correction for Stokes_cov and P_diluted_err propagation

package/FOC_reduction.py

@@ -40,13 +40,13 @@ 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 = 0.50
+    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 = 4
-    pxscale = "px"  # pixel, arcsec or full
+    pxsize = 0.05
+    pxscale = "arcsec"  # pixel, arcsec or full
     rebin_operation = "sum"  # sum or average
 
     # Alignement
@@ -59,8 +59,8 @@ 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 = 1.5  # If None, no smoothing is done
-    smoothing_scale = "px"  # pixel or arcsec
+    smoothing_FWHM = 0.075  # If None, no smoothing is done
+    smoothing_scale = "arcsec"  # pixel or arcsec
 
     # Rotation
     rotate_North = True
@@ -216,28 +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, s_IQU_stat = 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, s_IQU_stat_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, s_IQU_stat = proj_red.rotate_Stokes(
-            I_stokes, Q_stokes, U_stokes, Stokes_cov, data_mask, header_stokes, s_IQU_stat=s_IQU_stat, 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, s_IQU_stat_bkg = proj_red.rotate_Stokes(
-            I_bkg, Q_bkg, U_bkg, S_cov_bkg, np.array(True).reshape(1, 1), header_bkg, s_IQU_stat=s_IQU_stat_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, s_IQU_stat=s_IQU_stat)
-    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, s_IQU_stat=s_IQU_stat_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.
@@ -247,6 +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)
@@ -210,6 +230,7 @@ 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"],
@@ -221,7 +242,7 @@ def save_Stokes(
     ]:
         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")
@@ -2959,6 +2979,10 @@ 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
@@ -3079,7 +3103,7 @@ class pol_map(object):
             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
-            kwargs["vmin"], kwargs["vmax"] = 0.0, np.max(self.data[self.P > self.P_ERR])
+            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"]:
@@ -3092,14 +3116,12 @@ class pol_map(object):
             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
-            kwargs["alpha"] = 1.0 - 0.75 * (self.I < s_I)
             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.P_ERR > 0.0] = self.P[self.P_ERR > 0.0] / self.P_ERR[self.P_ERR > 0.0]
             self.data = SNRp
-            kwargs["alpha"] = 1.0 - 0.75 * (self.P < self.P_ERR)
             kwargs["vmin"], kwargs["vmax"] = 0.0, np.max(self.data[self.data > 0.0])
             label = r"$P/\sigma_{P}$"
 
@@ -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

@@ -1310,12 +1310,12 @@ 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_IQU_stat = np.zeros(Stokes_cov.shape)
+        Stokes_stat_cov = np.zeros(Stokes_cov.shape)
         for i in range(Stokes_cov.shape[0]):
-            s_IQU_stat[i, i] = np.sum([coeff_stokes[i, k] ** 2 * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=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]:
-                s_IQU_stat[i, j] = np.sum([coeff_stokes[i, k] * coeff_stokes[j, k] * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
-                s_IQU_stat[j, i] = np.sum([coeff_stokes[i, k] * coeff_stokes[j, k] * sigma_flux[k] ** 2 for k in range(len(sigma_flux))], axis=0)
+                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)
 
         # Compute the derivative of each Stokes parameter with respect to the polarizer orientation
         dIQU_dtheta = np.zeros(Stokes_cov.shape)
@@ -1368,19 +1368,23 @@ def compute_Stokes(data_array, error_array, data_mask, headers, FWHM=None, scale
             )
 
