correction for Stokes_cov and P_diluted_err propagation

package/FOC_reduction.py

@@ -40,12 +40,12 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
     display_crop = False
 
     # Background estimation
-    error_sub_type = "scott"  # sqrt, sturges, rice, scott, freedman-diaconis (default) or shape (example (51, 51))
-    subtract_error = 1.50
+    error_sub_type = "freedman-diaconis"  # sqrt, sturges, rice, scott, freedman-diaconis (default) or shape (example (51, 51))
+    subtract_error = 1.33
     display_bkg = True
 
     # Data binning
-    pxsize = 0.10
+    pxsize = 0.05
     pxscale = "arcsec"  # pixel, arcsec or full
     rebin_operation = "sum"  # sum or average
 
@@ -59,7 +59,7 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
 
     # Smoothing
     smoothing_function = "combine"  # gaussian_after, weighted_gaussian_after, gaussian, weighted_gaussian or combine
-    smoothing_FWHM = 0.150  # If None, no smoothing is done
+    smoothing_FWHM = 0.075  # If None, no smoothing is done
     smoothing_scale = "arcsec"  # pixel or arcsec
 
     # Rotation
@@ -117,10 +117,9 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
         figtype = "_".join([figtype, "not_aligned"] if figtype != "" else ["not_aligned"])
 
     #  Crop data to remove outside blank margins.
-    data_array, error_array, headers = proj_red.crop_array(
-        data_array, headers, step=5, null_val=0.0, inside=True, display=display_crop, savename=figname, plots_folder=plots_folder
+    data_array, error_array, data_mask, headers = proj_red.crop_array(
+        data_array, headers, step=5, null_val=0.0, crop=True, inside=True, display=display_crop, savename=figname, plots_folder=plots_folder
     )
-    data_mask = np.ones(data_array[0].shape, dtype=bool)
 
     #  Deconvolve data using Richardson-Lucy iterative algorithm with a gaussian PSF of given FWHM.
     if deconvolve:
@@ -217,26 +216,26 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
     # FWHM of FOC have been estimated at about 0.03" across 1500-5000 Angstrom band, which is about 2 detector pixels wide
     # see Jedrzejewski, R.; Nota, A.; Hack, W. J., A Comparison Between FOC and WFPC2
     # Bibcode : 1995chst.conf...10J
-    I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes = proj_red.compute_Stokes(
+    I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes = proj_red.compute_Stokes(
         data_array, error_array, data_mask, headers, FWHM=smoothing_FWHM, scale=smoothing_scale, smoothing=smoothing_function, transmitcorr=transmitcorr
     )
-    I_bkg, Q_bkg, U_bkg, S_cov_bkg, header_bkg = proj_red.compute_Stokes(
+    I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, header_bkg = proj_red.compute_Stokes(
         background, background_error, np.array(True).reshape(1, 1), headers, FWHM=None, scale=smoothing_scale, smoothing=smoothing_function, transmitcorr=False
     )
 
     # Step 3:
     # Rotate images to have North up
     if rotate_North:
-        I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes = proj_red.rotate_Stokes(
-            I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes, SNRi_cut=None
+        I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, data_mask, header_stokes = proj_red.rotate_Stokes(
+            I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, data_mask, header_stokes, SNRi_cut=None
         )
-        I_bkg, Q_bkg, U_bkg, S_cov_bkg, data_mask_bkg, header_bkg = proj_red.rotate_Stokes(
-            I_bkg, Q_bkg, U_bkg, S_cov_bkg, np.array(True).reshape(1, 1), header_bkg, SNRi_cut=None
+        I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, data_mask_bkg, header_bkg = proj_red.rotate_Stokes(
+            I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, np.array(True).reshape(1, 1), header_bkg, 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, header_stokes)
-    P_bkg, debiased_P_bkg, s_P_bkg, s_P_P_bkg, PA_bkg, s_PA_bkg, s_PA_P_bkg = proj_red.compute_pol(I_bkg, Q_bkg, U_bkg, S_cov_bkg, header_bkg)
+    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, Stokes_stat_cov, header_stokes)
+    P_bkg, debiased_P_bkg, s_P_bkg, s_P_P_bkg, PA_bkg, s_PA_bkg, s_PA_P_bkg = proj_red.compute_pol(I_bkg, Q_bkg, U_bkg, S_cov_bkg, S_stat_cov_bkg, header_bkg)
 
     # Step 4:
     # Save image to FITS.
@@ -246,6 +245,7 @@ def main(target=None, proposal_id=None, infiles=None, output_dir="./data", crop=
         Q_stokes,
         U_stokes,
         Stokes_cov,
+        Stokes_stat_cov,
         P,
         debiased_P,
         s_P,

package/lib/fits.py

@@ -106,7 +106,23 @@ def get_obs_data(infiles, data_folder="", compute_flux=False):
 
 
 def save_Stokes(
-    I_stokes, Q_stokes, U_stokes, Stokes_cov, P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P, header_stokes, data_mask, filename, data_folder="", return_hdul=False
+    I_stokes,
+    Q_stokes,
+    U_stokes,
+    Stokes_cov,
+    Stokes_stat_cov,
+    P,
+    debiased_P,
+    s_P,
+    s_P_P,
+    PA,
+    s_PA,
+    s_PA_P,
+    header_stokes,
+    data_mask,
+    filename,
+    data_folder="",
+    return_hdul=False,
 ):
     """
     Save computed polarimetry parameters to a single fits file,
@@ -186,11 +202,15 @@ def save_Stokes(
         s_PA_P = s_PA_P[vertex[2] : vertex[3], vertex[0] : vertex[1]]
 
         new_Stokes_cov = np.zeros((*Stokes_cov.shape[:-2], *shape[::-1]))
+        new_Stokes_stat_cov = np.zeros((*Stokes_stat_cov.shape[:-2], *shape[::-1]))
         for i in range(3):
             for j in range(3):
                 Stokes_cov[i, j][(1 - data_mask).astype(bool)] = 0.0
                 new_Stokes_cov[i, j] = Stokes_cov[i, j][vertex[2] : vertex[3], vertex[0] : vertex[1]]
+                Stokes_stat_cov[i, j][(1 - data_mask).astype(bool)] = 0.0
+                new_Stokes_stat_cov[i, j] = Stokes_stat_cov[i, j][vertex[2] : vertex[3], vertex[0] : vertex[1]]
         Stokes_cov = new_Stokes_cov
+        Stokes_stat_cov = new_Stokes_stat_cov
 
         data_mask = data_mask[vertex[2] : vertex[3], vertex[0] : vertex[1]]
     data_mask = data_mask.astype(float, copy=False)
@@ -210,18 +230,19 @@ def save_Stokes(
         [Q_stokes, "Q_stokes"],
         [U_stokes, "U_stokes"],
         [Stokes_cov, "IQU_cov_matrix"],
+        [Stokes_stat_cov, "IQU_stat_cov_matrix"],
         [P, "Pol_deg"],
         [debiased_P, "Pol_deg_debiased"],
         [s_P, "Pol_deg_err"],
-        [s_P_P, "Pol_deg_err_Poisson_noise"],
+        [s_P_P, "Pol_deg_stat_err"],
         [PA, "Pol_ang"],
         [s_PA, "Pol_ang_err"],
-        [s_PA_P, "Pol_ang_err_Poisson_noise"],
+        [s_PA_P, "Pol_ang_stat_err"],
         [data_mask, "Data_mask"],
     ]:
         hdu_header = header.copy()
         hdu_header["datatype"] = name
-        if not name == "IQU_cov_matrix":
+        if not name[-10:] == "cov_matrix":
             data[(1 - data_mask).astype(bool)] = 0.0
         hdu = fits.ImageHDU(data=data, header=hdu_header)
         hdu.name = name

