In order to use \ctsim\ effectively, some knowledge of how \ctsim\ works
and the approach taken is required. \ctsim\ deals with a variety of
-object, but the two we need to be concerned with are the 'phantom' and
+object, but the two objects we need to be concerned with are the 'phantom' and
the 'scanner'.
\section{Phantoms}\label{conceptphantom}\index{Concepts,Phantoms}%
\subsection{Overview}\label{phantomoverview}\index{Concepts,Phantoms,Overview}%
\ctsim\ uses geometrical objects to
-describe the object being scanned: rectangles, triangles, ellipses,
-sectors and segments. With these the standard phantoms used in the CT
-literature (the Herman and the Shepp-Logan) can be constructed. In fact
+describe the object being scanned. A phantom is composed a one or more
+phantom elements. These elements are simple geometric shapes,
+specifically, rectangles, triangles, ellipses, sectors and segments.
+With these the standard phantoms used in the CT literature (the Herman
+and the Shepp-Logan) can be constructed. In fact
\ctsim\ provides a shortcut to construct those phantoms for you. It also
allows you to write a file in which the composition of your own phantom is
described.
\subsubsection{ellipse}
Ellipses use dx and dy to define the semi-major and semi-minor axis lengths,
with the centre of the ellipse at cx and cy. Of note, the commonly used
-phantom described by Shepp and Logan\cite{SHEPP77} uses only ellipses.
+phantom described by Shepp and Logan\cite{SHEPP74} uses only ellipses.
\subsubsection{rectangle}
Rectangles use
The two other important variables are the field-of-view-ratio ($f_{vR}$)
and the focal-length-ratio ($f_{lR}$). These are used along with $l_p$ to
define the focal length and the field of view (not ratios) according to
-\begin{equation}
+\latexonly{\begin{equation}
f_l = \sqrt{2} (l_p/2)(f_{lR})= (l_p/\sqrt{2}) f_{lR}
\end{equation}
\begin{equation}
f_v = \sqrt{2}l_p f_{vR}
-\end{equation}
+\end{equation}}
So the field of view ratio is specified in units of the phantom diameter,
whereas the focal length is specified in units of the phantom radius. The
-factor of $\sqrt(2)$ can be understood if one refers to figure 1, where
+factor of
+\latexonly{$\sqrt(2)$}
+\latexignore{sqrt(2)}
+can be understood if one refers to figure 1, where
we consider the case of a first generation parallel beam CT scanner.
\subsubsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel}
For these geometries, the following logic is executed: A variable dHalfSquare
$d_{hs}$ is defined as
-\begin{equation}
+\latexonly{\begin{equation}
d_{hs} = (f_v)/(2\sqrt{2}) = (l_p/2) f_{vR}
-\end{equation}
+\end{equation}}
This is then subtracted from the focal length $f_l$ as calculated above, and
assigned to a new variable $\mathrm{dFocalPastPhm} = f_l - d_{hs}$. Since $f_l$ and
$d_{hs}$ are derived from the phantom dimension and the input focal length and field of view ratios, one can write,
+\latexonly{
\begin{equation}
\mathrm{dFocalPastPhm} = f_l -d_{hs}
= \sqrt{2}(l_p/2) f_{lR} - (l_p/2) f_{vR} = l_p(\sqrt{2}f_{lR} - f_{vR})
\end{equation}
+}
If this quantity is less than or equal to zero, then at least for some
projections the source is inside the phantom. Perhaps a figure will help at
this point. Consider first the case where $f_{vR} = f_{lR} =1 $, figure 3. The
square in the figure bounds the phantom and has sides $l_p$. For this case
then,
+\latexonly{
\[
f_l=\sqrt{2}l_p/2 = l_p/\sqrt{2},
\]
\[
\mathrm{dFocalPastPhm} = ({l_p}/{2}) (\sqrt{2}-1)
\]
+}
\begin{figure}
\includegraphics[height=0.5\textheight]{ctsimfig3.eps}
\caption{Equilinear and equiangluar geometry when focal length ratio =
projects / ctsim.git / blobdiff