+\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 objects 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},}
+is then
+\latexignore{\\$$\emph{Pl x sqrt(2)}$$\\}
+\latexonly{$$p_d = p_l \sqrt{2}$$}
+CT scanners actually collect projections around a circle rather than a
+square. The diameter of this circle is also the diameter of the boundary
+square
+\latexonly{$p_d$.}\latexignore{\emph{Pd}.}
+These relationships are diagrammed in figure 2.1.
+
+\subsubsection{View Diameter}
+The \emph{view diameter} is the area that is being processed during scanning of phantoms as
+well as during rasterization of phantoms. By default, the \emph{view diameter}
+is set equal to the \emph{phantom diameter}. It may be useful, especially for
+experimental reasons, to process an area larger (and maybe even smaller) than
+the phantom. Thus, during rasterization or during projections, \ctsim\ will
+ask for a \emph{view ratio},
+\latexonly{$v_{R}$.}\latexignore{\emph{VR}.}
+The \emph{view diameter} is then set as
+\latexonly{$$v_d = p_d v_{R}$$}\latexignore{\\$$\emph{Vd = Pd x VR}$$}
+
+By using a
+\latexonly{$v_{R}$}\latexignore{\emph{VR}}
+less than 1, \ctsim\ will allow
+for a \emph{view diameter} less than
+\emph{phantom diameter}.
+This will lead to significant artifacts. Physically, this would
+be impossible and is analagous to inserting an object into the CT
+scanner that is larger than the scanner itself!
+
+\subsubsection{Scan Diameter}
+By default, the entire \emph{view diameter} is scanned. For experimental
+purposes, it may be desirable to scan an area either larger or smaller than
+the \emph{view diameter}. Thus, the concept of \emph{scan ratio}
+\latexonly{$s_{R}$}\latexignore{\emph{SR}}
+is born. The scan diameter
+\latexonly{$s_d$}\latexignore{\emph{Sd}}
+is the diameter over which x-rays are collected and is defined as
+\latexonly{$$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}$$}
+
+For parallel geometry scanning, the focal length doesn't matter. However,
+divergent geometry scanning (equilinear and equiangular), the \emph{focal
+length ratio} should be set at \texttt{2} or more to avoid artifacts.
+
+\subsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel}
+
+As mentioned above, the focal length is not used in this simple
+geometry. The detector array is set to
+be the same size as the \emph{scan diameter}.
+For optimal scanning in this geometry, the \emph{scan diameter} should
+be equal to the \emph{phantom diameter}. This is accomplished by using
+the default values of \texttt{1} for the \emph{view diameter ratio} and
+the \emph{scan diameter ratio}. If values of less than \texttt{1} are
+used for these two variables, significant distortions will occur.
+
+\subsection{Divergent Geometries}\label{geometrydivergent}\index{Concepts,Scanner,Geometries,Divergent}
+\subsubsection{Overview}
+Next consider the case of equilinear (second generation) and equiangular
+(third, fourth, and fifth generation) geometries. In these cases,
+the x-ray beams diverge from a single source to a detector array.
+In the equilinear mode, a single
+source produces a fan beam which is read by a linear array of detectors. If
+the detectors occupy an arc of a circle, then the geometry is equiangular.
+See figure 2.2.
+\begin{figure}
+\image{10cm;0cm}{divergent.eps}
+\caption{Equilinear and equiangular geometries.}
+\end{figure}
+
+\subsubsection{Fan Beam Angle}
+For these divergent beam geometries, the \emph{fan beam angle} needs
+to be calculated. For real-world CT scanners, this is fixed at the
+time of manufacture. \ctsim, however, calculates the \emph{fan beam angle},
+\latexonly{$\alpha$,}\latexignore{\emph{alpha},}
+from the diameter of the \emph{scan diameter} and the \emph{focal length}
+\latexignore{\\$$\emph{alpha = 2 x asin ( (Sd / 2) / F)}$$\\}
+\latexonly{$$\alpha = 2 \sin^{-1} ((s_d / 2) / f)$$}
+This is illustrated in figure 2.3.
+\begin{figure}
+\image{10cm;0cm}{alphacalc.eps}
+\caption{Calculation of $\alpha$}
+\end{figure}
+
+Empiric testing with \ctsim\ shows that for very large \emph{fan beam angles},
+greater than approximately
+\latexonly{$120^{\circ}$,}\latexignore{120 degrees,}
+there are significant artifacts. The primary way to manage the
+\emph{fan beam angle} is by varying the \emph{focal length} since the
+\emph{scan diameter} by the size of the phantom.
+
+\subsubsection{Detector Array Size}
+In general, you do not need to be concerned with the detector array
+size. It is automatically calculated by \ctsim. The size of the
+detector array depends upon the \emph{focal length} and the
+\emph{scan diameter}. In general, increasing the \emph{focal length}
+decreases the size of the detector array and increasing the \emph{scan
+diameter} increases the detector array size.
+
+For equiangular geometry, the detectors are spaced around a
+circle covering an angular distance of
+\latexonly{$\alpha$.}\latexignore{\emph{alpha}.}
+The dotted circle in
+\begin{figure}
+\image{10cm;0cm}{equiangular.eps}
+\caption{Equiangluar geometry}
+\end{figure}
+figure 2.4 indicates the positions of the detectors in this case.
+
+For equilinear geometry, the detectors are space along a straight
+line. The length of the line depends upon
+\latexonly{$\alpha$}\latexignore{\emph{alpha}}
+and the \emph{focal length}. It is calculated as
+\latexonly{$$\mathrm{detLengh} = 4\,f \tan (\alpha / 2)$$}
+\latexignore{\\$$\emph{detLength} = 4 x F x tan(alpha/2)$$\\}
+\begin{figure}
+\image{10cm;0cm}{equilinear.eps}
+\caption{Equilinear geometry}
+\end{figure}
+An example of the this geometry is in figure 2.5.
+
+\subsubsection{Examples of Geometry Settings}
+Consider increasing the focal length ratio to two leaving the
+field of view ratio as 1, as in Figure 4. Now the detectors array is
+denser, and the real field of view is closer to that specified, but note
+again that the field of view is not used. Instead, the focal length is
+used to give a distance from the center of the phantom to the source, and
+the detector array is adjusted to give an angular coverage to include the
+whole phantom.
+
+