package/lib/plots.py

@@ -360,7 +360,7 @@ def polarization_map(
     if fig is None:
         ratiox = max(int(stkI.shape[1] / (stkI.shape[0])), 1)
         ratioy = max(int((stkI.shape[0]) / stkI.shape[1]), 1)
-        fig = plt.figure(figsize=(7 * ratiox, 7 * ratioy), layout="constrained")
+        fig = plt.figure(figsize=(8 * ratiox, 8 * ratioy), layout="constrained")
     if ax is None:
         ax = fig.add_subplot(111, projection=wcs)
         ax.set(aspect="equal", fc="k")  # , ylim=[-0.05 * stkI.shape[0], 1.05 * stkI.shape[0]])
@@ -435,33 +435,33 @@ def polarization_map(
         else:
             vmin, vmax = 1.0 / 2.0 * np.median(np.sqrt(stk_cov[0, 0][stkI > 0.0]) * convert_flux), np.max(stkI[stkI > 0.0] * convert_flux)
             pfmax = (stkI[stkI > 0.0] * pol[stkI > 0.0] * convert_flux).max()
-        im = ax.imshow(stkI * convert_flux * pol, norm=LogNorm(vmin, vmax), aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+        im = ax.imshow(stkI * convert_flux * pol, norm=LogNorm(vmin, vmax), aspect="equal", cmap=kwargs["cmap"], alpha=1.0 - 0.75 * (pol < pol_err))
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$F_{\lambda} \cdot P$ [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]")
         # levelsPf = np.linspace(0.0.60, 0.50, 5) * pfmax
-        levelsPf = np.array([1.73, 13.0, 33.0, 66.0]) / 100.0 * pfmax
+        levelsPf = np.array([13.0, 33.0, 66.0]) / 100.0 * pfmax
         print("Polarized flux density contour levels : ", levelsPf)
         ax.contour(stkI * convert_flux * pol, levels=levelsPf, colors="grey", linewidths=0.5)
     elif display.lower() in ["p", "pol", "pol_deg"]:
         # Display polarization degree map
         display = "p"
-        vmin, vmax = 0.0, min(pol[np.isfinite(pol)].max(), 1.0) * 100.0
-        im = ax.imshow(pol * 100.0, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+        vmin, vmax = 0.0, min(pol[pol > pol_err].max(), 1.0) * 100.0
+        im = ax.imshow(pol * 100.0, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0 - 0.75 * (pol < pol_err))
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$P$ [%]")
     elif display.lower() in ["pa", "pang", "pol_ang"]:
         # Display polarization degree map
         display = "pa"
         vmin, vmax = 0.0, 180.0
-        im = ax.imshow(princ_angle(pang), vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+        im = ax.imshow(princ_angle(pang), vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0 - 0.75 * (pol < pol_err))
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$\theta_P$ [°]")
     elif display.lower() in ["s_p", "pol_err", "pol_deg_err"]:
         # Display polarization degree error map
         display = "s_p"
         if (SNRp > P_cut).any():
             vmin, vmax = 0.0, np.max([pol_err[SNRp > P_cut].max(), 1.0]) * 100.0
-            im = ax.imshow(pol_err * 100.0, vmin=vmin, vmax=vmax, aspect="equal", cmap="inferno_r", alpha=1.0)
+            im = ax.imshow(pol_err * 100.0, vmin=vmin, vmax=vmax, aspect="equal", cmap="inferno_r", alpha=1.0 - 0.75 * (pol < pol_err))
         else:
             vmin, vmax = 0.0, 100.0
-            im = ax.imshow(pol_err * 100.0, vmin=vmin, vmax=vmax, aspect="equal", cmap="inferno_r", alpha=1.0)
+            im = ax.imshow(pol_err * 100.0, vmin=vmin, vmax=vmax, aspect="equal", cmap="inferno_r", alpha=1.0 - 0.75 * (pol < pol_err))
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$\sigma_P$ [%]")
     elif display.lower() in ["s_i", "i_err"]:
         # Display intensity error map
@@ -471,39 +471,41 @@ def polarization_map(
                 1.0 / 2.0 * np.median(np.sqrt(stk_cov[0, 0][stk_cov[0, 0] > 0.0]) * convert_flux),
                 np.max(np.sqrt(stk_cov[0, 0][stk_cov[0, 0] > 0.0]) * convert_flux),
             )
-            im = ax.imshow(np.sqrt(stk_cov[0, 0]) * convert_flux, norm=LogNorm(vmin, vmax), aspect="equal", cmap="inferno_r", alpha=1.0)
+            im = ax.imshow(
+                np.sqrt(stk_cov[0, 0]) * convert_flux, norm=LogNorm(vmin, vmax), aspect="equal", cmap="inferno_r", alpha=1.0 - 0.75 * (pol < pol_err)
+            )
         else:
-            im = ax.imshow(np.sqrt(stk_cov[0, 0]) * convert_flux, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+            im = ax.imshow(np.sqrt(stk_cov[0, 0]) * convert_flux, aspect="equal", cmap=kwargs["cmap"], alpha=1.0 - 0.75 * (pol < pol_err))
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$\sigma_I$ [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]")
     elif display.lower() in ["snri"]:
         # Display I_stokes signal-to-noise map
         display = "snri"
         vmin, vmax = 0.0, np.max(SNRi[np.isfinite(SNRi)])
-        if vmax * 0.99 > SNRi_cut:
-            im = ax.imshow(SNRi, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
-            levelsSNRi = np.linspace(SNRi_cut, vmax * 0.99, 5).astype(int)
+        if vmax * 0.99 > SNRi_cut + 3:
+            im = ax.imshow(SNRi, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"])
+            levelsSNRi = np.linspace(SNRi_cut, vmax * 0.99, 3).astype(int)
             print("SNRi contour levels : ", levelsSNRi)
             ax.contour(SNRi, levels=levelsSNRi, colors="grey", linewidths=0.5)
         else:
-            im = ax.imshow(SNRi, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+            im = ax.imshow(SNRi, aspect="equal", cmap=kwargs["cmap"])
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$I_{Stokes}/\sigma_{I}$")
     elif display.lower() in ["snr", "snrp"]:
         # Display polarization degree signal-to-noise map
         display = "snrp"
         vmin, vmax = 0.0, np.max(SNRp[np.isfinite(SNRp)])
-        if vmax * 0.99 > SNRp_cut:
-            im = ax.imshow(SNRp, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
-            levelsSNRp = np.linspace(P_cut, vmax * 0.99, 5).astype(int)
+        if vmax * 0.99 > SNRp_cut + 3:
+            im = ax.imshow(SNRp, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"])
+            levelsSNRp = np.linspace(SNRp_cut, vmax * 0.99, 3).astype(int)
             print("SNRp contour levels : ", levelsSNRp)
             ax.contour(SNRp, levels=levelsSNRp, colors="grey", linewidths=0.5)
         else:
-            im = ax.imshow(SNRp, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+            im = ax.imshow(SNRp, aspect="equal", cmap=kwargs["cmap"])
         fig.colorbar(im, ax=ax, aspect=50, shrink=0.60, pad=0.025, label=r"$P/\sigma_{P}$")
     elif display.lower() in ["conf", "confp"]:
         # Display polarization degree signal-to-noise map
         display = "confp"
         vmin, vmax = 0.0, 1.0
-        im = ax.imshow(confP, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"], alpha=1.0)
+        im = ax.imshow(confP, vmin=vmin, vmax=vmax, aspect="equal", cmap=kwargs["cmap"])
         levelsconfp = np.array([0.500, 0.900, 0.990, 0.999])
         print("confp contour levels : ", levelsconfp)
         ax.contour(confP, levels=levelsconfp, colors="grey", linewidths=0.5)
@@ -1895,7 +1897,7 @@ class crop_map(object):
         else:
             self.ax = ax
             self.mask_alpha = 0.75
-            self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1])
+            self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1], spancoords="pixels", useblit=True)
             self.embedded = True
         self.ax.set(xlabel="Right Ascension (J2000)", ylabel="Declination (J2000)")
         self.display(self.data, self.wcs, self.map_convert, **self.kwargs)
@@ -1956,7 +1958,7 @@ class crop_map(object):
         self.display()
 
         if self.fig.canvas.manager.toolbar.mode == "":
-            self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1])
+            self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1], spancoords="pixels", useblit=True)
 
         self.RSextent = deepcopy(self.extent)
         self.RScenter = deepcopy(self.center)
@@ -2016,7 +2018,7 @@ class crop_map(object):
             self.ax.set_ylim(0, ylim)
 
             if self.fig.canvas.manager.toolbar.mode == "":
-                self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1])
+                self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1], spancoords="pixels", useblit=True)
 
         self.fig.canvas.draw_idle()
 
@@ -2028,7 +2030,7 @@ class crop_map(object):
 
     def crop(self) -> None:
         if self.fig.canvas.manager.toolbar.mode == "":
-            self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1])
+            self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1], spancoords="pixels", useblit=True)
         self.bapply.on_clicked(self.apply_crop)
         self.breset.on_clicked(self.reset_crop)
         self.fig.canvas.mpl_connect("close_event", self.on_close)
@@ -2077,7 +2079,7 @@ class crop_Stokes(crop_map):
 
             # Crop dataset
             for dataset in self.hdul_crop:
-                if dataset.header["datatype"] == "IQU_cov_matrix":
+                if dataset.header["datatype"][-10:] == "cov_matrix":
                     stokes_cov = np.zeros((3, 3, shape[1], shape[0]))
                     for i in range(3):
                         for j in range(3):
@@ -2100,18 +2102,24 @@ class crop_Stokes(crop_map):
                 self.on_close(event)
 
             if self.fig.canvas.manager.toolbar.mode == "":
-                self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1])
+                self.rect_selector = RectangleSelector(self.ax, self.onselect_crop, button=[1], spancoords="pixels", useblit=True)
         # Update integrated values
-        mask = np.logical_and(self.hdul_crop["data_mask"].data.astype(bool), self.hdul_crop[0].data > 0)
-        I_diluted = self.hdul_crop["i_stokes"].data[mask].sum()
-        Q_diluted = self.hdul_crop["q_stokes"].data[mask].sum()
-        U_diluted = self.hdul_crop["u_stokes"].data[mask].sum()
-        I_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[0, 0][mask]))
-        Q_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[1, 1][mask]))
-        U_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[2, 2][mask]))
-        IQ_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[0, 1][mask] ** 2))
-        IU_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[0, 2][mask] ** 2))
-        QU_diluted_err = np.sqrt(np.sum(self.hdul_crop["iqu_cov_matrix"].data[1, 2][mask] ** 2))
+        mask = np.logical_and(self.hdul_crop["DATA_MASK"].data.astype(bool), self.hdul_crop[0].data > 0)
+        I_diluted = self.hdul_crop["I_STOKES"].data[mask].sum()
+        Q_diluted = self.hdul_crop["Q_STOKES"].data[mask].sum()
+        U_diluted = self.hdul_crop["U_STOKES"].data[mask].sum()
+        I_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[0, 0][mask]))
+        Q_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[1, 1][mask]))
+        U_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[2, 2][mask]))
+        IQ_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[0, 1][mask] ** 2))
+        IU_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[0, 2][mask] ** 2))
+        QU_diluted_err = np.sqrt(np.sum(self.hdul_crop["IQU_COV_MATRIX"].data[1, 2][mask] ** 2))
+        I_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[0, 0][mask]))
+        Q_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[1, 1][mask]))
+        U_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[2, 2][mask]))
+        IQ_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[0, 1][mask] ** 2))
+        IU_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[0, 2][mask] ** 2))
+        QU_diluted_stat_err = np.sqrt(np.sum(self.hdul_crop["IQU_STAT_COV_MATRIX"].data[1, 2][mask] ** 2))
 
