Change reduction to take into account transmittance, and try plotting FOC's FOV

src/FOC_reduction.py

@@ -8,20 +8,20 @@ Main script where are progressively added the steps for the FOC pipeline reducti
 import sys
 import numpy as np
 import copy
-import matplotlib.pyplot as plt
 import lib.fits as proj_fits        #Functions to handle fits files
 import lib.reduction as proj_red    #Functions used in reduction pipeline
 import lib.plots as proj_plots      #Functions for plotting data
+from lib.convex_hull import image_hull
 
 
 def main():
     ##### User inputs
     ## Input and output locations
-#    globals()['data_folder'] = "../data/NGC1068_x274020/"
+    globals()['data_folder'] = "../data/NGC1068_x274020/"
-#    infiles = ['x274020at.c0f.fits','x274020bt.c0f.fits','x274020ct.c0f.fits',
+    infiles = ['x274020at.c0f.fits','x274020bt.c0f.fits','x274020ct.c0f.fits',
-#            'x274020dt.c0f.fits','x274020et.c0f.fits','x274020ft.c0f.fits',
+            'x274020dt.c0f.fits','x274020et.c0f.fits','x274020ft.c0f.fits',
-#            'x274020gt.c0f.fits','x274020ht.c0f.fits','x274020it.c0f.fits']
+            'x274020gt.c0f.fits','x274020ht.c0f.fits','x274020it.c0f.fits']
-#    globals()['plots_folder'] = "../plots/NGC1068_x274020/"
+    globals()['plots_folder'] = "../plots/NGC1068_x274020/"
 
 #    globals()['data_folder'] = "../data/NGC1068_x14w010/"
 #    infiles = ['x14w0101t_c0f.fits','x14w0102t_c0f.fits','x14w0103t_c0f.fits',
@@ -44,13 +44,13 @@ def main():
 #    infiles = ['x3mc0101m_c0f.fits','x3mc0102m_c0f.fits','x3mc0103m_c0f.fits']
 #    globals()['plots_folder'] = "../plots/3C109_x3mc010/"
 
-    globals()['data_folder'] = "../data/MKN463_x2rp030/"
+#    globals()['data_folder'] = "../data/MKN463_x2rp030/"
-    infiles = ['x2rp0201t_c0f.fits', 'x2rp0202t_c0f.fits', 'x2rp0203t_c0f.fits',
+#    infiles = ['x2rp0201t_c0f.fits', 'x2rp0202t_c0f.fits', 'x2rp0203t_c0f.fits',
-            'x2rp0204t_c0f.fits', 'x2rp0205t_c0f.fits', 'x2rp0206t_c0f.fits',
+#            'x2rp0204t_c0f.fits', 'x2rp0205t_c0f.fits', 'x2rp0206t_c0f.fits',
-            'x2rp0207t_c0f.fits', 'x2rp0301t_c0f.fits', 'x2rp0302t_c0f.fits',
+#            'x2rp0207t_c0f.fits', 'x2rp0301t_c0f.fits', 'x2rp0302t_c0f.fits',
-            'x2rp0303t_c0f.fits', 'x2rp0304t_c0f.fits', 'x2rp0305t_c0f.fits',
+#            'x2rp0303t_c0f.fits', 'x2rp0304t_c0f.fits', 'x2rp0305t_c0f.fits',
-            'x2rp0306t_c0f.fits', 'x2rp0307t_c0f.fits']
+#            'x2rp0306t_c0f.fits', 'x2rp0307t_c0f.fits']
-    globals()['plots_folder'] = "../plots/MKN463_x2rp030/"
+#    globals()['plots_folder'] = "../plots/MKN463_x2rp030/"
 
 #    globals()['data_folder'] = "../data/PG1630+377_x39510/"
 #    infiles = ['x3990201m_c0f.fits', 'x3990205m_c0f.fits', 'x3995101r_c0f.fits',
@@ -108,10 +108,10 @@ def main():
     rotate_stokes = True           #rotation to North convention can give erroneous results
     rotate_data = False              #rotation to North convention can give erroneous results
     # Polarization map output
-    figname = 'MKN463_FOC'         #target/intrument name
+    figname = 'NGC1068_FOC'         #target/intrument name
-    figtype = '_combine_FWHM020_rot'    #additionnal informations
+    figtype = '_3_combine_FWHM020'    #additionnal informations
-    SNRp_cut = 3    #P measurments with SNR>3
+    SNRp_cut = 30    #P measurments with SNR>3
-    SNRi_cut = 30   #I measurments with SNR>30, which implies an uncertainty in P of 4.7%.
+    SNRi_cut = 300   #I measurments with SNR>30, which implies an uncertainty in P of 4.7%.
     step_vec = 1    #plot all vectors in the array. if step_vec = 2, then every other vector will be plotted
 
