-
-In figure 1A, the excursion of the source and detector need only be $l_p$,
-the height (or width) of the phantom's bounding square. However, if the
-field of view were only $l_p$, then the projection shown in figure 1B
-would clip the corners of the phantom. By increasing the field of view by
-$\sqrt{2}$ the whole phantom is included in every projection. Of course,
-if the field-of-view ratio $f_{vR}$ is larger than 1, there is no problem.
-However, if $f_{vR}$ is less than one and thus the scanner is smaller than
-the phantom, then distortions will occur without warning from the program.
-
-The code also sets the detector length equal to the field of view in this
-case. The focal length is chosen to be $\sqrt{2}l_p$ so the phantom will
-fit between the source and detector at all rotation angles, when the focal
-length ratio is specified as 1. Again, what happens if the focal length
-ratio is chosen less than 1?
-
-The other thing to note is that in this code the detector array is set to
-be the same size as the field-of-view $f_v$, equation (2). So, one has to
-know the size of the phantom to specify a given scanner geometry with a
-given source-detector distance (or $f_l$ here) and a given range of
-excursion ($f_v$ here).
-
-\subsubsection{Divergent Geometries}\label{geometrydivergent}\index{Concepts,Scanner,Geometries,Divergent}
-Next consider the case of equilinear (second generation) and equiangular
-(third, fourth, and fifth generation) geometries.
-The parts of the code relevant to this
-discussion are the same for both modes. In the equilinear mode, a single
+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}$$}
+
+By using a
+\latexonly{$v_r$}\latexignore{\emph{VR}}
+less than 1, \ctsim\ will allow
+for a \emph{view diameter} less than
+\emph{phantom diameter}.
+This will lead to significant artifacts. Physically, this would
+be impossible and is analagous to inserting an object into the CT
+scanner that is larger than the scanner itself!
+
+\subsubsection{Scan Diameter}
+By default, the entire \emph{view diameter} is scanned. For
+experimental purposes, it may be desirable to scan an area either
+larger or smaller than the \emph{view diameter}. Thus, the concept
+of \emph{scan ratio}, \latexonly{$s_r$,}\latexignore{\emph{SR},}
+is born. The scan diameter
+\latexonly{$s_d$}\latexignore{\emph{Sd}} is the diameter over
+which x-rays are collected and is defined as \latexonly{$$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. Moreover, a value of less than \texttt{1},
+though it can be given to \ctsim, is physically impossible and it
+analagous to have having the x-ray source with 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
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