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correct axis error estimation

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Thibault Barnouin
2021-06-26 12:52:06 +02:00
parent 7eb434e792
commit 7958246655
23 changed files with 211 additions and 31 deletions
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65
src/lib/reduction.py
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@@ -1106,21 +1106,22 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
pol_eff[1] = pol_efficiency['pol60']
pol_eff[2] = pol_efficiency['pol120']
theta = np.array([np.pi, np.pi/3., 2.*np.pi/3.])
theta = np.array([180.*np.pi/180., 60.*np.pi/180., 120.*np.pi/180.])
sigma_theta = np.array([3.*np.pi/180., 3.*np.pi/180., 3.*np.pi/180.])
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]) \
A = 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])
a_stokes = np.zeros((3,3))
coeff_stokes = np.zeros((3,3))
for i in range(3):
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
coeff_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])/A
coeff_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]))/A
coeff_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]))/A
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)
I_stokes = np.sum([coeff_stokes[0,i]*pol_flux[i] for i in range(3)], axis=0)
Q_stokes = np.sum([coeff_stokes[1,i]*pol_flux[i] for i in range(3)], axis=0)
U_stokes = np.sum([coeff_stokes[2,i]*pol_flux[i] for i in range(3)], axis=0)
# Remove nan
I_stokes[np.isnan(I_stokes)]=0.
@@ -1135,27 +1136,35 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
#Stokes covariance matrix
Stokes_cov = np.zeros((3,3,I_stokes.shape[0],I_stokes.shape[1]))
Stokes_cov[0,0] = a_stokes[0,0]**2*pol_cov[0,0]+a_stokes[0,1]**2*pol_cov[1,1]+a_stokes[0,2]**2*pol_cov[2,2] + 2*(a_stokes[0,0]*a_stokes[0,1]*pol_cov[0,1]+a_stokes[0,0]*a_stokes[0,2]*pol_cov[0,2]+a_stokes[0,1]*a_stokes[0,2]*pol_cov[1,2])
Stokes_cov[1,1] = a_stokes[1,0]**2*pol_cov[0,0]+a_stokes[1,1]**2*pol_cov[1,1]+a_stokes[1,2]**2*pol_cov[2,2] + 2*(a_stokes[1,0]*a_stokes[1,1]*pol_cov[0,1]+a_stokes[1,0]*a_stokes[1,2]*pol_cov[0,2]+a_stokes[1,1]*a_stokes[1,2]*pol_cov[1,2])
Stokes_cov[2,2] = a_stokes[2,0]**2*pol_cov[0,0]+a_stokes[2,1]**2*pol_cov[1,1]+a_stokes[2,2]**2*pol_cov[2,2] + 2*(a_stokes[2,0]*a_stokes[2,1]*pol_cov[0,1]+a_stokes[2,0]*a_stokes[2,2]*pol_cov[0,2]+a_stokes[2,1]*a_stokes[2,2]*pol_cov[1,2])
Stokes_cov[0,1] = Stokes_cov[1,0] = a_stokes[0,0]*a_stokes[1,0]*pol_cov[0,0]+a_stokes[0,1]*a_stokes[1,1]*pol_cov[1,1]+a_stokes[0,2]*a_stokes[1,2]*pol_cov[2,2]+(a_stokes[0,0]*a_stokes[1,1]+a_stokes[1,0]*a_stokes[0,1])*pol_cov[0,1]+(a_stokes[0,0]*a_stokes[1,2]+a_stokes[1,0]*a_stokes[0,2])*pol_cov[0,2]+(a_stokes[0,1]*a_stokes[1,2]+a_stokes[1,1]*a_stokes[0,2])*pol_cov[1,2]