         P_diluted = np.sqrt(Q_diluted**2 + U_diluted**2) / I_diluted
         P_diluted_err = (1.0 / I_diluted) * np.sqrt(
@@ -2120,6 +2128,18 @@ class crop_Stokes(crop_map):
             - 2.0 * (Q_diluted / I_diluted) * IQ_diluted_err
             - 2.0 * (U_diluted / I_diluted) * IU_diluted_err
         )
+        P_diluted_stat_err = (
+            P_diluted
+            / I_diluted
+            * np.sqrt(
+                I_diluted_stat_err
+                - 2.0 / (I_diluted * P_diluted**2) * (Q_diluted * IQ_diluted_stat_err + U_diluted * IU_diluted_stat_err)
+                + 1.0
+                / (I_diluted**2 * P_diluted**4)
+                * (Q_diluted**2 * Q_diluted_stat_err + U_diluted**2 * U_diluted_stat_err + 2.0 * Q_diluted * U_diluted * QU_diluted_stat_err)
+            )
+        )
+        debiased_P_diluted = np.sqrt(P_diluted**2 - P_diluted_stat_err**2) if P_diluted**2 > P_diluted_stat_err**2 else 0.0
 
         PA_diluted = princ_angle((90.0 / np.pi) * np.arctan2(U_diluted, Q_diluted))
         PA_diluted_err = (90.0 / (np.pi * (Q_diluted**2 + U_diluted**2))) * np.sqrt(
@@ -2129,7 +2149,7 @@ class crop_Stokes(crop_map):
         for dataset in self.hdul_crop:
             if dataset.header["FILENAME"][-4:] != "crop":
                 dataset.header["FILENAME"] += "_crop"
-            dataset.header["P_int"] = (P_diluted, "Integrated polarization degree")
+            dataset.header["P_int"] = (debiased_P_diluted, "Integrated polarization degree")
             dataset.header["sP_int"] = (np.ceil(P_diluted_err * 1000.0) / 1000.0, "Integrated polarization degree error")
             dataset.header["PA_int"] = (PA_diluted, "Integrated polarization angle")
             dataset.header["sPA_int"] = (np.ceil(PA_diluted_err * 10.0) / 10.0, "Integrated polarization angle error")
@@ -2463,9 +2483,11 @@ class pol_map(object):
         ax_snr_reset = self.fig.add_axes([0.060, 0.020, 0.05, 0.02])
         ax_snr_conf = self.fig.add_axes([0.115, 0.020, 0.05, 0.02])
         SNRi_max = np.max(self.I[self.IQU_cov[0, 0] > 0.0] / np.sqrt(self.IQU_cov[0, 0][self.IQU_cov[0, 0] > 0.0]))
-        SNRp_max = np.max(self.P[self.s_P > 0.0] / self.s_P[self.s_P > 0.0])
+        SNRp_max = np.max(self.P[self.P_ERR > 0.0] / self.P_ERR[self.P_ERR > 0.0])
         s_I_cut = Slider(ax_I_cut, r"$SNR^{I}_{cut}$", 1.0, int(SNRi_max * 0.95), valstep=1, valinit=self.SNRi_cut)
-        self.s_P_cut = Slider(self.ax_P_cut, r"$Conf^{P}_{cut}$", 0.50, 1.0, valstep=[0.500, 0.900, 0.990, 0.999], valinit=self.P_cut if P_cut <= 1.0 else 0.99)
+        self.P_ERR_cut = Slider(
+            self.ax_P_cut, r"$Conf^{P}_{cut}$", 0.50, 1.0, valstep=[0.500, 0.900, 0.990, 0.999], valinit=self.P_cut if P_cut <= 1.0 else 0.99
+        )
         s_vec_sc = Slider(ax_vec_sc, r"Vec scale", 0.0, 10.0, valstep=1, valinit=self.scale_vec)
         b_snr_reset = Button(ax_snr_reset, "Reset")
         b_snr_reset.label.set_fontsize(8)
@@ -2493,7 +2515,7 @@ class pol_map(object):
 
         def reset_snr(event):
             s_I_cut.reset()
-            self.s_P_cut.reset()
+            self.P_ERR_cut.reset()
             s_vec_sc.reset()
 
         def toggle_snr_conf(event=None):
@@ -2502,21 +2524,21 @@ class pol_map(object):
             if self.snr_conf:
                 self.snr_conf = 0
                 b_snr_conf.label.set_text("Conf")
-                self.s_P_cut = Slider(
+                self.P_ERR_cut = Slider(
                     self.ax_P_cut, r"$SNR^{P}_{cut}$", 1.0, max(int(SNRp_max * 0.95), 3), valstep=1, valinit=self.P_cut if P_cut >= 1.0 else 3
                 )
             else:
                 self.snr_conf = 1
                 b_snr_conf.label.set_text("SNR")
-                self.s_P_cut = Slider(
+                self.P_ERR_cut = Slider(
                     self.ax_P_cut, r"$Conf^{P}_{cut}$", 0.50, 1.0, valstep=[0.500, 0.900, 0.990, 0.999], valinit=self.P_cut if P_cut <= 1.0 else 0.99
                 )
-            self.s_P_cut.on_changed(update_snrp)
-            update_snrp(self.s_P_cut.val)
+            self.P_ERR_cut.on_changed(update_snrp)
+            update_snrp(self.P_ERR_cut.val)
             self.fig.canvas.draw_idle()
 
         s_I_cut.on_changed(update_snri)
-        self.s_P_cut.on_changed(update_snrp)
+        self.P_ERR_cut.on_changed(update_snrp)
         s_vec_sc.on_changed(update_vecsc)
         b_snr_reset.on_clicked(reset_snr)
         b_snr_conf.on_clicked(toggle_snr_conf)
@@ -2957,12 +2979,16 @@ class pol_map(object):
     def IQU_cov(self):
         return self.Stokes["IQU_COV_MATRIX"].data
 
+    @property
+    def IQU_stat_cov(self):
+        return self.Stokes["IQU_STAT_COV_MATRIX"].data
+
     @property
     def P(self):
         return self.Stokes["POL_DEG_DEBIASED"].data
 
     @property
-    def s_P(self):
+    def P_ERR(self):
         return self.Stokes["POL_DEG_ERR"].data
 
     @property
@@ -2970,7 +2996,7 @@ class pol_map(object):
         return self.Stokes["POL_ANG"].data
 
     @property
-    def s_PA(self):
+    def PA_ERR(self):
         return self.Stokes["POL_ANG_ERR"].data
 
     @property
@@ -2978,7 +3004,7 @@ class pol_map(object):
         return self.Stokes["DATA_MASK"].data
 
     def set_data_mask(self, mask):
-        self.Stokes[np.argmax([self.Stokes[i].header["datatype"] == "Data_mask" for i in range(len(self.Stokes))])].data = mask.astype(float)
+        self.Stokes["DATA_MASK"].data = mask.astype(float)
 
     @property
     def cut(self):
@@ -2986,7 +3012,7 @@ class pol_map(object):
         SNRp_mask, SNRi_mask = (np.zeros(self.P.shape).astype(bool), np.zeros(self.I.shape).astype(bool))
         SNRi_mask[s_I > 0.0] = self.I[s_I > 0.0] / s_I[s_I > 0.0] > self.SNRi
         if self.SNRp >= 1.0:
-            SNRp_mask[self.s_P > 0.0] = self.P[self.s_P > 0.0] / self.s_P[self.s_P > 0.0] > self.SNRp
+            SNRp_mask[self.P_ERR > 0.0] = self.P[self.P_ERR > 0.0] / self.P_ERR[self.P_ERR > 0.0] > self.SNRp
         else:
             SNRp_mask = self.conf > self.SNRp
         return np.logical_and(SNRi_mask, SNRp_mask)
@@ -3054,7 +3080,7 @@ class pol_map(object):
         ax.add_artist(self.north_dir)
 
     def display(self, fig=None, ax=None, flux_lim=None):
-        norm = None
+        kwargs = dict([])
         if self.display_selection is None:
             self.display_selection = "total_flux"
         if flux_lim is None:
@@ -3065,7 +3091,7 @@ class pol_map(object):
                 vmin, vmax = (1.0 / 2.0 * np.median(self.data[self.data > 0.0]), np.max(self.data[self.data > 0.0]))
             else:
                 vmin, vmax = flux_lim
-            norm = LogNorm(vmin, vmax)
+            kwargs["norm"] = LogNorm(vmin, vmax)
             label = r"$F_{\lambda}$ [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]"
         elif self.display_selection.lower() in ["pol_flux"]:
             self.data = self.I * self.map_convert * self.P
@@ -3073,28 +3099,30 @@ class pol_map(object):
                 vmin, vmax = (1.0 / 2.0 * np.median(self.I[self.I > 0.0] * self.map_convert), np.max(self.I[self.I > 0.0] * self.map_convert))
             else:
                 vmin, vmax = flux_lim
-            norm = LogNorm(vmin, vmax)
+            kwargs["norm"] = LogNorm(vmin, vmax)
             label = r"$P \cdot F_{\lambda}$ [$ergs \cdot cm^{-2} \cdot s^{-1} \cdot \AA^{-1}$]"
         elif self.display_selection.lower() in ["pol_deg"]:
             self.data = self.P * 100.0
-            vmin, vmax = 0.0, np.max(self.data[self.P > self.s_P])
+            kwargs["vmin"], kwargs["vmax"] = 0.0, min(np.max(self.data[self.P > self.P_ERR]), 100.0)
+            kwargs["alpha"] = 1.0 - 0.75 * (self.P < self.P_ERR)
             label = r"$P$ [%]"
         elif self.display_selection.lower() in ["pol_ang"]:
             self.data = princ_angle(self.PA)
-            vmin, vmax = 0, 180.0
+            kwargs["vmin"], kwargs["vmax"] = 0, 180.0
+            kwargs["alpha"] = 1.0 - 0.75 * (self.P < self.P_ERR)
             label = r"$\theta_{P}$ [°]"
         elif self.display_selection.lower() in ["snri"]:
             s_I = np.sqrt(self.IQU_cov[0, 0])
             SNRi = np.zeros(self.I.shape)
             SNRi[s_I > 0.0] = self.I[s_I > 0.0] / s_I[s_I > 0.0]
             self.data = SNRi
-            vmin, vmax = 0.0, np.max(self.data[self.data > 0.0])
+            kwargs["vmin"], kwargs["vmax"] = 0.0, np.max(self.data[self.data > 0.0])
             label = r"$I_{Stokes}/\sigma_{I}$"
         elif self.display_selection.lower() in ["snrp"]:
             SNRp = np.zeros(self.P.shape)
-            SNRp[self.s_P > 0.0] = self.P[self.s_P > 0.0] / self.s_P[self.s_P > 0.0]
+            SNRp[self.P_ERR > 0.0] = self.P[self.P_ERR > 0.0] / self.P_ERR[self.P_ERR > 0.0]
             self.data = SNRp
-            vmin, vmax = 0.0, np.max(self.data[self.data > 0.0])
+            kwargs["vmin"], kwargs["vmax"] = 0.0, np.max(self.data[self.data > 0.0])
             label = r"$P/\sigma_{P}$"
 
