2*alpha)*Q_stokes + np.cos(2*alpha)*U_stokes
# Compute new covariance matrix on rotated parameters
new_Stokes_cov = copy.deepcopy(Stokes_cov)
new_Stokes_cov[1,1] = np.cos(2.*alpha)**2*Stokes_cov[1,1] + np.sin(2.*alpha)**2*Stokes_cov[2,2] + 2.*np.cos(2.*alpha)*np.sin(2.*alpha)*Stokes_cov[1,2]
new_Stokes_cov[2,2] = np.sin(2.*alpha)**2*Stokes_cov[1,1] + np.cos(2.*alpha)**2*Stokes_cov[2,2] - 2.*np.cos(2.*alpha)*np.sin(2.*alpha)*Stokes_cov[1,2]
new_Stokes_cov[0,1] = new_Stokes_cov[1,0] = np.cos(2.*alpha)*Stokes_cov[0,1] + np.sin(2.*alpha)*Stokes_cov[0,2]
new_Stokes_cov[0,2] = new_Stokes_cov[2,0] = -np.sin(2.*alpha)*Stokes_cov[0,1] + np.cos(2.*alpha)*Stokes_cov[0,2]
new_Stokes_cov[1,2] = new_Stokes_cov[2,1] = np.cos(2.*alpha)*np.sin(2.*alpha)*(Stokes_cov[2,2] - Stokes_cov[1,1]) + (np.cos(2.*alpha)**2 - np.sin(2.*alpha)**2)*Stokes_cov[1,2]
# Compute new polarization parameters
P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P = compute_pol(new_I_stokes,
new_Q_stokes, new_U_stokes, new_Stokes_cov, headers)
# Rotate original images using scipy.ndimage.rotate
new_I_stokes = sc_rotate(new_I_stokes, ang, reshape=False,
cval=np.sqrt(new_Stokes_cov[0,0][0,0]))
new_Q_stokes = sc_rotate(new_Q_stokes, ang, reshape=False,
cval=np.sqrt(new_Stokes_cov[1,1][0,0]))
new_U_stokes = sc_rotate(new_U_stokes, ang, reshape=False,
cval=np.sqrt(new_Stokes_cov[2,2][0,0]))
P = sc_rotate(P, ang, reshape=False, cval=P.mean())
debiased_P = sc_rotate(debiased_P, ang, reshape=False,
cval=debiased_P.mean())
s_P = sc_rotate(s_P, ang, reshape=False, cval=s_P.mean())
s_P_P = sc_rotate(s_P_P, ang, reshape=False, cval=s_P_P.mean())
PA = sc_rotate(PA, ang, reshape=False, cval=PA.mean())
s_PA = sc_rotate(s_PA, ang, reshape=False, cval=s_PA.mean())
s_PA_P = sc_rotate(s_PA_P, ang, reshape=False, cval=s_PA_P.mean())
for i in range(3):
for j in range(3):
new_Stokes_cov[i,j] = sc_rotate(new_Stokes_cov[i,j], ang,
reshape=False, cval=new_Stokes_cov[i,j].mean())
#Update headers to new angle
new_headers = []
mrot = np.array([[np.cos(-alpha), -np.sin(-alpha)],
[np.sin(-alpha), np.cos(-alpha)]])
for header in headers:
new_header = copy.deepcopy(header)
new_header['orientat'] = header['orientat'] + ang
new_wcs = WCS(header).deepcopy()
if new_wcs.wcs.has_cd(): # CD matrix
del w.wcs.cd
keys = ['CD1_1','CD1_2','CD2_1','CD2_2']
for key in keys:
new_header.remove(key, ignore_missing=True)
w.wcs.cdelt = 3600.*np.sqrt(np.sum(w.wcs.get_pc()**2,axis=1))
elif new_wcs.wcs.has_pc(): # PC matrix + CDELT
newpc = np.dot(mrot, new_wcs.wcs.get_pc())
new_wcs.wcs.pc = newpc
new_wcs.wcs.set()
new_header.update(new_wcs.to_header())
new_headers.append(new_header)
# Nan handling :
fmax = np.finfo(np.float64).max
new_I_stokes[np.isnan(new_I_stokes)] = 0.
new_Q_stokes[new_I_stokes == 0.] = 0.
new_U_stokes[new_I_stokes == 0.] = 0.
new_Q_stokes[np.isnan(new_Q_stokes)] = 0.
new_U_stokes[np.isnan(new_U_stokes)] = 0.
new_Stokes_cov[np.isnan(new_Stokes_cov)] = fmax
P[np.isnan(P)] = 0.
s_P[np.isnan(s_P)] = fmax
s_PA[np.isnan(s_PA)] = fmax
debiased_P[np.isnan(debiased_P)] = 0.
s_P_P[np.isnan(s_P_P)] = fmax
s_PA_P[np.isnan(s_PA_P)] = fmax
return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, data_mask, P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P, new_headers
return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_pol_flux, new_data_mask, new_headers