     ##### Pipeline start
@@ -145,16 +145,26 @@ def main():
     for data in data_array:
         if (data < 0.).any():
             print("ETAPE 5 : ", data)
+
+    vertex = image_hull((1.-data_mask),step=5,null_val=0.,inside=True)
+    shape = np.array([vertex[1]-vertex[0],vertex[3]-vertex[2]])
+    rectangle = [vertex[2], vertex[0], shape[1], shape[0], 0., 'w']
+
 # Rotate data to have North up
     ref_header = copy.deepcopy(headers[0])
     if rotate_data:
+        alpha = ref_header['orientat']
+        mrot = np.array([[np.cos(-alpha), -np.sin(-alpha)],
+            [np.sin(-alpha), np.cos(-alpha)]])
+        rectangle[0:2] = np.dot(mrot, np.asarray(rectangle[0:2]))
+        rectangle[4] = alpha
         data_array, error_array, data_mask, headers = proj_red.rotate_data(data_array, error_array, data_mask, headers, -ref_header['orientat'])
         for data in data_array:
             if (data < 0.).any():
                 print("ETAPE 6 : ", data)
     #Plot array for checking output
     if display_data:
-        proj_plots.plot_obs(data_array, headers, vmin=data_array.min(), vmax=data_array.max(), savename=figname+"_center_"+align_center, plots_folder=plots_folder)
+        proj_plots.plot_obs(data_array, headers, vmin=data_array.min(), vmax=data_array.max(), rectangle =[rectangle,]*data_array.shape[0], savename=figname+"_center_"+align_center, plots_folder=plots_folder)
 
     ## Step 2:
     # Compute Stokes I, Q, U with smoothed polarized images
@@ -166,8 +176,13 @@ def main():
 
     ## Step 3:
     # Rotate images to have North up
-    if rotate_stokes:
     ref_header = copy.deepcopy(headers[0])
+    if rotate_stokes:
+        alpha = ref_header['orientat']
+        mrot = np.array([[np.cos(-alpha), -np.sin(-alpha)],
+            [np.sin(-alpha), np.cos(-alpha)]])
+        rectangle[0:2] = np.dot(mrot, np.asarray(rectangle[0:2]))
+        rectangle[4] = alpha
         I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers = proj_red.rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, headers, -ref_header['orientat'], SNRi_cut=None)
     # Compute polarimetric parameters (polarization degree and angle).
     P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P = proj_red.compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers)
@@ -178,11 +193,11 @@ def main():
 
     ## Step 5:
     # Plot polarization map (Background is either total Flux, Polarization degree or Polarization degree error).
-    proj_plots.polarization_map(copy.deepcopy(Stokes_test), data_mask, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype, plots_folder=plots_folder, display=None)
+    proj_plots.polarization_map(copy.deepcopy(Stokes_test), rectangle, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype, plots_folder=plots_folder, display=None)
-    proj_plots.polarization_map(copy.deepcopy(Stokes_test), data_mask, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_P", plots_folder=plots_folder, display='Pol_deg')
+    proj_plots.polarization_map(copy.deepcopy(Stokes_test), rectangle, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_P", plots_folder=plots_folder, display='Pol_deg')
-    proj_plots.polarization_map(copy.deepcopy(Stokes_test), data_mask, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_P_err", plots_folder=plots_folder, display='Pol_deg_err')
+    proj_plots.polarization_map(copy.deepcopy(Stokes_test), rectangle, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_P_err", plots_folder=plots_folder, display='Pol_deg_err')
-    proj_plots.polarization_map(copy.deepcopy(Stokes_test), data_mask, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_SNRi", plots_folder=plots_folder, display='SNRi')
+    proj_plots.polarization_map(copy.deepcopy(Stokes_test), rectangle, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_SNRi", plots_folder=plots_folder, display='SNRi')
-    proj_plots.polarization_map(copy.deepcopy(Stokes_test), data_mask, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_SNRp", plots_folder=plots_folder, display='SNRp')
+    proj_plots.polarization_map(copy.deepcopy(Stokes_test), rectangle, SNRp_cut=SNRp_cut, SNRi_cut=SNRi_cut, step_vec=step_vec, savename=figname+figtype+"_SNRp", plots_folder=plots_folder, display='SNRp')
 