         if fig is None:
@@ -3105,20 +3133,14 @@ class pol_map(object):
                 self.cbar.remove()
             if hasattr(self, "im"):
                 self.im.remove()
-            if norm is not None:
-                self.im = ax.imshow(self.data, norm=norm, aspect="equal", cmap="inferno")
-            else:
-                self.im = ax.imshow(self.data, vmin=vmin, vmax=vmax, aspect="equal", cmap="inferno")
+            self.im = ax.imshow(self.data, aspect="equal", cmap="inferno", **kwargs)
             plt.rcParams.update({"font.size": 14})
             self.cbar = fig.colorbar(self.im, ax=ax, aspect=50, shrink=0.75, pad=0.025, label=label)
             plt.rcParams.update({"font.size": 10})
             fig.canvas.draw_idle()
             return self.im
         else:
-            if norm is not None:
-                im = ax.imshow(self.data, norm=norm, aspect="equal", cmap="inferno")
-            else:
-                im = ax.imshow(self.data, vmin=vmin, vmax=vmax, aspect="equal", cmap="inferno")
+            im = ax.imshow(self.data, aspect="equal", cmap="inferno", **kwargs)
             ax.set_xlim(0, self.data.shape[1])
             ax.set_ylim(0, self.data.shape[0])
             plt.rcParams.update({"font.size": 14})
@@ -3163,12 +3185,12 @@ class pol_map(object):
             )
             if self.pa_err:
                 XY_U_err1, XY_V_err1 = (
-                    P_cut * np.cos(np.pi / 2.0 + (self.PA + 3.0 * self.s_PA) * np.pi / 180.0),
-                    P_cut * np.sin(np.pi / 2.0 + (self.PA + 3.0 * self.s_PA) * np.pi / 180.0),
+                    P_cut * np.cos(np.pi / 2.0 + (self.PA + 3.0 * self.P_ERRA) * np.pi / 180.0),
+                    P_cut * np.sin(np.pi / 2.0 + (self.PA + 3.0 * self.P_ERRA) * np.pi / 180.0),
                 )
                 XY_U_err2, XY_V_err2 = (
-                    P_cut * np.cos(np.pi / 2.0 + (self.PA - 3.0 * self.s_PA) * np.pi / 180.0),
-                    P_cut * np.sin(np.pi / 2.0 + (self.PA - 3.0 * self.s_PA) * np.pi / 180.0),
+                    P_cut * np.cos(np.pi / 2.0 + (self.PA - 3.0 * self.P_ERRA) * np.pi / 180.0),
+                    P_cut * np.sin(np.pi / 2.0 + (self.PA - 3.0 * self.P_ERRA) * np.pi / 180.0),
                 )
                 if hasattr(self, "quiver_err1"):
                     self.quiver_err1.remove()
@@ -3232,12 +3254,12 @@ class pol_map(object):
             )
             if self.pa_err:
                 XY_U_err1, XY_V_err1 = (
-                    P_cut * np.cos(np.pi / 2.0 + (self.PA + 3.0 * self.s_PA) * np.pi / 180.0),
-                    P_cut * np.sin(np.pi / 2.0 + (self.PA + 3.0 * self.s_PA) * np.pi / 180.0),
+                    P_cut * np.cos(np.pi / 2.0 + (self.PA + 3.0 * self.P_ERRA) * np.pi / 180.0),
+                    P_cut * np.sin(np.pi / 2.0 + (self.PA + 3.0 * self.P_ERRA) * np.pi / 180.0),
                 )
                 XY_U_err2, XY_V_err2 = (
-                    P_cut * np.cos(np.pi / 2.0 + (self.PA - 3.0 * self.s_PA) * np.pi / 180.0),
-                    P_cut * np.sin(np.pi / 2.0 + (self.PA - 3.0 * self.s_PA) * np.pi / 180.0),
+                    P_cut * np.cos(np.pi / 2.0 + (self.PA - 3.0 * self.P_ERRA) * np.pi / 180.0),
+                    P_cut * np.sin(np.pi / 2.0 + (self.PA - 3.0 * self.P_ERRA) * np.pi / 180.0),
                 )
                 ax.quiver(
                     X[:: self.step_vec, :: self.step_vec],
@@ -3283,27 +3305,26 @@ class pol_map(object):
             s_I = np.sqrt(self.IQU_cov[0, 0])
             I_reg = self.I.sum()
             I_reg_err = np.sqrt(np.sum(s_I**2))
-            P_reg = self.Stokes[0].header["P_int"]
+            debiased_P_reg = self.Stokes[0].header["P_int"]
             P_reg_err = self.Stokes[0].header["sP_int"]
             PA_reg = self.Stokes[0].header["PA_int"]
             PA_reg_err = self.Stokes[0].header["sPA_int"]
 
-            s_I = np.sqrt(self.IQU_cov[0, 0])
-            s_Q = np.sqrt(self.IQU_cov[1, 1])
-            s_U = np.sqrt(self.IQU_cov[2, 2])
-            s_IQ = self.IQU_cov[0, 1]
-            s_IU = self.IQU_cov[0, 2]
-            s_QU = self.IQU_cov[1, 2]
-
             I_cut = self.I[self.cut].sum()
             Q_cut = self.Q[self.cut].sum()
             U_cut = self.U[self.cut].sum()
-            I_cut_err = np.sqrt(np.sum(s_I[self.cut] ** 2))
-            Q_cut_err = np.sqrt(np.sum(s_Q[self.cut] ** 2))
-            U_cut_err = np.sqrt(np.sum(s_U[self.cut] ** 2))
-            IQ_cut_err = np.sqrt(np.sum(s_IQ[self.cut] ** 2))
-            IU_cut_err = np.sqrt(np.sum(s_IU[self.cut] ** 2))
-            QU_cut_err = np.sqrt(np.sum(s_QU[self.cut] ** 2))
+            I_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 0][self.cut]))
+            Q_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 1][self.cut]))
+            U_cut_err = np.sqrt(np.sum(self.IQU_cov[2, 2][self.cut]))
+            IQ_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 1][self.cut] ** 2))
+            IU_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 2][self.cut] ** 2))
+            QU_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 2][self.cut] ** 2))
+            I_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 0][self.cut]))
+            Q_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 1][self.cut]))
+            U_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[2, 2][self.cut]))
+            IQ_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 1][self.cut] ** 2))
+            IU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 2][self.cut] ** 2))
+            QU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 2][self.cut] ** 2))
 
             with np.errstate(divide="ignore", invalid="ignore"):
                 P_cut = np.sqrt(Q_cut**2 + U_cut**2) / I_cut
@@ -3316,6 +3337,16 @@ class pol_map(object):
                     )
                     / I_cut
                 )
+                P_cut_stat_err = (
+                    P_cut
+                    / I_cut
+                    * np.sqrt(
+                        I_cut_stat_err
+                        - 2.0 / (I_cut * P_cut**2) * (Q_cut * IQ_cut_stat_err + U_cut * IU_cut_stat_err)
+                        + 1.0 / (I_cut**2 * P_cut**4) * (Q_cut**2 * Q_cut_stat_err + U_cut**2 * U_cut_stat_err + 2.0 * Q_cut * U_cut * QU_cut_stat_err)
+                    )
+                )
+                debiased_P_cut = np.sqrt(P_cut**2 - P_cut_stat_err**2) if P_cut**2 > P_cut_stat_err**2 else 0.0
 
