X-Git-Url: http://git.kpe.io/?p=ctsim.git;a=blobdiff_plain;f=doc%2Fctsim-concepts.tex;h=12cdc3f603942ad4ccc1abfe63b1bb3d912e81b7;hp=64a870dc1a88fe545610fa531d4d414966ea585f;hb=3b389ec4d6e6c5a720ea096b8f504e02b984d237;hpb=17f20398d8bb0e4b97b5884b999bbe8d58c5254f diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex index 64a870d..12cdc3f 100644 --- a/doc/ctsim-concepts.tex +++ b/doc/ctsim-concepts.tex @@ -119,10 +119,6 @@ length}. These variables are input into \ctsim\ in terms of ratios rather than absolute values. \subsubsection{Phantom Diameter}\index{Phantom!Diameter} -\begin{figure} -$$\image{5cm;0cm}{scangeometry.eps}$$ -\caption{\label{phantomgeomfig} Phantom Geometry} -\end{figure} The phantom diameter is automatically calculated by \ctsim\ from the phantom definition. The maximum of the phantom length and height is used to define the square that completely surrounds the @@ -134,9 +130,13 @@ Pythagorean theorem and is \latexonly{\begin{equation}p_d = p_l \sqrt{2}\end{equation}} CT scanners collect projections around a circle rather than a square. The diameter of this circle is -the diameter of the boundary square \latexonly{$p_d$. These -relationships are diagrammed in figure~\ref{phantomgeomfig}.} -\latexignore{emph{Pd}.} +the diameter of the boundary square \latexonly{$p_d$.} +\latexignore{\emph{Pd}.} +\latexonly{These relationships are diagrammed in figure~\ref{phantomgeomfig}.} +\begin{figure} +\centerline{\image{5cm;0cm}{scangeometry.eps}} +\latexonly{\caption{\label{phantomgeomfig} Phantom Geometry}} +\end{figure} \subsubsection{View Diameter}\index{View diameter} The \emph{view diameter} is the area that is being processed @@ -218,8 +218,8 @@ source produces a fan beam which is read by a linear array of detectors. If the detectors occupy an arc of a circle, then the geometry is equiangular. \latexonly{These configurations are shown in figure~\ref{divergentfig}.} \begin{figure} -\image{10cm;0cm}{divergent.eps} -\caption{\label{divergentfig} Equilinear and equiangular geometries.} +\centerline{\image{10cm;0cm}{divergent.eps}} +\latexonly{\caption{\label{divergentfig} Equilinear and equiangular geometries.}} \end{figure} @@ -232,11 +232,11 @@ the \emph{focal length}: \latexignore{\centerline{\emph{alpha = 2 x asin ( (Sd / 2) / f)}}} \latexonly{\begin{equation}\label{alphacalc}\alpha = 2 \sin^{-1} -((s_d / 2) / f)\end{equation} - This is illustrated in figure~\ref{alphacalcfig}.} +((s_d / 2) / f)\end{equation}} +\latexonly{This is illustrated in figure~\ref{alphacalcfig}.} \begin{figure} -\image{10cm;0cm}{alphacalc.eps} -\caption{\label{alphacalcfig} Calculation of $\alpha$} +\centerline{\image{10cm;0cm}{alphacalc.eps}} +\latexonly{\caption{\label{alphacalcfig} Calculation of $\alpha$}} \end{figure} @@ -283,13 +283,15 @@ the \emph{scan diameter} increases the detector array size. For equiangular geometry, the detectors are spaced around a circle covering an angular distance of -\latexonly{$2\,\alpha$.}\latexignore{\emph{2 \alpha}.} The dotted -circle in +\latexonly{$2\,\alpha$.}\latexignore{\emph{2 \alpha}.} +The dotted circle +\latexonly{in figure~\ref{equiangularfig}} +indicates the positions of the detectors in this case. + \begin{figure} -\image{10cm;0cm}{equiangular.eps} -\caption{\label{equiangularfig}Equiangular geometry} +\centerline{\image{10cm;0cm}{equiangular.eps}} +\latexonly{\caption{\label{equiangularfig}Equiangular geometry}} \end{figure} -figure~\ref{equiangularfig} indicates the positions of the detectors in this case. For equilinear geometry, the detectors are space along a straight line. The length of the line depends upon @@ -297,11 +299,11 @@ line. The length of the line depends upon length}. It is calculated as \latexonly{\begin{equation}4\,f \tan (\alpha / 2)\end{equation}} \latexignore{\\\centerline{\emph{4 x F x tan(\alpha/2)}}} +\latexonly{This geometry is shown in figure~\ref{equilinearfig}.} \begin{figure}\label{equilinearfig} -\image{10cm;0cm}{equilinear.eps} -\caption{\label{equilinearfig} Equilinear geometry} +\centerline{\image{10cm;0cm}{equilinear.eps}} +\latexonly{\caption{\label{equilinearfig} Equilinear geometry}} \end{figure} -\latexonly{This geometry is shown in figure~\ref{equilinearfig}.} \section{Reconstruction}\label{conceptreconstruction}\index{Reconstruction Overview}%