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zx(oOI9uZrc4z}N!UrMa@!4;|U`pylfzZE>1z|yRoUk<oz?wF*p+IOE`TtXB=$IGjr Iu1NR40Bc?3%K!iX diff --git a/Doc/FFCatalog/FormFactors.tex b/Doc/FFCatalog/FormFactors.tex index a61aceb980d..e08a90bc84d 100644 --- a/Doc/FFCatalog/FormFactors.tex +++ b/Doc/FFCatalog/FormFactors.tex @@ -408,7 +408,7 @@ except for factors $1/2$ in the definitions of parameters $L$, $W$, $H$. \item \ffref{AnisoPyramid} or \ffref{Pyramid} if sides are not vertical, \item \ffref{TruncatedCube} if $L=W=H$ and corners are facetted, -\item Sect.~\ref{SElongatedBox} if elongated in one horizontal direction. +\item Sect.~\ref{SBar} if elongated in one horizontal direction. \end{itemize} %=============================================================================== @@ -1908,26 +1908,55 @@ Different profiles in the $yz$ plane can be chosen: box, sinusoidal [\ffref{Ripple1}], saw-tooth [\ffref{Ripple2}]. For each of them, different profiles can also be chosen in the $xz$ plane, -namely box, Gauss, and Lorentzian, each of them characterized by a single parameter \texttt{length},~$L$. -The corresponding form factor along the elongation axis~$x$ is +Their transverse form factor, +\index{Transverse form factor}% +along the elongation axis~$x$, is \begin{equation}\label{EFparallel} f_\parallel(q_x) = \left\{\begin{array}{l@{\quad}l} - L\sinc(q_x L/2) &\text{box,}\\ - L\exp(-(q_x L)^2/8) &\text{Gauss,}\\ - L/(1+(q_x L)^2) &\text{Lorentz.} + L\sinc(q_x L/2) &\texttt{box,}\\ + L\exp(-(q_x L)^2/8) &\texttt{Gauss,}\\ + L/(1+(q_x L)^2) &\texttt{Lorentz.} \end{array}\right. \end{equation} Constant factors have been chosen so that the forward scattering is the same in all three cases, $f_\parallel(0)=L$. +The form factor is the Fourier transform of a correlation function. +The \texttt{box} form factor with its characteristic sinc function +is the Fourier transform of a rectangle function. +A typical application could be a sample with tiny lateral extension +that is fully illuminated by a coherent incoming plane wave. +In most other situations, the correlation function is smooth rather than rectangular. +The \texttt{length} parameter then stands for a correlation length. +\index{Correlation length}% +It is dominated either by a finite extension of the ripple, +or by the coherence length +\index{Coherence length}% +of the scattering setup. +The \texttt{Gauss} form factor is the Fourier transform of +a Gaussian +\index{Gaussian!transverse form factor} +correlation function; +the \texttt{Lorentz} +\index{Lorentzian!transverse form factor} + form factor is the Fourier transform of an exponential in~$|x|$. + +\paragraph{History}\strut\\ +The \texttt{Box} variant of \E{Ripple1} and \E{Ripple2} replicates +two form factors from \FitGISAXS\ \cite{Bab13}. + +Full documentation and API support for all ripple form factors appeared in BornAgain-1.17. +Before that release, the \texttt{Lorentz} factor~$f_\parallel$ +had an extra factor of 2.5 in the form factor. + %=============================================================================== -\ffsection{Elongated box} \label{SElongatedBox} +\ffsection{Bar (elongated box)} \label{SBar} %=============================================================================== \index{Box} \index{FormFactorBox@\Code{FormFactorBox}} -\index{FormFactorLongBoxGauss@\Code{FormFactorLongBoxGauss}} -\index{FormFactorLongBoxLorentz@\Code{FormFactorLongBoxLorentz}} +\index{FormFactorBarGauss@\Code{FormFactorBarGauss}} +\index{FormFactorBarLorentz@\Code{FormFactorBarLorentz}} \paragraph{Real-space geometry}\strut\\ @@ -1939,7 +1968,7 @@ in all three cases, $f_\parallel(0)=L$. \hfill \subfigure[Side view]{\raisebox{2mm}{\includefinal{.3\TW}{fig/cuts/Box2dxz.pdf}}} \hfill -\caption{A rectangular cuboid.} +\caption{A bar.} \end{figure} \FloatBarrier @@ -1948,9 +1977,9 @@ in all three cases, $f_\parallel(0)=L$. \begin{lstlisting} FormFactorBox( double length, double width, double height) - FormFactorLongBoxGauss( + FormFactorBarGauss( double length, double width, double height) - FormFactorLongBoxLorentz( + FormFactorBarLorentz( double length, double width, double height) \end{lstlisting} with the parameters @@ -1974,7 +2003,6 @@ with $f_\parallel$ as defined in~\cref{EFparallel}, S = LW. \end{equation*} - %=============================================================================== \ffsection{Ripple1 (sinusoidal)} \label{SRipple1} %=============================================================================== @@ -2058,9 +2086,9 @@ Agrees with the \E{Ripple1} form factor of \FitGISAXS\ \cite{Bab13}. %=============================================================================== \index{Ripple!saw-tooth} \index{Saw-tooth ripple} -\index{FormFactorRipple2@\Code{FormFactorRipple2}} -\index{FormFactorLongRipple2Gauss@\Code{FormFactorLongRipple2Gauss}} -\index{FormFactorLongRipple2Lorentz@\Code{FormFactorLongRipple2Lorentz}} +\index{FormFactorRipple2@\Code{FormFactorRipple2Box}} +\index{FormFactorRipple2Gauss@\Code{FormFactorRipple2Gauss}} +\index{FormFactorRipple2Lorentz@\Code{FormFactorRipple2Lorentz}} \paragraph{Real-space geometry}\strut\\ @@ -2079,12 +2107,12 @@ Agrees with the \E{Ripple1} form factor of \FitGISAXS\ \cite{Bab13}. \paragraph{Syntax and parameters}\strut\\[-2ex plus .2ex minus .2ex] \begin{lstlisting} - FormFactorRipple2( + FormFactorRipple2Box( + double length, double width, double height, asymmetry) + FormFactorRipple2Gauss( + double length, double width, double height, asymmetry) + FormFactorRipple2Lorentz( double length, double width, double height, asymmetry) - FormFactorLongRipple2Gauss( - double length, double width, double height) - FormFactorLongRipple2Lorentz( - double length, double width, double height) \end{lstlisting} with the parameters \begin{itemize} -- GitLab