                 PA_cut = princ_angle((90.0 / np.pi) * np.arctan2(U_cut, Q_cut))
                 PA_cut_err = (90.0 / (np.pi * (Q_cut**2 + U_cut**2))) * np.sqrt(
@@ -3323,22 +3354,21 @@ class pol_map(object):
                 )
 
         else:
-            s_I = np.sqrt(self.IQU_cov[0, 0])
-            s_Q = np.sqrt(self.IQU_cov[1, 1])
-            s_U = np.sqrt(self.IQU_cov[2, 2])
-            s_IQ = self.IQU_cov[0, 1]
-            s_IU = self.IQU_cov[0, 2]
-            s_QU = self.IQU_cov[1, 2]
-
             I_reg = self.I[self.region].sum()
             Q_reg = self.Q[self.region].sum()
             U_reg = self.U[self.region].sum()
-            I_reg_err = np.sqrt(np.sum(s_I[self.region] ** 2))
-            Q_reg_err = np.sqrt(np.sum(s_Q[self.region] ** 2))
-            U_reg_err = np.sqrt(np.sum(s_U[self.region] ** 2))
-            IQ_reg_err = np.sqrt(np.sum(s_IQ[self.region] ** 2))
-            IU_reg_err = np.sqrt(np.sum(s_IU[self.region] ** 2))
-            QU_reg_err = np.sqrt(np.sum(s_QU[self.region] ** 2))
+            I_reg_err = np.sqrt(np.sum(self.IQU_cov[0, 0][self.region]))
+            Q_reg_err = np.sqrt(np.sum(self.IQU_cov[1, 1][self.region]))
+            U_reg_err = np.sqrt(np.sum(self.IQU_cov[2, 2][self.region]))
+            IQ_reg_err = np.sqrt(np.sum(self.IQU_cov[0, 1][self.region] ** 2))
+            IU_reg_err = np.sqrt(np.sum(self.IQU_cov[0, 2][self.region] ** 2))
+            QU_reg_err = np.sqrt(np.sum(self.IQU_cov[1, 2][self.region] ** 2))
+            I_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 0][self.region]))
+            Q_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 1][self.region]))
+            U_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[2, 2][self.region]))
+            IQ_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 1][self.region] ** 2))
+            IU_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 2][self.region] ** 2))
+            QU_reg_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 2][self.region] ** 2))
 
             conf = PCconf(QN=Q_reg / I_reg, QN_ERR=Q_reg_err / I_reg, UN=U_reg / I_reg, UN_ERR=U_reg_err / I_reg)
             if 1.0 - conf > 1e-3:
@@ -3355,6 +3385,16 @@ class pol_map(object):
                     )
                     / I_reg
                 )
+                P_reg_stat_err = (
+                    P_reg
+                    / I_reg
+                    * np.sqrt(
+                        I_reg_stat_err
+                        - 2.0 / (I_reg * P_reg**2) * (Q_reg * IQ_reg_stat_err + U_reg * IU_reg_stat_err)
+                        + 1.0 / (I_reg**2 * P_reg**4) * (Q_reg**2 * Q_reg_stat_err + U_reg**2 * U_reg_stat_err + 2.0 * Q_reg * U_reg * QU_reg_stat_err)
+                    )
+                )
+                debiased_P_reg = np.sqrt(P_reg**2 - P_reg_stat_err**2) if P_reg**2 > P_reg_stat_err**2 else 0.0
 
                 PA_reg = princ_angle((90.0 / np.pi) * np.arctan2(U_reg, Q_reg))
                 PA_reg_err = (90.0 / (np.pi * (Q_reg**2 + U_reg**2))) * np.sqrt(
@@ -3365,12 +3405,18 @@ class pol_map(object):
             I_cut = self.I[new_cut].sum()
             Q_cut = self.Q[new_cut].sum()
             U_cut = self.U[new_cut].sum()
-            I_cut_err = np.sqrt(np.sum(s_I[new_cut] ** 2))
-            Q_cut_err = np.sqrt(np.sum(s_Q[new_cut] ** 2))
-            U_cut_err = np.sqrt(np.sum(s_U[new_cut] ** 2))
-            IQ_cut_err = np.sqrt(np.sum(s_IQ[new_cut] ** 2))
-            IU_cut_err = np.sqrt(np.sum(s_IU[new_cut] ** 2))
-            QU_cut_err = np.sqrt(np.sum(s_QU[new_cut] ** 2))
+            I_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 0][new_cut]))
+            Q_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 1][new_cut]))
+            U_cut_err = np.sqrt(np.sum(self.IQU_cov[2, 2][new_cut]))
+            IQ_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 1][new_cut] ** 2))
+            IU_cut_err = np.sqrt(np.sum(self.IQU_cov[0, 2][new_cut] ** 2))
+            QU_cut_err = np.sqrt(np.sum(self.IQU_cov[1, 2][new_cut] ** 2))
+            I_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 0][new_cut]))
+            Q_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 1][new_cut]))
+            U_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[2, 2][new_cut]))
+            IQ_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 1][new_cut] ** 2))
+            IU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[0, 2][new_cut] ** 2))
+            QU_cut_stat_err = np.sqrt(np.sum(self.IQU_stat_cov[1, 2][new_cut] ** 2))
 
             with np.errstate(divide="ignore", invalid="ignore"):
                 P_cut = np.sqrt(Q_cut**2 + U_cut**2) / I_cut
@@ -3383,6 +3429,16 @@ class pol_map(object):
                     )
                     / I_cut
                 )
+                P_cut_stat_err = (
+                    P_cut
+                    / I_cut
+                    * np.sqrt(
+                        I_cut_stat_err
+                        - 2.0 / (I_cut * P_cut**2) * (Q_cut * IQ_cut_stat_err + U_cut * IU_cut_stat_err)
+                        + 1.0 / (I_cut**2 * P_cut**4) * (Q_cut**2 * Q_cut_stat_err + U_cut**2 * U_cut_stat_err + 2.0 * Q_cut * U_cut * QU_cut_stat_err)
+                    )
+                )
+                debiased_P_cut = np.sqrt(P_cut**2 - P_cut_stat_err**2) if P_cut**2 > P_cut_stat_err**2 else 0.0
 
                 PA_cut = princ_angle((90.0 / np.pi) * np.arctan2(U_cut, Q_cut))
                 PA_cut_err = (90.0 / (np.pi * (Q_cut**2 + U_cut**2))) * np.sqrt(
@@ -3403,7 +3459,7 @@ class pol_map(object):
                     self.pivot_wav, sci_not(I_reg * self.map_convert, I_reg_err * self.map_convert, 2)
                 )
                 + "\n"
-                + r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
+                + r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
                 + "\n"
                 + r"$\theta_{{P}}^{{int}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_reg, np.ceil(PA_reg_err * 10.0) / 10.0)
                 + str_conf
@@ -3415,7 +3471,7 @@ class pol_map(object):
             #         self.pivot_wav, sci_not(I_cut * self.map_convert, I_cut_err * self.map_convert, 2)
             #     )
             #     + "\n"
-            #     + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
+            #     + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
             #     + "\n"
             #     + r"$\theta_{{P}}^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_cut, np.ceil(PA_cut_err * 10.0) / 10.0)
             # )
@@ -3439,7 +3495,7 @@ class pol_map(object):
                     self.pivot_wav, sci_not(I_reg * self.map_convert, I_reg_err * self.map_convert, 2)
                 )
                 + "\n"
-                + r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
+                + r"$P^{{int}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_reg * 100.0, np.ceil(P_reg_err * 1000.0) / 10.0)
                 + "\n"
                 + r"$\theta_{{P}}^{{int}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_reg, np.ceil(PA_reg_err * 10.0) / 10.0)
                 + str_conf
@@ -3451,7 +3507,7 @@ class pol_map(object):
             #         self.pivot_wav, sci_not(I_cut * self.map_convert, I_cut_err * self.map_convert, 2)
             #     )
             #     + "\n"
-            #     + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
+            #     + r"$P^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} %".format(debiased_P_cut * 100.0, np.ceil(P_cut_err * 1000.0) / 10.0)
             #     + "\n"
             #     + r"$\theta_{{P}}^{{cut}}$ = {0:.1f} $\pm$ {1:.1f} °".format(PA_cut, np.ceil(PA_cut_err * 10.0) / 10.0)
             # )

package/lib/reduction.py

@@ -224,7 +224,9 @@ def bin_ndarray(ndarray, new_shape, operation="sum"):
     return ndarray
 
 
-def crop_array(data_array, headers, error_array=None, data_mask=None, step=5, null_val=None, inside=False, display=False, savename=None, plots_folder=""):
+def crop_array(
+    data_array, headers, error_array=None, data_mask=None, step=5, null_val=None, crop=True, inside=False, display=False, savename=None, plots_folder=""
+):
     """
     Homogeneously crop an array: all contained images will have the same shape.
     'inside' parameter will decide how much should be cropped.
@@ -256,6 +258,10 @@ def crop_array(data_array, headers, error_array=None, data_mask=None, step=5, nu
         If None, will be put to 75% of the mean value of the associated error
         array.
         Defaults to None.
+    crop : boolean, optional
+        If True, data_array will be cropped down to contain only relevant data.
+        If False, this information will be kept in the crop_mask output.
+        Defaults to True.
     inside : boolean, optional
         If True, the cropped image will be the maximum rectangle included
         inside the image. If False, the cropped image will be the minimum
@@ -295,6 +301,9 @@ def crop_array(data_array, headers, error_array=None, data_mask=None, step=5, nu
         v_array[1] = np.max(vertex[:, 1]).astype(int)
         v_array[2] = np.min(vertex[:, 2]).astype(int)
         v_array[3] = np.max(vertex[:, 3]).astype(int)
+    if data_mask is None:
+        data_mask = np.zeros(data_array[0].shape).astype(bool)
+        data_mask[v_array[0] : v_array[1], v_array[2] : v_array[3]] = True
 
     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], 0.0, "b"]
@@ -352,11 +361,11 @@ def crop_array(data_array, headers, error_array=None, data_mask=None, step=5, nu
             )
         plt.show()
 
-    if data_mask is not None:
+    if crop:
         crop_mask = data_mask[v_array[0] : v_array[1], v_array[2] : v_array[3]]
         return crop_array, crop_error_array, crop_mask, crop_headers
     else:
-        return crop_array, crop_error_array, crop_headers
+        return data_array, error_array, data_mask, headers
 
 
 def deconvolve_array(data_array, headers, psf="gaussian", FWHM=1.0, scale="px", shape=None, iterations=20, algo="richardson"):
@@ -1243,6 +1252,7 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
         # Orientation and error for each polarizer
         # fmax = np.finfo(np.float64).max
         pol_flux = np.array([corr[0] * pol0, corr[1] * pol60, corr[2] * pol120])
+        pol_flux_corr = np.array([pf * 2.0 / t for (pf, t) in zip(pol_flux, transmit)])
 
         coeff_stokes = np.zeros((3, 3))
         # Coefficients linking each polarizer flux to each Stokes parameter
@@ -1258,6 +1268,7 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
         # Normalization parameter for Stokes parameters computation
         N = (coeff_stokes[0, :] * transmit / 2.0).sum()
         coeff_stokes = coeff_stokes / N
+        coeff_stokes_corr = np.array([cs * t / 2.0 for (cs, t) in zip(coeff_stokes.T, transmit)]).T
         I_stokes = np.zeros(pol_array[0].shape)
         Q_stokes = np.zeros(pol_array[0].shape)
         U_stokes = np.zeros(pol_array[0].shape)
@@ -1299,121 +1310,81 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
 
