Cleanup equation notation

doc/jointcal.lyx

@@ -1939,8 +1939,12 @@ As an illustrative example, we will work through a particular photometry
 \begin_inset Formula $f_{0}$
 \end_inset
 
-: the CCD filter response) and a 3th order 2-D Chebyshev polynomial (
-\begin_inset Formula $\sum a_{j,k}T_{j,k}(u,v)$
+: the CCD filter response) and an 
+\begin_inset Formula $(n+m)$
+\end_inset
+
+th order 2-D Chebyshev polynomial (
+\begin_inset Formula $\sum a_{j,k}T_{j}(u)T_{k}(v)$
 \end_inset
 
 : the optics+sky response, where 
@@ -1955,7 +1959,7 @@ As an illustrative example, we will work through a particular photometry
  Thus, the mapping will be
 \begin_inset Formula 
 \[
-M_{\gamma i}(\eta,S_{\gamma i})=M_{CCD}(f_{0}^{-1},f_{\gamma i})M_{visit}(a_{j,k},x_{\gamma i},y_{\gamma i})=f_{\gamma i}[f_{0}]^{-1}\sum_{j=0}^{j=3}\sum_{k=0}^{k=3}a_{j,k}T_{j,k}(u_{\gamma i},v_{\gamma i})=\phi_{\gamma i}
+M_{\gamma i}(\eta,S_{\gamma i})=M_{CCD}(f_{0}^{-1},f_{\gamma i})M_{visit}(a_{j,k},x_{\gamma i},y_{\gamma i})=f_{\gamma i}[f_{0}]^{-1}\sum_{j=0}^{j=n}\sum_{k=0}^{k=m}a_{j,k}T_{j}(u_{\gamma i})T_{k}(v_{\gamma i})=\phi_{\gamma i}
 \]
 
 \end_inset
@@ -1976,7 +1980,7 @@ where we will fit
  Computing those derivatives gives us:
 \begin_inset Formula 
 \begin{eqnarray*}
-\nabla D_{\gamma i} & = & (\frac{\partial D_{\gamma i}}{\partial f_{0}^{-1}},\frac{\partial D_{\gamma i}}{a_{0,0}},\ldots,\frac{\partial D_{\gamma i}}{a_{3,3}},\frac{\partial D_{\gamma i}}{F_{i}})
+\nabla D_{\gamma i} & = & (\frac{\partial D_{\gamma i}}{\partial f_{0}^{-1}},\frac{\partial D_{\gamma i}}{\partial a_{0,0}},\ldots,\frac{\partial D_{\gamma i}}{\partial a_{n,m}},\frac{\partial D_{\gamma i}}{\partial F_{i}})
 \end{eqnarray*}
 
 \end_inset

doc/jointcal.tex

@@ -287,9 +287,9 @@ \subsection{Choice of projectors}
 In the least squares expression \ref{eq:astrometry-chi2}, the residuals
 of the measurement terms read: 
 \[
-D_{\gamma i}=M_{\gamma}(S_{\gamma,i})-P_{\gamma}(F_{j})
+D_{\gamma i}=M_{\gamma}(S_{\gamma i})-P_{\gamma}(F_{i})
 \]
-If the coordinates $F_{j}$ are sidereal coordinates, the projector
+If the coordinates $F_{i}$ are sidereal coordinates, the projector
 $P_{\gamma}$ determine the meaning of the mapping $M_{\gamma}$.
 If one is aiming at producing WCS's for the image, it seems wise to
 choose for $P_{\gamma}$ the projection used foe the envisioned WCS,
@@ -492,18 +492,18 @@ \subsection{Photometry example}
 
 As an illustrative example, we will work through a particular photometry
 mapping, consisting of a constant zero-point per CCD ($f_{0}$: the
-CCD filter response) and a 3th order 2-D Chebyshev polynomial ($\sum a_{j,k}T_{j,k}(u,v)$:
-the optics+sky response, where $(u(x,y),v(x,y))$ are the focal plane
-coordinates of pixel $(x,y)$ on a given CCD) per visit. Thus, the
-mapping will be
+CCD filter response) and an $(n+m)$th order 2-D Chebyshev polynomial
+($\sum a_{j,k}T_{j}(u)T_{k}(v)$: the optics+sky response, where $(u(x,y),v(x,y))$
+are the focal plane coordinates of pixel $(x,y)$ on a given CCD)
+per visit. Thus, the mapping will be
 \[
-M_{\gamma i}(\eta,S_{\gamma i})=M_{CCD}(f_{0}^{-1},f_{\gamma i})M_{visit}(a_{j,k},x_{\gamma i},y_{\gamma i})=f_{\gamma i}[f_{0}]^{-1}\sum_{j=0}^{j=3}\sum_{k=0}^{k=3}a_{j,k}T_{j,k}(u_{\gamma i},v_{\gamma i})=\phi_{\gamma i}
+M_{\gamma i}(\eta,S_{\gamma i})=M_{CCD}(f_{0}^{-1},f_{\gamma i})M_{visit}(a_{j,k},x_{\gamma i},y_{\gamma i})=f_{\gamma i}[f_{0}]^{-1}\sum_{j=0}^{j=n}\sum_{k=0}^{k=m}a_{j,k}T_{j}(u_{\gamma i})T_{k}(v_{\gamma i})=\phi_{\gamma i}
 \]
 where we will fit $f_{0}^{-1}$ instead of $f_{0}$ in order to simplify
 the derivatives (with respect to $\eta=\left(f_{0}^{-1},a_{j,k}\forall j,k\right)$).
 Computing those derivatives gives us:
 \begin{eqnarray*}
-\nabla D_{\gamma i} & = & (\frac{\partial D_{\gamma i}}{\partial f_{0}^{-1}},\frac{\partial D_{\gamma i}}{a_{0,0}},\ldots,\frac{\partial D_{\gamma i}}{a_{3,3}},\frac{\partial D_{\gamma i}}{F_{i}})
+\nabla D_{\gamma i} & = & (\frac{\partial D_{\gamma i}}{\partial f_{0}^{-1}},\frac{\partial D_{\gamma i}}{\partial a_{0,0}},\ldots,\frac{\partial D_{\gamma i}}{\partial a_{n,m}},\frac{\partial D_{\gamma i}}{\partial F_{i}})
 \end{eqnarray*}
 where, for the measurement terms we have (recall eq. \ref{eq:photometry_residual_vector_measurement}),
 \begin{eqnarray*}