     return 0
 

src/lib/plots.py

@@ -73,16 +73,20 @@ def plot_obs(data_array, headers, shape=None, vmin=0., vmax=6., rectangle=None,
         #plots
         im = ax.imshow(data, vmin=vmin, vmax=vmax, origin='lower')
         if not(rectangle is None):
-            x, y, width, height, color = rectangle[i]
+            x, y, width, height, angle, color = rectangle[i]
-            ax.add_patch(Rectangle((x, y), width, height, edgecolor=color, fill=False))
+            ax.add_patch(Rectangle((x, y), width, height, angle=angle,
+                edgecolor=color, fill=False))
         #position of centroid
         ax.plot([data.shape[1]/2, data.shape[1]/2], [0,data.shape[0]-1], lw=1,
                 color='black')
         ax.plot([0,data.shape[1]-1], [data.shape[1]/2, data.shape[1]/2], lw=1,
                 color='black')
-        ax.annotate(instr+":"+rootname, color='white', fontsize=5, xy=(0.02, 0.95), xycoords='axes fraction')
+        ax.annotate(instr+":"+rootname,color='white',fontsize=5,xy=(0.02, 0.95),
-        ax.annotate(filt, color='white', fontsize=10, xy=(0.02, 0.02), xycoords='axes fraction')
+                xycoords='axes fraction')
-        ax.annotate(exptime, color='white', fontsize=5, xy=(0.80, 0.02), xycoords='axes fraction')
+        ax.annotate(filt,color='white',fontsize=10,xy=(0.02, 0.02),
+                xycoords='axes fraction')
+        ax.annotate(exptime,color='white',fontsize=5,xy=(0.80, 0.02),
+                xycoords='axes fraction')
 
     fig.subplots_adjust(hspace=0, wspace=0, right=0.85)
     cbar_ax = fig.add_axes([0.9, 0.12, 0.02, 0.75])
@@ -144,7 +148,7 @@ def plot_Stokes(Stokes, savename=None, plots_folder=""):
     return 0
 
 
-def polarization_map(Stokes, data_mask, SNRp_cut=3., SNRi_cut=30., step_vec=1,
+def polarization_map(Stokes, rectangle=None, SNRp_cut=3., SNRi_cut=30., step_vec=1,
         savename=None, plots_folder="", display=None):
     """
     Plots polarization map from Stokes HDUList.
@@ -153,6 +157,10 @@ def polarization_map(Stokes, data_mask, SNRp_cut=3., SNRi_cut=30., step_vec=1,
     Stokes : astropy.io.fits.hdu.hdulist.HDUList
         HDUList containing I, Q, U, P, s_P, PA, s_PA (in this particular order)
         for one observation.
+    rectangle : numpy.ndarray, optional
+        Array of parameters for matplotlib.patches.Rectangle objects that will
+        be displayed on each output image. If None, no rectangle displayed.
+        Defaults to None.
     SNRp_cut : float, optional
         Cut that should be applied to the signal-to-noise ratio on P.
         Any SNR < SNRp_cut won't be displayed.
@@ -279,6 +287,12 @@ def polarization_map(Stokes, data_mask, SNRp_cut=3., SNRi_cut=30., step_vec=1,
     north_dir = AnchoredDirectionArrows(ax.transAxes, "E", "N", length=-0.08, fontsize=0.03, loc=1, aspect_ratio=-1, sep_y=0.01, sep_x=0.01, angle=-Stokes[0].header['orientat'], color='w', arrow_props={'ec': 'w', 'fc': 'w', 'alpha': 1,'lw': 2})
     ax.add_artist(north_dir)
 