         # Statistical error: Poisson noise is assumed
         sigma_flux = np.array([np.sqrt(flux / head["exptime"]) for flux, head in zip(pol_flux, pol_headers)])
-        s_I2_stat = np.sum([coeff_stokes[0, i] ** 2 * sigma_flux[i] ** 2 for i in range(len(sigma_flux))], axis=0)
-        s_Q2_stat = np.sum([coeff_stokes[1, i] ** 2 * sigma_flux[i] ** 2 for i in range(len(sigma_flux))], axis=0)
-        s_U2_stat = np.sum([coeff_stokes[2, i] ** 2 * sigma_flux[i] ** 2 for i in range(len(sigma_flux))], axis=0)
+        Stokes_stat_cov = np.zeros(Stokes_cov.shape)
+        for i in range(Stokes_cov.shape[0]):
+            Stokes_stat_cov[i, i] = np.sum([coeff_stokes[i, k] ** 2 * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
+            for j in [k for k in range(3) if k > i]:
+                Stokes_stat_cov[i, j] = np.sum([abs(coeff_stokes[i, k] * coeff_stokes[j, k]) * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
+                Stokes_stat_cov[j, i] = np.sum([abs(coeff_stokes[i, k] * coeff_stokes[j, k]) * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
 
-        pol_flux_corr = np.array([pf * 2.0 / t for (pf, t) in zip(pol_flux, transmit)])
-        coeff_stokes_corr = np.array([cs * t / 2.0 for (cs, t) in zip(coeff_stokes.T, transmit)]).T
         # Compute the derivative of each Stokes parameter with respect to the polarizer orientation
-        dI_dtheta1 = (
-            2.0
-            * pol_eff[0]
-            / N
-            * (
-                pol_eff[2] * np.cos(-2.0 * theta[2] + 2.0 * theta[0]) * (pol_flux_corr[1] - I_stokes)
-                - pol_eff[1] * np.cos(-2.0 * theta[0] + 2.0 * theta[1]) * (pol_flux_corr[2] - I_stokes)
-                + coeff_stokes_corr[0, 0] * (np.sin(2.0 * theta[0]) * Q_stokes - np.cos(2 * theta[0]) * U_stokes)
-            )
-        )
-        dI_dtheta2 = (
-            2.0
-            * pol_eff[1]
-            / N
-            * (
-                pol_eff[0] * np.cos(-2.0 * theta[0] + 2.0 * theta[1]) * (pol_flux_corr[2] - I_stokes)
-                - pol_eff[2] * np.cos(-2.0 * theta[1] + 2.0 * theta[2]) * (pol_flux_corr[0] - I_stokes)
-                + coeff_stokes_corr[0, 1] * (np.sin(2.0 * theta[1]) * Q_stokes - np.cos(2 * theta[1]) * U_stokes)
-            )
-        )
-        dI_dtheta3 = (
-            2.0
-            * pol_eff[2]
-            / N
-            * (
-                pol_eff[1] * np.cos(-2.0 * theta[1] + 2.0 * theta[2]) * (pol_flux_corr[0] - I_stokes)
-                - pol_eff[0] * np.cos(-2.0 * theta[2] + 2.0 * theta[0]) * (pol_flux_corr[1] - I_stokes)
-                + coeff_stokes_corr[0, 2] * (np.sin(2.0 * theta[2]) * Q_stokes - np.cos(2 * theta[2]) * U_stokes)
-            )
-        )
-        dI_dtheta = np.array([dI_dtheta1, dI_dtheta2, dI_dtheta3])
+        dIQU_dtheta = np.zeros(Stokes_cov.shape)
 
-        dQ_dtheta1 = (
-            2.0
-            * pol_eff[0]
-            / N
-            * (
-                np.cos(2.0 * theta[0]) * (pol_flux_corr[1] - pol_flux_corr[2])
-                - (pol_eff[2] * np.cos(-2.0 * theta[2] + 2.0 * theta[0]) - pol_eff[1] * np.cos(-2.0 * theta[0] + 2.0 * theta[1])) * Q_stokes
-                + coeff_stokes_corr[1, 0] * (np.sin(2.0 * theta[0]) * Q_stokes - np.cos(2 * theta[0]) * U_stokes)
+        # Derivative of I_stokes wrt theta_1, 2, 3
+        for j in range(3):
+            dIQU_dtheta[0, j] = (
+                2.0
+                * pol_eff[j]
+                / N
+                * (
+                    pol_eff[(j + 2) % 3] * np.cos(-2.0 * theta[(j + 2) % 3] + 2.0 * theta[j]) * (pol_flux_corr[(j + 1) % 3] - I_stokes)
+                    - pol_eff[(j + 1) % 3] * np.cos(-2.0 * theta[j] + 2.0 * theta[(j + 1) % 3]) * (pol_flux_corr[(j + 2) % 3] - I_stokes)
+                    + coeff_stokes_corr[0, j] * (np.sin(2.0 * theta[j]) * Q_stokes - np.cos(2 * theta[j]) * U_stokes)
+                )
             )
-        )
-        dQ_dtheta2 = (
-            2.0
-            * pol_eff[1]
-            / N
-            * (
-                np.cos(2.0 * theta[1]) * (pol_flux_corr[2] - pol_flux_corr[0])
-                - (pol_eff[0] * np.cos(-2.0 * theta[0] + 2.0 * theta[1]) - pol_eff[2] * np.cos(-2.0 * theta[1] + 2.0 * theta[2])) * Q_stokes
-                + coeff_stokes_corr[1, 1] * (np.sin(2.0 * theta[1]) * Q_stokes - np.cos(2 * theta[1]) * U_stokes)
-            )
-        )
-        dQ_dtheta3 = (
-            2.0
-            * pol_eff[2]
-            / N
-            * (
-                np.cos(2.0 * theta[2]) * (pol_flux_corr[0] - pol_flux_corr[1])
-                - (pol_eff[1] * np.cos(-2.0 * theta[1] + 2.0 * theta[2]) - pol_eff[0] * np.cos(-2.0 * theta[2] + 2.0 * theta[0])) * Q_stokes
-                + coeff_stokes_corr[1, 2] * (np.sin(2.0 * theta[2]) * Q_stokes - np.cos(2 * theta[2]) * U_stokes)
-            )
-        )
-        dQ_dtheta = np.array([dQ_dtheta1, dQ_dtheta2, dQ_dtheta3])
 
-        dU_dtheta1 = (
-            2.0
-            * pol_eff[0]
-            / N
-            * (
-                np.sin(2.0 * theta[0]) * (pol_flux_corr[1] - pol_flux_corr[2])
-                - (pol_eff[2] * np.cos(-2.0 * theta[2] + 2.0 * theta[0]) - pol_eff[1] * np.cos(-2.0 * theta[0] + 2.0 * theta[1])) * U_stokes
-                + coeff_stokes_corr[2, 0] * (np.sin(2.0 * theta[0]) * Q_stokes - np.cos(2 * theta[0]) * U_stokes)
+        # Derivative of Q_stokes wrt theta_1, 2, 3
+        for j in range(3):
+            dIQU_dtheta[1, j] = (
+                2.0
+                * pol_eff[j]
+                / N
+                * (
+                    np.cos(2.0 * theta[j]) * (pol_flux_corr[(j + 1) % 3] - pol_flux_corr[(j + 2) % 3])
+                    - (
+                        pol_eff[(j + 2) % 3] * np.cos(-2.0 * theta[(j + 2) % 3] + 2.0 * theta[j])
+                        - pol_eff[(j + 1) % 3] * np.cos(-2.0 * theta[j] + 2.0 * theta[(j + 1) % 3])
+                    )
+                    * Q_stokes
+                    + coeff_stokes_corr[1, j] * (np.sin(2.0 * theta[j]) * Q_stokes - np.cos(2 * theta[j]) * U_stokes)
+                )
             )
-        )
-        dU_dtheta2 = (
-            2.0
-            * pol_eff[1]
-            / N
-            * (
-                np.sin(2.0 * theta[1]) * (pol_flux_corr[2] - pol_flux_corr[0])
-                - (pol_eff[0] * np.cos(-2.0 * theta[0] + 2.0 * theta[1]) - pol_eff[2] * np.cos(-2.0 * theta[1] + 2.0 * theta[2])) * U_stokes
-                + coeff_stokes_corr[2, 1] * (np.sin(2.0 * theta[1]) * Q_stokes - np.cos(2 * theta[1]) * U_stokes)
+
+        # Derivative of U_stokes wrt theta_1, 2, 3
+        for j in range(3):
+            dIQU_dtheta[2, j] = (
+                2.0
+                * pol_eff[j]
+                / N
+                * (
+                    np.sin(2.0 * theta[j]) * (pol_flux_corr[(j + 1) % 3] - pol_flux_corr[(j + 2) % 3])
+                    - (
+                        pol_eff[(j + 2) % 3] * np.cos(-2.0 * theta[(j + 2) % 3] + 2.0 * theta[j])
+                        - pol_eff[(j + 1) % 3] * np.cos(-2.0 * theta[j] + 2.0 * theta[(j + 1) % 3])
+                    )
+                    * U_stokes
+                    + coeff_stokes_corr[2, j] * (np.sin(2.0 * theta[j]) * Q_stokes - np.cos(2 * theta[j]) * U_stokes)
+                )
             )
-        )
-        dU_dtheta3 = (
-            2.0
-            * pol_eff[2]
-            / N
-            * (
-                np.sin(2.0 * theta[2]) * (pol_flux_corr[0] - pol_flux_corr[1])
-                - (pol_eff[1] * np.cos(-2.0 * theta[1] + 2.0 * theta[2]) - pol_eff[0] * np.cos(-2.0 * theta[2] + 2.0 * theta[0])) * U_stokes
-                + coeff_stokes_corr[2, 2] * (np.sin(2.0 * theta[2]) * Q_stokes - np.cos(2 * theta[2]) * U_stokes)
-            )
-        )
-        dU_dtheta = np.array([dU_dtheta1, dU_dtheta2, dU_dtheta3])
 
