r495: no message

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

diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex
index 93e1d4506fdf351c9ebc08cdd8c80fa2b53d57a0..368c5e5334c94193bf922efe9b971bc3a4ed1c68 100644 (file)
--- a/doc/ctsim-concepts.tex
+++ b/doc/ctsim-concepts.tex
@@ -68,7 +68,7 @@ applied about the origin.
 It appears that dx and dy
 define the end points of a radius of the sector, from which the radius and
 the angle of the two arms of the sector are calculated.  But then
 It appears that dx and dy
 define the end points of a radius of the sector, from which the radius and
 the angle of the two arms of the sector are calculated.  But then

-orientation and centreing of the sector don't make much sense yet.
+orientation and centering of the sector don't make much sense yet.

 
 \subsubsection{segment}
 Segments are the segments of a circle between a chord and the
 
 \subsubsection{segment}
 Segments are the segments of a circle between a chord and the


@@ -79,7 +79,8 @@ translated and then rotated (???).
 
 \subsection{Phantom Size}
 Also note that the overall dimensions of the phantom are increased by 1\%
 
 \subsection{Phantom Size}
 Also note that the overall dimensions of the phantom are increased by 1\%

-above the specified sizes to avoid clipping due to round-off errors.  If the phantom is defined as
+above the specified sizes to avoid clipping due to round-off errors.  
+So, if the phantom is defined as

 a rectangle of size 0.1 by 0.1, the actual phantom has extent $\pm$0.101 in
 each direction.
 
 a rectangle of size 0.1 by 0.1, the actual phantom has extent $\pm$0.101 in
 each direction.
 


@@ -106,27 +107,20 @@ all dimensions are determined in terms of the phantom size, which is used
 as the standard length scale.     Remember, as mentioned above, the
 phantom dimensions are also padded by 1\%.
 
 as the standard length scale.     Remember, as mentioned above, the
 phantom dimensions are also padded by 1\%.
 

-The maximum of the phantom length and height is used as the phantom
-dimension, and one can think of a square bounding box of this size
-which completely contains the phantom.  Let $l_p$ be the width (or height)
-of this square.
+The maximum of the phantom length and height is used to define the square
+that completely surrounds the phantom. Let $p_l$ be the width (also height)
+of this square. The diameter of this boundary box, $p_d$ is then
+\latexonly{\begin{equation}p_d = \sqrt{2} (p_l/2)\end{equation}}
+\latexignore{sqrt(2) * $p_l$.}
+This relationship can be seen in figure 1.

 
 \subsubsection{Focal Length \& Field of View}
 
 \subsubsection{Focal Length \& Field of View}

-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
-\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}}
-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
-\latexonly{$\sqrt(2)$}
-\latexignore{sqrt(2)}
-can be understood if one refers to figure 1, where
+The two important variables is the focal-length-ratio $f_lr$.
+This is used along with $p_d$ to
+define the focal length according to
+\latexonly{\begin{equation}f_l = f_lr p_d\end{equation}}
+\latexignore{$f_l$ = $f_lr$ x $p_d$\\}
+where

 we consider the case of a first generation parallel beam CT scanner.
 
 \subsubsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel}
 we consider the case of a first generation parallel beam CT scanner.
 
 \subsubsection{Parallel Geometry}\label{geometryparallel}\index{Concepts,Scanner,Geometries,Parallel}