Stokes_cov[0,2] = Stokes_cov[2,0] = a_stokes[0,0]*a_stokes[2,0]*pol_cov[0,0]+a_stokes[0,1]*a_stokes[2,1]*pol_cov[1,1]+a_stokes[0,2]*a_stokes[2,2]*pol_cov[2,2]+(a_stokes[0,0]*a_stokes[2,1]+a_stokes[2,0]*a_stokes[0,1])*pol_cov[0,1]+(a_stokes[0,0]*a_stokes[2,2]+a_stokes[2,0]*a_stokes[0,2])*pol_cov[0,2]+(a_stokes[0,1]*a_stokes[2,2]+a_stokes[2,1]*a_stokes[0,2])*pol_cov[1,2]
Stokes_cov[1,2] = Stokes_cov[2,1] = a_stokes[1,0]*a_stokes[2,0]*pol_cov[0,0]+a_stokes[1,1]*a_stokes[2,1]*pol_cov[1,1]+a_stokes[1,2]*a_stokes[2,2]*pol_cov[2,2]+(a_stokes[1,0]*a_stokes[2,1]+a_stokes[2,0]*a_stokes[1,1])*pol_cov[0,1]+(a_stokes[1,0]*a_stokes[2,2]+a_stokes[2,0]*a_stokes[1,2])*pol_cov[0,2]+(a_stokes[1,1]*a_stokes[2,2]+a_stokes[2,1]*a_stokes[1,2])*pol_cov[1,2]
Stokes_cov[0,0] = coeff_stokes[0,0]**2*pol_cov[0,0]+coeff_stokes[0,1]**2*pol_cov[1,1]+coeff_stokes[0,2]**2*pol_cov[2,2] + 2*(coeff_stokes[0,0]*coeff_stokes[0,1]*pol_cov[0,1]+coeff_stokes[0,0]*coeff_stokes[0,2]*pol_cov[0,2]+coeff_stokes[0,1]*coeff_stokes[0,2]*pol_cov[1,2])
Stokes_cov[1,1] = coeff_stokes[1,0]**2*pol_cov[0,0]+coeff_stokes[1,1]**2*pol_cov[1,1]+coeff_stokes[1,2]**2*pol_cov[2,2] + 2*(coeff_stokes[1,0]*coeff_stokes[1,1]*pol_cov[0,1]+coeff_stokes[1,0]*coeff_stokes[1,2]*pol_cov[0,2]+coeff_stokes[1,1]*coeff_stokes[1,2]*pol_cov[1,2])
Stokes_cov[2,2] = coeff_stokes[2,0]**2*pol_cov[0,0]+coeff_stokes[2,1]**2*pol_cov[1,1]+coeff_stokes[2,2]**2*pol_cov[2,2] + 2*(coeff_stokes[2,0]*coeff_stokes[2,1]*pol_cov[0,1]+coeff_stokes[2,0]*coeff_stokes[2,2]*pol_cov[0,2]+coeff_stokes[2,1]*coeff_stokes[2,2]*pol_cov[1,2])
Stokes_cov[0,1] = Stokes_cov[1,0] = coeff_stokes[0,0]*coeff_stokes[1,0]*pol_cov[0,0]+coeff_stokes[0,1]*coeff_stokes[1,1]*pol_cov[1,1]+coeff_stokes[0,2]*coeff_stokes[1,2]*pol_cov[2,2]+(coeff_stokes[0,0]*coeff_stokes[1,1]+coeff_stokes[1,0]*coeff_stokes[0,1])*pol_cov[0,1]+(coeff_stokes[0,0]*coeff_stokes[1,2]+coeff_stokes[1,0]*coeff_stokes[0,2])*pol_cov[0,2]+(coeff_stokes[0,1]*coeff_stokes[1,2]+coeff_stokes[1,1]*coeff_stokes[0,2])*pol_cov[1,2]
Stokes_cov[0,2] = Stokes_cov[2,0] = coeff_stokes[0,0]*coeff_stokes[2,0]*pol_cov[0,0]+coeff_stokes[0,1]*coeff_stokes[2,1]*pol_cov[1,1]+coeff_stokes[0,2]*coeff_stokes[2,2]*pol_cov[2,2]+(coeff_stokes[0,0]*coeff_stokes[2,1]+coeff_stokes[2,0]*coeff_stokes[0,1])*pol_cov[0,1]+(coeff_stokes[0,0]*coeff_stokes[2,2]+coeff_stokes[2,0]*coeff_stokes[0,2])*pol_cov[0,2]+(coeff_stokes[0,1]*coeff_stokes[2,2]+coeff_stokes[2,1]*coeff_stokes[0,2])*pol_cov[1,2]