         # Compute the uncertainty associated with the polarizers' orientation (see Kishimoto 1999)
-        s_IQU_axis = np.zeros(Stokes_cov.shape)
+        Stokes_axis_cov = np.zeros(Stokes_cov.shape)
         for i in range(Stokes_cov.shape[0]):
-            s_IQU_axis[i, i] = np.sum([dIQU_dtheta[i, k] ** 2 * globals()["sigma_theta"][k] ** 2 for k in range(len(globals()["sigma_theta"]))], axis=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]:
-                s_IQU_axis[i, j] = np.sum(
-                    [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[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
                 )
-                s_IQU_axis[j, i] = np.sum(
-                    [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 += s_IQU_axis + s_IQU_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]
@@ -1414,8 +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]
@@ -1430,6 +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
@@ -1443,29 +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, s_IQU_stat
+    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, s_IQU_stat=None):
+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.
@@ -1540,45 +1563,34 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_s
     s_P[np.isnan(s_P)] = fmax
     s_PA[np.isnan(s_PA)] = fmax
 
-    # Compute the total exposure time so that
-    # I_stokes*exp_tot = N_tot the total number of events
-    N_obs = I_stokes * float(header_stokes["exptime"])
-
     # 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)
-    if s_IQU_stat is not None:
-        # If IQU covariance matrix containing only statistical error is given propagate to P and PA
-        # Catch Invalid value in sqrt when diagonal terms are big
-        with warnings.catch_warnings(record=True) as _:
-            s_P_P[maskP] = (
-                P[maskP]
-                / I_stokes[maskP]
-                * np.sqrt(
-                    s_IQU_stat[0, 0][maskP]
-                    - 2.0 / (I_stokes[maskP] * P[maskP] ** 2) * (Q_stokes[maskP] * s_IQU_stat[0, 1][maskP] + U_stokes[maskP] * s_IQU_stat[0, 2][maskP])
-                    + 1.0
-                    / (I_stokes[maskP] ** 2 * P[maskP] ** 4)
-                    * (
-                        Q_stokes[maskP] ** 2 * s_IQU_stat[1, 1][maskP]
-                        + U_stokes[maskP] ** 2 * s_IQU_stat[2, 2][maskP] * Q_stokes[maskP] * U_stokes[maskP] * s_IQU_stat[1, 2][maskP]
-                    )
-                )
+    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 * s_IQU_stat[2, 2][maskP]
-                    + U_stokes[maskP] * s_IQU_stat[1, 1][maskP]
-                    - 2.0 * Q_stokes[maskP] * U_stokes[maskP] * s_IQU_stat[1, 2][maskP]
-                )
-            )
-    else:
-        # Approximate Poisson error for P and PA
-        s_P_P[mask] = np.sqrt(2.0 / N_obs[mask])
-        s_PA_P[maskP] = s_P_P[maskP] / P[maskP] * 90.0 / np.pi
+        )
+    )
+    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 _:
@@ -1600,7 +1612,7 @@ def compute_pol(I_stokes, Q_stokes, U_stokes, Stokes_cov, header_stokes, s_IQU_s
     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, s_IQU_stat=None, 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
@@ -1617,7 +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
@@ -1639,6 +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.
@@ -1670,11 +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)
@@ -1683,6 +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)
@@ -1693,16 +1713,16 @@ 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))
 
-    if s_IQU_stat is not None:
-        s_IQU_stat = zeropad(s_IQU_stat, [*s_IQU_stat.shape[:-2], *shape])
-        new_s_IQU_stat = np.zeros((*s_IQU_stat.shape[:-2], *shape))
-        for i in range(3):
-            for j in range(3):
-                new_s_IQU_stat[i, j] = sc_rotate(s_IQU_stat[i, j], ang, order=1, reshape=False, cval=0.0)
-            new_s_IQU_stat[i, i] = np.abs(new_s_IQU_stat[i, i])
-        for i in range(shape[0]):
-            for j in range(shape[1]):
-                new_s_IQU_stat[:, :, i, j] = np.dot(mrot, np.dot(new_s_IQU_stat[:, :, 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)]])
@@ -1732,12 +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(
@@ -1746,21 +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")
 
-    if s_IQU_stat is not None:
-        return new_I_stokes, new_Q_stokes, new_U_stokes, new_Stokes_cov, new_data_mask, new_header_stokes, new_s_IQU_stat
-    else:
-        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)