+    # Display instrument FOV
+    if not(rectangle is None):
+        x, y, width, height, angle, color = rectangle
+        ax.add_patch(Rectangle((x, y), width, height, angle=angle,
+            edgecolor=color, fill=False))
+
     # Compute integrated parameters and associated errors for pixels in the cut
     n_pix = mask.size
     I_int = stkI.data[mask].sum()
@@ -294,7 +308,7 @@ def polarization_map(Stokes, data_mask, SNRp_cut=3., SNRi_cut=30., step_vec=1,
     P_int = np.sqrt(Q_int**2+U_int**2)/I_int*100.
     P_int_err = (100./I_int)*np.sqrt((Q_int**2*Q_int_err**2 + U_int**2*U_int_err**2 + 2.*Q_int*U_int*QU_int_err)/(Q_int**2 + U_int**2) + ((Q_int/I_int)**2 + (U_int/I_int)**2)*I_int_err**2 - 2.*(Q_int/I_int)*IQ_int_err - 2.*(U_int/I_int)*IU_int_err)
 
-    PA_int = (90./np.pi)*np.arctan2(U_int,Q_int)+90.
+    PA_int = (90./np.pi)*np.arctan2(U_int,Q_int)+90.*2
     PA_int_err = (90./(np.pi*(Q_int**2 + U_int**2)))*np.sqrt(U_int**2*Q_int_err**2 + Q_int**2*U_int_err**2 - 2.*Q_int*U_int*QU_int_err)
 
     # Compute integrated parameters and associated errors for all pixels
@@ -313,7 +327,7 @@ def polarization_map(Stokes, data_mask, SNRp_cut=3., SNRi_cut=30., step_vec=1,
     P_diluted_err = (100./I_diluted)*np.sqrt((Q_diluted**2*Q_diluted_err**2 + U_diluted**2*U_diluted_err**2 + 2.*Q_diluted*U_diluted*QU_diluted_err)/(Q_diluted**2 + U_diluted**2) + ((Q_diluted/I_diluted)**2 + (U_diluted/I_diluted)**2)*I_diluted_err**2 - 2.*(Q_diluted/I_diluted)*IQ_diluted_err - 2.*(U_diluted/I_diluted)*IU_diluted_err)
     P_diluted_err = np.sqrt(2/n_pix)*100.
 
-    PA_diluted = (90./np.pi)*np.arctan2(U_diluted,Q_diluted)+90.
+    PA_diluted = (90./np.pi)*np.arctan2(U_diluted,Q_diluted)+90.*2
     PA_diluted_err = (90./(np.pi*(Q_diluted**2 + U_diluted**2)))*np.sqrt(U_diluted**2*Q_diluted_err**2 + Q_diluted**2*U_diluted_err**2 - 2.*Q_diluted*U_diluted*QU_diluted_err)
     PA_diluted_err = P_diluted_err/(2.*P_diluted)*180./np.pi
 

src/lib/reduction.py

@@ -215,7 +215,7 @@ def crop_array(data_array, headers, error_array=None, step=5, null_val=None,
     if null_val is None:
         null_val = [1.00*error.mean() for error in error_array]
     elif type(null_val) is float:
-        null_val = [null_val,]*len(error_array)
+        null_val = [null_val,]*error_array.shape[0]
 
     vertex = np.zeros((data_array.shape[0],4),dtype=int)
     for i,image in enumerate(data_array):
@@ -233,7 +233,7 @@ def crop_array(data_array, headers, error_array=None, step=5, null_val=None,
         v_array[3] = np.max(vertex[:,3]).astype(int)
 
     new_shape = np.array([v_array[1]-v_array[0],v_array[3]-v_array[2]])
-    rectangle = [v_array[2], v_array[0], new_shape[1], new_shape[0], 'b']
+    rectangle = [v_array[2], v_array[0], new_shape[1], new_shape[0], 0., 'b']
     if display:
         fig, ax = plt.subplots()
         data = data_array[0]
@@ -243,7 +243,7 @@ def crop_array(data_array, headers, error_array=None, step=5, null_val=None,
         filt = headers[0]['filtnam1']
         #plots
         im = ax.imshow(data, vmin=data.min(), vmax=data.max(), origin='lower')
-        x, y, width, height, color = rectangle
+        x, y, width, height, angle, color = rectangle
         ax.add_patch(Rectangle((x, y),width,height,edgecolor=color,fill=False))
         #position of centroid
         ax.plot([data.shape[1]/2, data.shape[1]/2], [0,data.shape[0]-1], lw=1,
@@ -432,7 +432,7 @@ def get_error(data_array, sub_shape=(15,15), display=False, headers=None,
     minima = np.unravel_index(np.argmin(temp.sum(axis=0)),temp.shape[1:])
 
