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
\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.
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}
-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}
\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
-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.
+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}
+Backprojection is the process of ``smearing'' the filtered projections over
+the reconstructing image.
\ No newline at end of file
projects / ctsim.git / blobdiff