From 78b1a5e3fc2880a7916db6e992148ab547a80c48 Mon Sep 17 00:00:00 2001
From: sgiardie <grdsrn1@unife.it>
Date: Thu, 19 Sep 2024 10:27:37 +0100
Subject: [PATCH] more docs

---
 mflike/foreground.py | 21 +++++++++++++--------
 1 file changed, 13 insertions(+), 8 deletions(-)

diff --git a/mflike/foreground.py b/mflike/foreground.py
index ca8ca6e..9e64825 100644
--- a/mflike/foreground.py
+++ b/mflike/foreground.py
@@ -596,13 +596,17 @@ def _bandpass_construction(self, _initialize=False, **params):
 
         When the chromatic beam is considered, we compute
         :math:`r_{\ell}^T(\nu+\Delta \nu) = \frac{\frac{\partial B_{\nu+\Delta \nu}}{\partial T}
-        \tau(\nu+\Delta \nu) b^T_{\ell}(\nu + \Delta \nu)}
+        \tau(\nu+\Delta \nu) b^T_{\ell}(\nu)}
         {\int d\nu
         \frac{\partial B_{\nu+\Delta \nu}}{\partial T} \tau(\nu+\Delta \nu)
-        b^T_{\ell}(\nu + \Delta \nu)}`
+        b^T_{\ell}(\nu)}`
         for the temperature field, and a corresponding expression for the polarization field,
         replacing the temperature beam with the polarization one
-        :math:`b^P_{\ell}(\nu + \Delta \nu)`.
+        :math:`b^P_{\ell}(\nu)`. If we want to propagate the bandpass shifts to the beam, we
+        compute instead :math:`r_{\ell}^T(\nu+\Delta \nu) = \frac{\frac{\partial B_{\nu+\Delta \nu}}{
+        \partial T} \tau(\nu+\Delta \nu) b^T_{\ell}(\nu + \Delta \nu)}
+        {\int d\nu \frac{\partial B_{\nu+\Delta \nu}}{\partial T} \tau(\nu+\Delta \nu)
+        b^T_{\ell}(\nu + \Delta \nu)}`.
 
         :param \**params: dictionary of nuisance parameters
         :return: the list of [nu, transmission] in the multifrequency case
@@ -855,11 +859,12 @@ def return_beams(self, exp, nu, dnu):
         to normalize them in the correct way (temperature beam = 1 for :math:`\ell = 0`).
         The polarization beam is normalized by the temperature one (as in ``hp.gauss_beam``).
 
-        In the presence of bandpass shift, we have to select the monochromatic beam :math:`b_{\ell}`
-        computed from the planet beam assuming that bandpass shift. This has to be present in the 
-        ``self.bandpass_shifted_beams`` dictionary. From each of these :math:`b_{\ell}`, the 
-        chromatic beam is computed with the scaling :math:`b_{\ell (\nu / \nu_0)^{-\alpha / 2}}`,
-        where :math:`\nu_0` and :math:`\alpha` are also found in the same dictionary.
+        If we want to propagate bandpass shifts to the beams, we have to select the 
+        monochromatic beam :math:`b_{\ell}` computed from the planet beam assuming 
+        that bandpass shift. This has to be present in the ``self.bandpass_shifted_beams`` 
+        dictionary. From each of these :math:`b_{\ell}`, the chromatic beam is computed 
+        with the scaling :math:`b_{\ell (\nu / \nu_0)^{-\alpha / 2}}`, where :math:`\nu_0` 
+        and :math:`\alpha` are also found in the same dictionary.
 
         :param nu: the frequency array in GHz (for now, the math:`\nu` array is the same
                    between bandpass file and beam file for the same experiment/array.