     for i, image in enumerate(data):
-        rectangle.append([minima[1], minima[0], sub_shape[1], sub_shape[0], 'r'])
+        rectangle.append([minima[1], minima[0], sub_shape[1], sub_shape[0], 0., 'r'])
         # Compute error : root mean square of the background
         sub_image = image[minima[0]:minima[0]+sub_shape[0],minima[1]:minima[1]+sub_shape[1]]
         #error =  np.std(sub_image)    # Previously computed using standard deviation over the background
@@ -819,7 +819,7 @@ def smooth_data(data_array, error_array, data_mask, headers, FWHM=1.,
             for c in range(smoothed.shape[1]):
                 # Compute distance from current pixel
                 dist_rc = np.where(data_mask, fmax, np.sqrt((r-xx)**2+(c-yy)**2))
-                g_rc = np.array([np.exp(-0.5*(dist_rc/stdev)**2),]*len(data_array))
+                g_rc = np.array([np.exp(-0.5*(dist_rc/stdev)**2),]*data_array.shape[0])
                 # Apply weighted combination
                 smoothed[r,c] = (1.-data_mask[r,c])*np.sum(data_array*weight*g_rc)/np.sum(weight*g_rc)
                 error[r,c] = np.sqrt(np.sum(weight*g_rc**2))/np.sum(weight*g_rc)
@@ -1064,9 +1064,55 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
             print("WARNING : Negative value in polarizer array.")
 
         # Stokes parameters
-        I_stokes = (2./3.)*(pol0 + pol60 + pol120)
+        #default
-        Q_stokes = (2./3.)*(2*pol0 - pol60 - pol120)
+        #I_stokes = (2./3.)*(pol0 + pol60 + pol120)
-        U_stokes = (2./np.sqrt(3.))*(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']
+        filt4 = headers[0]['filtnam4']
+        same_filt2 = np.array([filt2 == header['filtnam2'] for header in headers]).all()
+        same_filt3 = np.array([filt3 == header['filtnam3'] for header in headers]).all()
+        same_filt4 = np.array([filt4 == header['filtnam4'] for header in headers]).all()
+        if not (same_filt2 and same_filt3 and same_filt4):
+            print("WARNING : All images in data_array are not from the same \
+                    band filter, the limiting transmittance will be taken.")
+            transmit2 = np.min([trans2[header['filtnam2'].lower()] for header in headers])
+            transmit3 = np.min([trans3[header['filtnam3'].lower()] for header in headers])
+            transmit4 = np.min([trans4[header['filtnam4'].lower()] for header in headers])
+        else :
+            transmit2 = trans2[filt2.lower()]
+            transmit3 = trans3[filt3.lower()]
+            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]])
+
+        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))
+        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
+
+        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)
 
         # Remove nan
         I_stokes[np.isnan(I_stokes)]=0.
@@ -1077,7 +1123,7 @@ def compute_Stokes(data_array, error_array, data_mask, headers,
 
         mask = (Q_stokes**2 + U_stokes**2) > I_stokes**2
         if mask.any():
-            print("WARNING : I_pol > I_stokes : ", len(I_stokes[mask]))
+            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()
@@ -1156,10 +1202,10 @@ 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
+    PA = (90./np.pi)*np.arctan2(U_stokes,Q_stokes)+90.*2.
 
     if (P>100.).any():
-        print("WARNING : found pixels for which P > 100%", len(P[P>100.]))
+        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])
@@ -1169,7 +1215,7 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, headers):
     debiased_P = np.sqrt(P**2 - s_P**2)
 
     if (debiased_P>100.).any():
-        print("WARNING : found pixels for which debiased_P > 100%", len(debiased_P[debiased_P>100.]))
+        print("WARNING : found pixels for which debiased_P > 100%", debiased_P[debiased_P>100.].size)
 
     #Compute the total exposure time so that
     #I_stokes*exp_tot = N_tot the total number of events
@@ -1226,7 +1272,7 @@ def rotate_data(data_array, error_array, data_mask, headers, ang):
     #Rotate original images using scipy.ndimage.rotate
     new_data_array = []
     new_error_array = []
-    for i in range(len(data_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,
@@ -1235,7 +1281,7 @@ def rotate_data(data_array, error_array, data_mask, headers, ang):
     new_data_mask = sc_rotate(data_mask, ang, reshape=False, cval=True)
     new_error_array = np.array(new_error_array)
 
-    for i in range(len(new_data_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