r591: Added Center-Detector length to scanning and reconstruction

[ctsim.git] / doc / ctsim-concepts.tex

diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex
index 1b53d60671da122a033dee3f618b4582452542c2..86a94bccae69761ea5e5370600f1e50940b85da3 100644 (file)
--- a/doc/ctsim-concepts.tex
+++ b/doc/ctsim-concepts.tex
@@ -116,8 +116,8 @@ the phantom, the \emph{phantom diameter}. Remember, as mentioned
 above, the phantom dimensions are padded by 1\%.
 
 The other important geometry variables for scanning phantoms are
 above, the phantom dimensions are 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 input into \ctsim\ in terms of
+the \emph{view diameter}, \emph{scan diameter}, \emph{focal
+length}, and \emph{center-detector length}. These variables are input into \ctsim\ in terms of

 ratios rather than absolute values.
 
 \subsubsection{Phantom Diameter}\index{Phantom!Diameter}
 ratios rather than absolute values.
 
 \subsubsection{Phantom Diameter}\index{Phantom!Diameter}


@@ -192,9 +192,24 @@ For parallel geometry scanning, the focal length doesn't matter.
 However, for 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
 However, for 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
+physically impossible and it analagous to having the x-ray

 source inside of the \emph{view diameter}.
 
 source inside of the \emph{view diameter}.
 

+\subsubsection{Center-Detector Length}\index{Center-Detector length}
+The \emph{center-detector length},
+\latexonly{$c$,}\latexignore{\emph{C},}
+is the distance from the center of
+the phantom to the center of the detector array. The center-detector length is set as a ratio,
+\latexonly{$c_r$,}\latexignore{\emph{CR},}
+of the view radius. The center-detector length is
+calculated as
+\latexonly{\begin{equation}f = (v_d / 2) c_r\end{equation}}
+\latexignore{\\\centerline{\emph{F = (Vd / 2) x CR}}}
+
+For parallel geometry scanning, the center-detector length doesn't matter.
+A value of less than \texttt{1} is physically impossible and it analagous to
+having the detector array inside of the \emph{view diameter}.
+

 
 \subsection{Parallel Geometry}\label{geometryparallel}\index{Parallel geometry}\index{Scanner!Parallel}
 
 
 \subsection{Parallel Geometry}\label{geometryparallel}\index{Parallel geometry}\index{Scanner!Parallel}
 


@@ -282,8 +297,10 @@ depends upon the \emph{focal length}: increasing the \emph{focal
 length} decreases the size of the detector array.
 
 For equiangular geometry, the detectors are equally spaced around a arc
 length} decreases the size of the detector array.
 
 For equiangular geometry, the detectors are equally spaced around a arc

-covering an angular distance of
-\latexonly{$2\,\alpha$.}\latexignore{\emph{2 \alpha}.}
+covering an angular distance of $\alpha$ as viewed from the source. When
+viewed from the center of the scanning, the angular distance is
+\latexonly{$$\pi + \alpha - 2 \, \cos^{-1} \Big( \frac{s_d / 2}{c} \Big)$$}
+\latexignore{\\\emph{pi + \alpha - 2 x acos ((Sd / 2) / C))}\\}

 The dotted circle
 \latexonly{in figure~\ref{equiangularfig}}
 indicates the positions of the detectors in this case.
 The dotted circle
 \latexonly{in figure~\ref{equiangularfig}}
 indicates the positions of the detectors in this case.


@@ -298,8 +315,8 @@ line. The detector length depends upon
 \latexonly{$\alpha$}\latexignore{\emph{alpha}} and the \emph{focal
 length}. This length,
 \latexonly{$d_l$,}\latexignore{Dl,} is calculated as
 \latexonly{$\alpha$}\latexignore{\emph{alpha}} and the \emph{focal
 length}. This length,
 \latexonly{$d_l$,}\latexignore{Dl,} is calculated as

-\latexonly{\begin{equation} d_l = 4\,f \tan (\alpha / 2)\end{equation}}
-\latexignore{\\\centerline{\emph{4 x F x tan(\alpha/2)}}}
+\latexonly{\begin{equation} d_l = 2\,(f + c) \tan (\alpha / 2)\end{equation}}
+\latexignore{\\\centerline{\emph{2 x (F + C) x tan(\alpha/2)}}}

 \latexonly{This geometry is shown in figure~\ref{equilinearfig}.}
 \begin{figure}
 \centerline{\image{10cm;0cm}{equilinear.eps}}
 \latexonly{This geometry is shown in figure~\ref{equilinearfig}.}
 \begin{figure}
 \centerline{\image{10cm;0cm}{equilinear.eps}}


@@ -316,7 +333,7 @@ accurate as filtered backprojection. This is due primarily
 to interpolation occurring in the frequency domain rather than the
 spatial domain.
 
 to interpolation occurring in the frequency domain rather than the
 spatial domain.
 

-\subsection{Filtered Backprojection}\index{Filtered backprojection}
+\subsection{Filtered Backprojection}\index{Filtered backprojection}\index{Symmetric multiprocessing}\index{SMP}

 The technique is comprised of two sequential steps:
 filtering projections followed by backprojecting the filtered projections. Though
 these two steps are sequential, each view position can be processed independently.
 The technique is comprised of two sequential steps:
 filtering projections followed by backprojecting the filtered projections. Though
 these two steps are sequential, each view position can be processed independently.


@@ -324,9 +341,18 @@ these two steps are sequential, each view position can be processed independentl
 \subsubsection{Parallel Computer Processing}\index{Parallel processing}
 Since each view can be processed independently, filtered backprojection is amendable to
 parallel processing. Indeed, this has been used in commercial scanners to speed reconstruction.
 \subsubsection{Parallel Computer Processing}\index{Parallel processing}
 Since each view can be processed independently, filtered backprojection is amendable to
 parallel processing. Indeed, this has been used in commercial scanners to speed reconstruction.

-This parallelism is exploited in the MPI versions of \ctsim\ where the
-data from all the views are spread about amongst all of the
-processors. This has been testing in a cluster of 16 computers with excellent
+This parallelism is exploited both in the \ctsim\ graphical shell and
+in the \helpref{LAM}{ctsimtextlam} version of \ctsimtext. \ctsim\ can distribute it's workload
+amongst multiple processors working in parallel.
+
+The graphical shell will automatically take advantage of multiple CPU's when
+running on a \emph{Symmetric Multiprocessing}
+computer. Dual-CPU computers are commonly available which provide a near doubling
+in reconstruction speeds. \ctsim, though, has no limits on the number of CPU's
+that can be used in parallel. The \emph{LAM} version
+of \ctsimtext\ is designed to work in a cluster of computers.
+This has been testing with a cluster of 16 computers in a
+\urlref{Beowulf-class}{http://www.beowulf.org} cluster with excellent

 results.
 
 \subsubsection{Filter projections}
 results.
 
 \subsubsection{Filter projections}