+\subsection{Dimensions}
+Understanding the scanning geometry is the most complicated aspect of
+using \ctsim. For real-world CT simulators, this is actually quite
+simple. The geometry is fixed by the manufacturer during the
+construction of the scanner and can not be changed. Conversely,
+real-world CT scanners can only take objects up to a fixed size.
+
+\ctsim, being a very flexible simulator,
+gives tremendous options in setting up the geometry for a scan.
+
+In general, the geometry for a scan all starts from the size of the
+phantom being scanned. This is because \ctsim\ allows for statistical
+comparisons between the original phantom image and it's reconstructions.
+Since CT scanners scan a circular area, the first important
+variable is the diameter of the circle surround the phantom, or the
+\emph{phantom diameter}. Remember, as mentioned above, the
+phantom dimensions are also padded by 1\%.
+
+The other important geometry variables for scanning phantoms are
+the \emph{view diameter}, \emph{scan diameter}, and \emph{focal
+length}. These variables are all input into \ctsim\ in terms of
+ratios rather than absolute values.
+
+\subsubsection{Phantom Diameter}
+\begin{figure}
+$$\image{5cm;0cm}{scangeometry.eps}$$
+\caption{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 phantom. Let
+\latexonly{$p_l$}\latexignore{\emph{Pl}}
+be the width and height of this square. The diameter of this boundary box,
+\latexonly{$p_d$,}\latexignore{\emph{Pd},}
+\rtfsp is then
+\latexignore{\\$$\emph{Pl x sqrt(2)}$$\\}
+\latexonly{$$p_d = p_l \sqrt{2}$$}
+CT scanners actually collect projections around a circle rather than a
+square. The diameter of this circle is also the diameter of the boundary
+square
+\latexonly{$p_d$.}\latexignore{\rtfsp\emph{Pd}.}
+These relationships are diagrammed in figure 2.1.
+
+\subsubsection{View Diameter}
+The \emph{view diameter} is the area that is being processed
+during scanning of phantoms as well as during rasterization of
+phantoms. By default, the \emph{view diameter} \rtfsp is set equal
+to the \emph{phantom diameter}. It may be useful, especially for
+experimental reasons, to process an area larger (and maybe even
+smaller) than the phantom. Thus, during rasterization or during
+projections, \ctsim\ will ask for a \emph{view ratio},
+\latexonly{$v_r$.}\latexignore{\rtfsp \emph{VR}.} The \emph{view
+diameter} is then calculated as \latexonly{$$v_d = p_d
+v_r$$}\latexignore{\\$$\emph{Vd = Pd x VR}$$}
+
+By using a
+\latexonly{$v_r$}\latexignore{\emph{VR}}
+less than 1, \ctsim\ will allow
+for a \emph{view diameter} less than
+\emph{phantom diameter}.
+This will lead to significant artifacts. Physically, this would
+be impossible and is analagous to inserting an object into the CT
+scanner that is larger than the scanner itself!
+
+\subsubsection{Scan Diameter}
+By default, the entire \emph{view diameter} is scanned. For
+experimental purposes, it may be desirable to scan an area either
+larger or smaller than the \emph{view diameter}. Thus, the concept
+of \emph{scan ratio}, \latexonly{$s_r$,}\latexignore{\emph{SR},}
+is arises. The scan diameter
+\latexonly{$s_d$}\latexignore{\emph{Sd}} is the diameter over
+which x-rays are collected and is defined as \latexonly{$$s_d =
+v_d s_r$$}\latexignore{\\$$\emph{Sd = Vd x SR}$$\\} By default and
+for all ordinary scanning, the \emph{scan ratio} is to \texttt{1}.
+If the \emph{scan ratio} is less than \texttt{1}, you can expect
+significant artifacts.
+
+\subsubsection{Focal Length}
+The \emph{focal length},
+\latexonly{$f$,}\latexignore{\emph{F},}
+is the distance of the X-ray source to the center of
+the phantom. The focal length is set as a ratio,
+\latexonly{$f_r$,}\latexignore{\emph{FR},}
+of the view radius. Focal length is
+calculated as
+\latexonly{$$f = (v_d / 2) f_r$$}\latexignore{\\$$\emph{F = (Vd / 2) x FR}$$}
+
+For parallel geometry scanning, the focal length doesn't matter.
+However, divergent geometry scanning (equilinear and equiangular),
+the \emph{focal length ratio} should be set at \texttt{2} or more
+to avoid artifacts. Moreover, a value of less than \texttt{1} is
+physically impossible and it analagous to have having the x-ray
+source inside of the \emph{view diameter}.
