DevRef...; gitignore + nls

.gitignore

@@ -15,6 +15,7 @@
 *.ind
 *.log
 *.nlo
+*.nls
 *.out
 *.toc
 *.trs

Doc/DevRef/DevRef.tex

@@ -21,8 +21,8 @@
 %   makeindex -s nomencl.ist $T.nlo -o $T.nls
 %   xelatex $T
 
-\documentclass[a4paper,11pt,fleqn]{report}\usepackage[final]{graphicx}
-%\documentclass[a4paper,11pt,fleqn,draft]{report}\usepackage[final]{graphicx}
+%\documentclass[a4paper,11pt,fleqn]{report}\usepackage[final]{graphicx}
+\documentclass[a4paper,11pt,fleqn,draft]{report}\usepackage[final]{graphicx}
 %\documentclass[a4paper,11pt,fleqn,draft]{report}\usepackage[draft]{graphicx}
 
 \def\shorttitle{BornAgain Developers Reference}

Doc/DevRef/Roughness.tex

@@ -45,6 +45,8 @@ How to account for these losses in the R/T computation is an open research quest
 \subsection{Interface with tanh profile}
 %==================================================================================================%
 
+\def\RF{\mathcal{R}}
+
 Graded interfaces have a smooth SLD profile,
 i.e.\ the function $\overline{v}(z)$ or $\kappa^2(z)$ evolves continuously
 from one bulk value to the other.
@@ -113,42 +115,25 @@ with $x\coloneqq \pi\tau\kappa_a$ and $y\coloneqq \pi\tau\kappa_b$.
 We write $\text{tanhc}\; x \coloneqq (\tanh x)/x$ (\cref{Ftanhc}a)
 and define the roughness factor
 \begin{equation}\label{ERba}
-R_{ab} \coloneqq \sqrt{ \frac{\text{tanhc}\; \pi\tau\kappa_b}{\text{tanhc}\; \pi\tau\kappa_a } }.
+\RF_{ab} \coloneqq \sqrt{ \frac{\text{tanhc}\; \pi\tau\kappa_b}{\text{tanhc}\; \pi\tau\kappa_a } }.
 \end{equation}
 With all this, \cref{ErTanh} can be cast as
 \begin{equation}\label{ErTanh2}
- r_{ab} = \frac{R_{ab}^{-1}\kappa_a - R_{ab} \kappa_b}{R_{ab}^{-1}\kappa_a + R_{ab}\kappa_b},
+ r_{ab} = \frac{\RF_{ab}^{-1}\kappa_a - \RF_{ab} \kappa_b}{\RF_{ab}^{-1}\kappa_a + \RF_{ab}\kappa_b},
 \end{equation}
 which has the form of the Fresnel reflection coefficient~\cref{ErFresnel},
-except for the factors $R_{ab}^{-1}$ and $R_{ab}$.
+except for the factors $\RF_{ab}^{-1}$ and $\RF_{ab}$.
 For $\tau\to0$, these factors go to~1 so that \cref{ErFresnel} is fully recovered
 (\cref{Ftanhc}b).
-
-Neglecting again the phase factor, we can compute the transmission coefficient
-from \cref{EConservation}. We obtain
-\begin{equation}\label{EtTanh2}
- t_{ab} = \frac{2\kappa_a}{R_{ab}^{-1}\kappa_a + R_{ab}\kappa_b}.
-\end{equation}
-\textbf{TODO: Is this correct? Is this implemented in BornAgain?}
-Tests confirm that flux conservation is fulfilled at machine precision.\footnote
-{\textbf{TODO:} provide name of tests.}
-
-With the Fresnel coefficients \cref{EtFresnel,ErFresnel},
-we write the refraction matrix as
-\begin{equation}\label{ESab2}
-  S_{ab}
-   \coloneqq
-   \frac{1}{t_{ab}}
-   \left(\begin{array}{ll}
-     1&r_{ab}\\
-     r_{ab}&1
-   \end{array}\right).
-\end{equation}
-This form remains valid for our modified coefficients \cref{ErTanh2} and~\cref{EtTanh2}.
-Accordingly, the coefficients~\cref{Dslpm} must be replaced by
+The reduced $r_{ab}$ of \cref{ErTanh2} can be obtained from
+the basic transfer matrix equation~\cref{EcMc}
+if the coefficients~$s^\pm$ of \cref{Dslpm} are replaced by\footnote
+{Implemented in file \SRC{Resample/Specular}{ComputeFluxScalar.cpp},
+function \T{transition} [30may23].}
 \begin{equation}\label{EslpmTanh}
-  s^\pm_l = R_{l,l-1}^{-1} \pm R_{l,l-1}\kappa_{l-1}/\kappa_l.
+  s^\pm_a = \RF_{ab}^{-1} \pm \RF_{ab}\kappa_{b}/\kappa_a.
 \end{equation}
+It is easily verified that the energy conservation~\cref{EConservation} still holds.
 
 %==================================================================================================%
 \subsection{N\'evot-Croce factor}
@@ -180,11 +165,13 @@ where $t_{ab}$ is the Fresnel coefficient \cref{EtFresnel}.
 This is the result obtained by Tolan \cite[Eq.~2.35]{Tol99},
 and is also given by de Boer \cite{BoLe96} as a result from formal perturbation theory
 in the limit of very small lateral correlation length.
-With \cref{ESab2}, we obtain the coefficients to replace~\cref{Dslpm},
+To obtain $\tilde r_{ab}$ and $\tilde t_{ab}$ from
+the basic transfer matrix equation~\cref{EcMc},
+we need to replace the coefficients $s^\pm$ of~\cref{Dslpm} by
 \begin{equation}\label{EslpmNC}
   s^\pm_l = (1 \pm \kappa_{l-1}/\kappa_l) \exp(-(\kappa_{l-1}\mp\kappa_l)^2\sigma^2/2),
 \end{equation}
-which shows that the above is also consistent with \cite[Eq.~3.114]{GiVi09}.
+which is consistent with \cite[Eq.~3.114]{GiVi09}.
 
 However, the total reflected and transmitted flux
 $\kappa_a|\tilde r_{ab}|^2+\kappa_b|\tilde t_{ab}|^2$,