Stokes_cov[1,2] = Stokes_cov[2,1] = coeff_stokes[1,0]*coeff_stokes[2,0]*pol_cov[0,0]+coeff_stokes[1,1]*coeff_stokes[2,1]*pol_cov[1,1]+coeff_stokes[1,2]*coeff_stokes[2,2]*pol_cov[2,2]+(coeff_stokes[1,0]*coeff_stokes[2,1]+coeff_stokes[2,0]*coeff_stokes[1,1])*pol_cov[0,1]+(coeff_stokes[1,0]*coeff_stokes[2,2]+coeff_stokes[2,0]*coeff_stokes[1,2])*pol_cov[0,2]+(coeff_stokes[1,1]*coeff_stokes[2,2]+coeff_stokes[2,1]*coeff_stokes[1,2])*pol_cov[1,2]
C1 = 2.*pol_eff[0]*pol_eff[1]*pol_eff[2]/norm
dI_dtheta1 = C1*(np.cos(-2.*theta[2]+2.*theta[0])/pol_eff[1]*(pol_flux[1]-I_stokes) - np.cos(-2.*theta[0]+2.*theta[1])/pol_eff[2]*(pol_flux[2]-I_stokes))
dI_dtheta2 = C1*(np.cos(-2.*theta[0]+2.*theta[1])/pol_eff[2]*(pol_flux[2]-I_stokes) - np.cos(-2.*theta[1]+2.*theta[2])/pol_eff[0]*(pol_flux[0]-I_stokes))
dI_dtheta3 = C1*(np.cos(-2.*theta[1]+2.*theta[2])/pol_eff[0]*(pol_flux[0]-I_stokes) - np.cos(-2.*theta[2]+2.*theta[0])/pol_eff[1]*(pol_flux[1]-I_stokes))
dQ_dtheta1 = C1*((np.cos(2.*theta[0])*pol_flux[1]-np.cos(2.*theta[0])*pol_flux[2])/(pol_eff[1]*pol_eff[2]) - (np.cos(-2.*theta[2]+2.*theta[0])/pol_eff[1]-np.cos(-2.*theta[0]+2.*theta[1])/pol_eff[2])*Q_stokes)
dQ_dtheta2 = C1*((np.cos(2.*theta[1])*pol_flux[2]-np.cos(2.*theta[1])*pol_flux[0])/(pol_eff[0]*pol_eff[2]) - (np.cos(-2.*theta[0]+2.*theta[1])/pol_eff[2]-np.cos(-2.*theta[1]+2.*theta[2])/pol_eff[0])*Q_stokes)
dQ_dtheta3 = C1*((np.cos(2.*theta[2])*pol_flux[0]-np.cos(2.*theta[2])*pol_flux[1])/(pol_eff[0]*pol_eff[1]) - (np.cos(-2.*theta[1]+2.*theta[2])/pol_eff[0]-np.cos(-2.*theta[2]+2.*theta[0])/pol_eff[1])*Q_stokes)
dU_dtheta1 = C1*((np.sin(2.*theta[0])*pol_flux[1]-np.sin(2.*theta[1])*pol_flux[2])/(pol_eff[1]*pol_eff[2]) - (np.cos(-2.*theta[2]+2.*theta[0])/pol_eff[1]-np.cos(-2.*theta[0]+2.*theta[1])/pol_eff[2])*U_stokes)
dU_dtheta2 = C1*((np.sin(2.*theta[1])*pol_flux[2]-np.sin(2.*theta[1])*pol_flux[0])/(pol_eff[0]*pol_eff[2]) - (np.cos(-2.*theta[0]+2.*theta[1])/pol_eff[2]-np.cos(-2.*theta[1]+2.*theta[2])/pol_eff[0])*U_stokes)
dU_dtheta3 = C1*((np.sin(2.*theta[2])*pol_flux[0]-np.sin(2.*theta[2])*pol_flux[1])/(pol_eff[0]*pol_eff[1]) - (np.cos(-2.*theta[1]+2.*theta[2])/pol_eff[0]-np.cos(-2.*theta[2]+2.*theta[0])/pol_eff[1])*U_stokes)
dI_dtheta1 = 2.*pol_eff[0]/A*(pol_eff[2]*np.cos(-2.*theta[2]+2.*theta[0])*(pol_flux[1]-I_stokes) - pol_eff[1]*np.cos(-2.*theta[0]+2.*theta[1])*(pol_flux[2]-I_stokes) + A*coeff_stokes[0,0]*(np.sin(2.*theta[0]*Q_stokes) - np.cos(2.*theta[0]*U_stokes)))
dI_dtheta2 = 2.*pol_eff[1]/A*(pol_eff[0]*np.cos(-2.*theta[0]+2.*theta[1])*(pol_flux[2]-I_stokes) - pol_eff[2]*np.cos(-2.*theta[1]+2.*theta[2])*(pol_flux[0]-I_stokes) + A*coeff_stokes[0,1]*(np.sin(2.*theta[1]*Q_stokes) - np.cos(2.*theta[1]*U_stokes)))
dI_dtheta3 = 2.*pol_eff[2]/A*(pol_eff[1]*np.cos(-2.*theta[1]+2.*theta[2])*(pol_flux[0]-I_stokes) - pol_eff[0]*np.cos(-2.*theta[2]+2.*theta[0])*(pol_flux[1]-I_stokes) + A*coeff_stokes[0,2]*(np.sin(2.*theta[2]*Q_stokes) - np.cos(2.*theta[2]*U_stokes)))