+
+
+\subsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel}
+
+As mentioned above, the focal length is not used in this simple
+geometry. The detector array is set to be the same size as the
+\emph{scan diameter}. For optimal scanning in this geometry, the
+\emph{scan diameter} should be equal to the \emph{phantom
+diameter}. This is accomplished by using the default values of
+\texttt{1} for the \emph{view ratio} and the \emph{scan ratio}. If
+values of less than \texttt{1} are used for these two variables,
+significant distortions will occur.
+
+
+\subsection{Divergent Geometries}\label{geometrydivergent}\index{Concepts,Scanner,Geometries,Divergent}
+\subsubsection{Overview}
+Next consider the case of equilinear (second generation) and equiangular
+(third, fourth, and fifth generation) geometries. In these cases,
+the x-ray beams diverge from a single source to a detector array.
+In the equilinear mode, a single
+source produces a fan beam which is read by a linear array of detectors. If
+the detectors occupy an arc of a circle, then the geometry is equiangular.
+See figure 2.2.
+\begin{figure}
+\image{10cm;0cm}{divergent.eps}
+\caption{Equilinear and equiangular geometries.}
+\end{figure}
+
+
+\subsubsection{Fan Beam Angle}
+For these divergent beam geometries, the \emph{fan beam angle}
+needs to be calculated. For real-world CT scanners, this is fixed
+at the time of manufacture. \ctsim, however, calculates the
+\emph{fan beam angle}, $\alpha$, from the \emph{scan diameter} and
+the \emph{focal length} \latexignore{\\$$\emph{alpha = 2 x asin (
+(Sd / 2) / f)}$$\\}
+\latexonly{\begin{equation}\label{alphacalc}\alpha = 2 \sin^{-1}
+((s_d / 2) / f)\end{equation}} This is illustrated in figure 2.3.
+\begin{figure}
+\image{10cm;0cm}{alphacalc.eps}
+\caption{Calculation of $\alpha$}
+\end{figure}
+
+
+Empiric testing with \ctsim\ shows that for very large \emph{fan beam angles},
+greater than approximately
+\latexonly{$120^\circ$,}\latexignore{120 degrees,}
+there are significant artifacts. The primary way to manage the
+\emph{fan beam angle} is by varying the \emph{focal length} since the
+\emph{scan diameter} by the size of the phantom.
+
+To illustrate, the \emph{scan diameter} can be defined as
+\latexonly{$$s_d = s_r v_r p_d$$}\latexignore{\\$$Sd = Sr x Vr x Pd$$\\}
+
+Further, $f$ can be defined as \latexonly{$$f = f_r (v_r p_d /
+2)$$}\latexignore{\\$$F = FR x (VR x Pd)$$\\}
+
+Substituting these equations into \latexignore{the above
+equation,}\latexonly{equation~\ref{alphacalc},} We have,
+\latexonly{
+\begin{eqnarray}
+\alpha &= 2\,\sin^{-1} \frac{s_r v_r p_d / 2}{f_r v_r (p_d / 2)} \nonumber \\
+&= 2\,\sin^{-1} (s_r / f_r)
+\end{eqnarray}
+} \latexignore{\\$$\alpha = 2 sin (Sr / Fr$$\\}
+
+Since in normal scanning $s_r$ = 1, $\alpha$ depends only upon the
+\emph{focal length ratio}.
+
+\subsubsection{Detector Array Size}
+In general, you do not need to be concerned with the detector
+array size. It is automatically calculated by \ctsim. For the
+particularly interested, this section explains how the detector
+array size is calculated.
+
+For parallel geometry, the detector length is equal to the scan
+diameter.
+
+For divergent beam geometries, the size of the detector array also
+depends upon the \emph{focal length}. Increasing the \emph{focal
+length} decreases the size of the detector array while increasing
+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
+\begin{figure}\label{equiangularfig}
+\image{10cm;0cm}{equiangular.eps} \caption{Equiangular geometry}
+\end{figure}
+figure 2.4 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
+\latexonly{$\alpha$}\latexignore{\emph{alpha}} and the \emph{focal
+length}. It is calculated as \latexonly{$4\,f \tan (\alpha / 2)$}
+\latexignore{\emph{4 x F x tan(\alpha/2)}}
+\begin{figure}\label{equilinearfig}
+\image{10cm;0cm}{equilinear.eps}
+\caption{Equilinear geometry}
+\end{figure}
+This geometry is shown in figure~2.5.
+
+
+\subsubsection{Examples of Geometry Settings}
+