         # Compute the uncertainty associated with the polarizers' orientation (see Kishimoto 1999)
-        s_I2_axis = np.sum([dI_dtheta[i] ** 2 * globals()["sigma_theta"][i] ** 2 for i in range(len(globals()["sigma_theta"]))], axis=0)
-        s_Q2_axis = np.sum([dQ_dtheta[i] ** 2 * globals()["sigma_theta"][i] ** 2 for i in range(len(globals()["sigma_theta"]))], axis=0)
-        s_U2_axis = np.sum([dU_dtheta[i] ** 2 * globals()["sigma_theta"][i] ** 2 for i in range(len(globals()["sigma_theta"]))], axis=0)
-        # np.savetxt("output/sI_dir.txt", np.sqrt(s_I2_axis))
-        # np.savetxt("output/sQ_dir.txt", np.sqrt(s_Q2_axis))
-        # np.savetxt("output/sU_dir.txt", np.sqrt(s_U2_axis))
+        Stokes_axis_cov = np.zeros(Stokes_cov.shape)
+        for i in range(Stokes_cov.shape[0]):
+            Stokes_axis_cov[i, i] = np.sum([dIQU_dtheta[i, k] ** 2 * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0)
+            for j in [k for k in range(3) if k > i]:
+                Stokes_axis_cov[i, j] = np.sum(
+                    [abs(dIQU_dtheta[i, k] * dIQU_dtheta[j, k]) * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0
+                )
+                Stokes_axis_cov[j, i] = np.sum(
+                    [abs(dIQU_dtheta[i, k] * dIQU_dtheta[j, k]) * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=0
+                )
 
         # Add quadratically the uncertainty to the Stokes covariance matrix
-        Stokes_cov[0, 0] += s_I2_axis + s_I2_stat
-        Stokes_cov[1, 1] += s_Q2_axis + s_Q2_stat
-        Stokes_cov[2, 2] += s_U2_axis + s_U2_stat
+        for i in range(Stokes_cov.shape[0]):
+            Stokes_cov[i, i] += Stokes_axis_cov[i, i] + Stokes_stat_cov[i, i]
+            for j in [k for k in range(Stokes_cov.shape[0]) if k > i]:
+                Stokes_cov[i, j] = np.sqrt(Stokes_cov[i, j] ** 2 + Stokes_axis_cov[i, j] ** 2 + Stokes_stat_cov[i, j] ** 2)
+                Stokes_cov[j, i] = np.sqrt(Stokes_cov[j, i] ** 2 + Stokes_axis_cov[j, i] ** 2 + Stokes_stat_cov[j, i] ** 2)
 
         # Save values to single header
         header_stokes = pol_headers[0]
@@ -1447,8 +1418,8 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
         for i in range(3):
             Stokes_cov[i, i] = np.sum([exp**2 * cov for exp, cov in zip(all_exp, all_Stokes_cov[:, i, i])], axis=0) / all_exp.sum() ** 2
             for j in [x for x in range(3) if x != i]:
-                Stokes_cov[i, j] = np.sqrt(np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, i, j])], axis=0) / all_exp.sum() ** 2)
-                Stokes_cov[j, i] = np.sqrt(np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, j, i])], axis=0) / all_exp.sum() ** 2)
+                Stokes_cov[i, j] = np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, i, j])], axis=0) / all_exp.sum() ** 2
+                Stokes_cov[j, i] = np.sum([exp**2 * cov**2 for exp, cov in zip(all_exp, all_Stokes_cov[:, j, i])], axis=0) / all_exp.sum() ** 2
 
         # Save values to single header
         header_stokes = all_header_stokes[0]
@@ -1463,6 +1434,7 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
     Q_stokes[np.isnan(Q_stokes)] = 0.0
     U_stokes[np.isnan(U_stokes)] = 0.0
     Stokes_cov[np.isnan(Stokes_cov)] = fmax
+    Stokes_stat_cov[np.isnan(Stokes_cov)] = fmax
 
     if integrate:
         # Compute integrated values for P, PA before any rotation
@@ -1476,29 +1448,47 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
         IQ_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 1][mask] ** 2))
         IU_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 2][mask] ** 2))
         QU_diluted_err = np.sqrt(np.sum(Stokes_cov[1, 2][mask] ** 2))
+        I_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 0][mask]))
+        Q_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 1][mask]))
+        U_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[2, 2][mask]))
+        IQ_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 1][mask] ** 2))
+        IU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 2][mask] ** 2))
+        QU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 2][mask] ** 2))
 
         P_diluted = np.sqrt(Q_diluted**2 + U_diluted**2) / I_diluted
-        P_diluted_err = np.sqrt(
+        P_diluted_err = (1.0 / I_diluted) * np.sqrt(
             (Q_diluted**2 * Q_diluted_err**2 + U_diluted**2 * U_diluted_err**2 + 2.0 * 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
             - 2.0 * (Q_diluted / I_diluted) * IQ_diluted_err
             - 2.0 * (U_diluted / I_diluted) * IU_diluted_err
         )
+        P_diluted_stat_err = (
+            P_diluted
+            / I_diluted
+            * np.sqrt(
+                I_diluted_stat_err
+                - 2.0 / (I_diluted * P_diluted**2) * (Q_diluted * IQ_diluted_stat_err + U_diluted * IU_diluted_stat_err)
+                + 1.0
+                / (I_diluted**2 * P_diluted**4)
+                * (Q_diluted**2 * Q_diluted_stat_err + U_diluted**2 * U_diluted_stat_err + 2.0 * Q_diluted * U_diluted * QU_diluted_stat_err)
+            )
+        )
+        debiased_P_diluted = np.sqrt(P_diluted**2 - P_diluted_stat_err**2) if P_diluted**2 > P_diluted_stat_err**2 else 0.0
 
         PA_diluted = princ_angle((90.0 / np.pi) * np.arctan2(U_diluted, Q_diluted))
         PA_diluted_err = (90.0 / (np.pi * (Q_diluted**2 + U_diluted**2))) * np.sqrt(
             U_diluted**2 * Q_diluted_err**2 + Q_diluted**2 * U_diluted_err**2 - 2.0 * Q_diluted * U_diluted * QU_diluted_err
         )
 
-        header_stokes["P_int"] = (P_diluted, "Integrated polarization degree")
+        header_stokes["P_int"] = (debiased_P_diluted, "Integrated polarization degree")
         header_stokes["sP_int"] = (np.ceil(P_diluted_err * 1000.0) / 1000.0, "Integrated polarization degree error")
         header_stokes["PA_int"] = (PA_diluted, "Integrated polarization angle")
         header_stokes["sPA_int"] = (np.ceil(PA_diluted_err * 10.0) / 10.0, "Integrated polarization angle error")
 
-    return I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes
+    return I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes
 
 
-def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes):
+def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, header_stokes):
     """
     Compute the polarization degree (in %) and angle (in deg) and their
     respective errors from given Stokes parameters.
@@ -1573,27 +1563,44 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes):
     s_P[np.isnan(s_P)] = fmax
     s_PA[np.isnan(s_PA)] = fmax
 
+    # Errors on P, PA supposing Poisson noise
+    s_P_P = np.ones(I_stokes.shape) * fmax
+    s_PA_P = np.ones(I_stokes.shape) * fmax
+    maskP = np.logical_and(mask, P > 0.0)
+    s_P_P[maskP] = (
+        P[maskP]
+        / I_stokes[maskP]
+        * np.sqrt(
+            Stokes_stat_cov[0, 0][maskP]
+            - 2.0 / (I_stokes[maskP] * P[maskP] ** 2) * (Q_stokes[maskP] * Stokes_stat_cov[0, 1][maskP] + U_stokes[maskP] * Stokes_stat_cov[0, 2][maskP])
+            + 1.0
+            / (I_stokes[maskP] ** 2 * P[maskP] ** 4)
+            * (
+                Q_stokes[maskP] ** 2 * Stokes_stat_cov[1, 1][maskP]
+                + U_stokes[maskP] ** 2 * Stokes_stat_cov[2, 2][maskP]
+                + 2.0 * Q_stokes[maskP] * U_stokes[maskP] * Stokes_stat_cov[1, 2][maskP]
+            )
+        )
+    )
+    s_PA_P[maskP] = (
+        90.0
+        / (np.pi * I_stokes[maskP] ** 2 * P[maskP] ** 2)
+        * (
+            Q_stokes[maskP] ** 2 * Stokes_stat_cov[2, 2][maskP]
+            + U_stokes[maskP] * Stokes_stat_cov[1, 1][maskP]
+            - 2.0 * Q_stokes[maskP] * U_stokes[maskP] * Stokes_stat_cov[1, 2][maskP]
+        )
+    )
+
     # Catch expected "OverflowWarning" as wrong pixel have an overflowing error
     with warnings.catch_warnings(record=True) as _:
-        mask2 = P**2 >= s_P**2
+        mask2 = P**2 >= s_P_P**2
     debiased_P = np.zeros(I_stokes.shape)
-    debiased_P[mask2] = np.sqrt(P[mask2] ** 2 - s_P[mask2] ** 2)
+    debiased_P[mask2] = np.sqrt(P[mask2] ** 2 - s_P_P[mask2] ** 2)
 
     if (debiased_P > 1.0).any():
         print("WARNING : found {0:d} pixels for which debiased_P > 100%".format(debiased_P[debiased_P > 1.0].size))
 