dQ_dtheta1 = 2.*pol_eff[0]/A*(np.cos(2.*theta[0])*(pol_flux[1]-pol_flux[2]) - (pol_eff[2]*np.cos(-2.*theta[2]+2.*theta[0]) - pol_eff[1]*np.cos(-2.*theta[0]+2.*theta[1]))*Q_stokes + A*coeff_stokes[1,0]*(np.sin(2.*theta[0]*Q_stokes) - np.cos(2.*theta[0]*U_stokes)))
dQ_dtheta2 = 2.*pol_eff[1]/A*(np.cos(2.*theta[1])*(pol_flux[2]-pol_flux[0]) - (pol_eff[0]*np.cos(-2.*theta[0]+2.*theta[1]) - pol_eff[2]*np.cos(-2.*theta[1]+2.*theta[2]))*Q_stokes + A*coeff_stokes[1,1]*(np.sin(2.*theta[1]*Q_stokes) - np.cos(2.*theta[1]*U_stokes)))
dQ_dtheta3 = 2.*pol_eff[2]/A*(np.cos(2.*theta[2])*(pol_flux[0]-pol_flux[1]) - (pol_eff[1]*np.cos(-2.*theta[1]+2.*theta[2]) - pol_eff[0]*np.cos(-2.*theta[2]+2.*theta[0]))*Q_stokes + A*coeff_stokes[1,2]*(np.sin(2.*theta[2]*Q_stokes) - np.cos(2.*theta[2]*U_stokes)))
dU_dtheta1 = 2.*pol_eff[0]/A*(np.sin(2.*theta[0])*(pol_flux[1]-pol_flux[2]) - (pol_eff[2]*np.cos(-2.*theta[2]+2.*theta[0]) - pol_eff[1]*np.cos(-2.*theta[0]+2.*theta[1]))*U_stokes + A*coeff_stokes[2,0]*(np.sin(2.*theta[0]*Q_stokes) - np.cos(2.*theta[0]*U_stokes)))
dU_dtheta2 = 2.*pol_eff[1]/A*(np.sin(2.*theta[1])*(pol_flux[2]-pol_flux[0]) - (pol_eff[0]*np.cos(-2.*theta[0]+2.*theta[1]) - pol_eff[2]*np.cos(-2.*theta[1]+2.*theta[2]))*U_stokes + A*coeff_stokes[2,1]*(np.sin(2.*theta[1]*Q_stokes) - np.cos(2.*theta[1]*U_stokes)))
dU_dtheta3 = 2.*pol_eff[2]/A*(np.sin(2.*theta[2])*(pol_flux[0]-pol_flux[1]) - (pol_eff[1]*np.cos(-2.*theta[1]+2.*theta[2]) - pol_eff[0]*np.cos(-2.*theta[2]+2.*theta[0]))*U_stokes + A*coeff_stokes[2,2]*(np.sin(2.*theta[2]*Q_stokes) - np.cos(2.*theta[2]*U_stokes)))
#Stokes_cov[0,0] += (dI_dtheta1 + dI_dtheta2 + dI_dtheta3)**2*3.*np.pi/180.
#Stokes_cov[1,1] += (dQ_dtheta1 + dQ_dtheta2 + dQ_dtheta3)**2*3.*np.pi/180.
#Stokes_cov[2,2] += (dU_dtheta1 + dU_dtheta2 + dU_dtheta3)**2*3.*np.pi/180.
Stokes_cov[0,0] += (dI_dtheta1**2*sigma_theta[0]**2 + dI_dtheta2**2*sigma_theta[1]**2 + dI_dtheta3**2*sigma_theta[2]**2)
Stokes_cov[1,1] += (dQ_dtheta1**2*sigma_theta[0]**2 + dQ_dtheta2**2*sigma_theta[1]**2 + dQ_dtheta3**2*sigma_theta[2]**2)
Stokes_cov[2,2] += (dU_dtheta1**2*sigma_theta[0]**2 + dU_dtheta2**2*sigma_theta[1]**2 + dU_dtheta3**2*sigma_theta[2]**2)
plt.imshow(np.abs(Stokes_cov[0,0]/I_stokes)*100., origin='lower')
plt.colorbar()
plt.show()
plt.imshow(np.abs(Stokes_cov[1,1]/Q_stokes)*100., origin='lower')
plt.colorbar()
plt.show()
plt.imshow(np.abs(Stokes_cov[2,2]/U_stokes)*100., origin='lower')
plt.colorbar()
plt.show()
if not(FWHM is None) and (smoothing.lower() in ['gaussian_after','gauss_after']):
Stokes_array = np.array([I_stokes, Q_stokes, U_stokes])