r495: no message

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

diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex
index 3c6aad14e7cab0310cc82d11f5bbb0d9f43a1801..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}


@@ -260,10 +254,16 @@ in a 16-CPU cluster with good results.
 
 \subsubsection{Filter projections}
 The projections for a single view have their frequency data multipled by
 
 \subsubsection{Filter projections}
 The projections for a single view have their frequency data multipled by

-a filter of absolute(w). \ctsim\ permits four different ways to accomplish this
+a filter of $|w|$. \ctsim\ permits four different ways to accomplish this

 filtering. Two of the methods use convolution of the projection data with the
 filtering. Two of the methods use convolution of the projection data with the

-inverse fourier transform of absolute(x). The other two methods perform an fourier
-transform of the projection data and multiply that by the absolute(x) filter and
+inverse fourier transform of $|w|$. The other two methods perform an fourier
+transform of the projection data and multiply that by the $|w|$ filter and

 then perform an inverse fourier transform.
 
 then perform an inverse fourier transform.
 

+Though multiplying by $|w|$ gives the sharpest reconstructions, in practice, superior results are obtained by mutiplying the $|w|$ filter by
+another filter that attenuates the higher frequencies. \ctsim\ has multiple
+filters for this purpose.
+

 \subsubsection{Backprojection of filtered projections}
 \subsubsection{Backprojection of filtered projections}

+Backprojection is the process of ``smearing'' the filtered projections over
+the reconstructing image.
\ No newline at end of file