-    # Compute the total exposure time so that
-    # I_stokes*exp_tot = N_tot the total number of events
-    exp_tot = header_stokes["exptime"]
-    # print("Total exposure time : {} sec".format(exp_tot))
-    N_obs = I_stokes * exp_tot
-
-    # Errors on P, PA supposing Poisson noise
-    s_P_P = np.ones(I_stokes.shape) * fmax
-    s_P_P[mask] = np.sqrt(2.0) / np.sqrt(N_obs[mask]) * 100.0
-    s_PA_P = np.ones(I_stokes.shape) * fmax
-    s_PA_P[mask2] = s_P_P[mask2] / (2.0 * P[mask2]) * 180.0 / np.pi
-
     # Nan handling :
     P[np.isnan(P)] = 0.0
     s_P[np.isnan(s_P)] = fmax
@@ -1605,7 +1612,7 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes):
     return P, debiased_P, s_P, s_P_P, PA, s_PA, s_PA_P
 
 
-def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes, SNRi_cut=None):
+def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, Stokes_stat_cov, data_mask, header_stokes, 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
@@ -1622,7 +1629,11 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
         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.
+        Covariance matrix containing all uncertainties of the Stokes
+        parameters I, Q, U.
+    Stokes_stat_cov : numpy.ndarray
+        Covariance matrix containing statistical uncertainty of the Stokes
+        parameters I, Q, U.
     data_mask : numpy.ndarray
         2D boolean array delimiting the data to work on.
     header_stokes : astropy.fits.header.Header
@@ -1644,6 +1655,8 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
         accounting for +45/-45deg linear polarization intensity.
     new_Stokes_cov : numpy.ndarray
         Updated covariance matrix of the Stokes parameters I, Q, U.
+    new_Stokes_stat_cov : numpy.ndarray
+        Updated statistical covariance matrix of the Stokes parameters I, Q, U.
     new_header_stokes : astropy.fits.header.Header
         Updated Header file associated with the Stokes fluxes accounting
         for the new orientation angle.
@@ -1675,11 +1688,9 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
     Q_stokes = zeropad(Q_stokes, shape)
     U_stokes = zeropad(U_stokes, shape)
     data_mask = zeropad(data_mask, shape)
-    Stokes_cov = zeropad(Stokes_cov, [*Stokes_cov.shape[:-2], *shape])
     new_I_stokes = np.zeros(shape)
     new_Q_stokes = np.zeros(shape)
     new_U_stokes = np.zeros(shape)
-    new_Stokes_cov = np.zeros((*Stokes_cov.shape[:-2], *shape))
 
     # Rotate original images using scipy.ndimage.rotate
     new_I_stokes = sc_rotate(I_stokes, ang, order=1, reshape=False, cval=0.0)
@@ -1688,6 +1699,10 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
     new_data_mask = sc_rotate(data_mask.astype(float) * 10.0, ang, order=1, reshape=False, cval=0.0)
     new_data_mask[new_data_mask < 1.0] = 0.0
     new_data_mask = new_data_mask.astype(bool)
+
+    # Rotate covariance matrix
+    Stokes_cov = zeropad(Stokes_cov, [*Stokes_cov.shape[:-2], *shape])
+    new_Stokes_cov = np.zeros((*Stokes_cov.shape[:-2], *shape))
     for i in range(3):
         for j in range(3):
             new_Stokes_cov[i, j] = sc_rotate(Stokes_cov[i, j], ang, order=1, reshape=False, cval=0.0)
@@ -1698,6 +1713,17 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
             new_I_stokes[i, j], new_Q_stokes[i, j], new_U_stokes[i, j] = np.dot(mrot, np.array([new_I_stokes[i, j], new_Q_stokes[i, j], new_U_stokes[i, j]])).T
             new_Stokes_cov[:, :, i, j] = np.dot(mrot, np.dot(new_Stokes_cov[:, :, i, j], mrot.T))
 
+    # Rotate statistical covariance matrix
+    Stokes_stat_cov = zeropad(Stokes_stat_cov, [*Stokes_stat_cov.shape[:-2], *shape])
+    new_Stokes_stat_cov = np.zeros((*Stokes_stat_cov.shape[:-2], *shape))
+    for i in range(3):
+        for j in range(3):
+            new_Stokes_stat_cov[i, j] = sc_rotate(Stokes_stat_cov[i, j], ang, order=1, reshape=False, cval=0.0)
+        new_Stokes_stat_cov[i, i] = np.abs(new_Stokes_stat_cov[i, i])
+    for i in range(shape[0]):
+        for j in range(shape[1]):
+            new_Stokes_stat_cov[:, :, i, j] = np.dot(mrot, np.dot(new_Stokes_stat_cov[:, :, i, j], mrot.T))
+
     # Update headers to new angle
     mrot = np.array([[np.cos(-alpha), -np.sin(-alpha)], [np.sin(-alpha), np.cos(-alpha)]])
 
@@ -1726,12 +1752,18 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
     I_diluted = new_I_stokes[mask].sum()
     Q_diluted = new_Q_stokes[mask].sum()
     U_diluted = new_U_stokes[mask].sum()
-    I_diluted_err = np.sqrt(np.sum(new_Stokes_cov[0, 0][mask]))
-    Q_diluted_err = np.sqrt(np.sum(new_Stokes_cov[1, 1][mask]))
-    U_diluted_err = np.sqrt(np.sum(new_Stokes_cov[2, 2][mask]))
-    IQ_diluted_err = np.sqrt(np.sum(new_Stokes_cov[0, 1][mask] ** 2))
-    IU_diluted_err = np.sqrt(np.sum(new_Stokes_cov[0, 2][mask] ** 2))
-    QU_diluted_err = np.sqrt(np.sum(new_Stokes_cov[1, 2][mask] ** 2))
+    I_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 0][mask]))
+    Q_diluted_err = np.sqrt(np.sum(Stokes_cov[1, 1][mask]))
+    U_diluted_err = np.sqrt(np.sum(Stokes_cov[2, 2][mask]))
+    IQ_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 1][mask] ** 2))
+    IU_diluted_err = np.sqrt(np.sum(Stokes_cov[0, 2][mask] ** 2))
+    QU_diluted_err = np.sqrt(np.sum(Stokes_cov[1, 2][mask] ** 2))
+    I_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 0][mask]))
+    Q_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 1][mask]))
+    U_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[2, 2][mask]))
+    IQ_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 1][mask] ** 2))
+    IU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[0, 2][mask] ** 2))
+    QU_diluted_stat_err = np.sqrt(np.sum(Stokes_stat_cov[1, 2][mask] ** 2))
 
     P_diluted = np.sqrt(Q_diluted**2 + U_diluted**2) / I_diluted
     P_diluted_err = (1.0 / I_diluted) * np.sqrt(
@@ -1740,18 +1772,30 @@ def rotate_Stokes(I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_st
         - 2.0 * (Q_diluted / I_diluted) * IQ_diluted_err
         - 2.0 * (U_diluted / I_diluted) * IU_diluted_err
     )
+    P_diluted_stat_err = (
+        P_diluted
+        / I_diluted
+        * np.sqrt(
+            I_diluted_stat_err
+            - 2.0 / (I_diluted * P_diluted**2) * (Q_diluted * IQ_diluted_stat_err + U_diluted * IU_diluted_stat_err)
+            + 1.0
+            / (I_diluted**2 * P_diluted**4)
+            * (Q_diluted**2 * Q_diluted_stat_err + U_diluted**2 * U_diluted_stat_err + 2.0 * Q_diluted * U_diluted * QU_diluted_stat_err)
+        )
+    )
+    debiased_P_diluted = np.sqrt(P_diluted**2 - P_diluted_stat_err**2) if P_diluted**2 > P_diluted_stat_err**2 else 0.0
 
     PA_diluted = princ_angle((90.0 / np.pi) * np.arctan2(U_diluted, Q_diluted))
     PA_diluted_err = (90.0 / (np.pi * (Q_diluted**2 + U_diluted**2))) * np.sqrt(
         U_diluted**2 * Q_diluted_err**2 + Q_diluted**2 * U_diluted_err**2 - 2.0 * Q_diluted * U_diluted * QU_diluted_err
     )
 
-    new_header_stokes["P_int"] = (P_diluted, "Integrated polarization degree")
+    new_header_stokes["P_int"] = (debiased_P_diluted, "Integrated polarization degree")
     new_header_stokes["sP_int"] = (np.ceil(P_diluted_err * 1000.0) / 1000.0, "Integrated polarization degree error")
     new_header_stokes["PA_int"] = (PA_diluted, "Integrated polarization angle")
     new_header_stokes["sPA_int"] = (np.ceil(PA_diluted_err * 10.0) / 10.0, "Integrated polarization angle error")
 
-    return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_data_mask, new_header_stokes
+    return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_Stokes_stat_cov, new_data_mask, new_header_stokes
 
 
 def rotate_data(data_array, error_array, data_mask, headers):

package/src/emission_center.py

@@ -43,7 +43,9 @@ def main(infile, P_cut=0.99, target=None, display="pf", output_dir=None):
     if target is None:
         target = Stokes[0].header["TARGNAME"]
 
-    fig = figure(figsize=(8, 8.5), layout="constrained")
+    ratiox = max(int(stkI.shape[1] / (stkI.shape[0])), 1)
+    ratioy = max(int((stkI.shape[0]) / stkI.shape[1]), 1)
+    fig = figure(figsize=(8 * ratiox, 8 * ratioy), layout="constrained")
     fig, ax = polarization_map(Stokes, P_cut=P_cut, step_vec=1, scale_vec=5, display=display, fig=fig, width=0.33, linewidth=0.5)
 
     ax.plot(*Stokescenter, marker="+", color="k", lw=3)