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<head><title>Dimensions</title></head>
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<A HREF="ctsim_contents.html">Contents</A> <A HREF="ctsim15.html#conceptscanner">Up</A> <A HREF="ctsim15.html#conceptscanner"><<</A> <A HREF="ctsim17.html#topic11">>></A> </CENTER><HR>
<H3>Dimensions</H3>
The geometry for a scan starts with the size of
the phantom being scanned. This is because <TT>CTSim</TT> allows for
statistical comparisons between the original phantom image and
it's reconstructions. Since CT scanners scan a circular area, the
first important variable is the diameter of the circle surround
the phantom, the <EM>phantom diameter</EM>. Remember, as mentioned
above, the phantom dimensions are padded by 1%.<P>
The other important geometry variables for scanning phantoms are
the <EM>view diameter</EM>, <EM>scan diameter</EM>, <EM>focal
length</EM>, and <EM>center-detector length</EM>. These variables are input into <TT>CTSim</TT> in terms of
ratios rather than absolute values.<P>
<A HREF="ctsim17.html#topic11"><B>Phantom Diameter</B></A><BR>
The phantom diameter is automatically calculated by <TT>CTSim</TT> from
the phantom definition. The maximum of the phantom length and
height is used to define the square that completely surrounds the
phantom. Let <EM>Pl</EM> be the width
and height of this square. The diameter of this boundary box,
<EM>Pd</EM>, is given by the
Pythagorean theorem and is
<BR>
<CENTER><EM>Pl x sqrt(2)</EM></CENTER><BR>
CT scanners collect projections around a
circle rather than a square. The diameter of this circle is
the diameter of the boundary square
<EM>Pd</EM>.
<CENTER><img src="scangeometry.gif"></CENTER>
<P>
<A HREF="ctsim18.html#topic12"><B>View Diameter</B></A><BR>
The <EM>view diameter</EM> is the area that is being processed
during scanning of phantoms as well as during rasterization of
phantoms. By default, the <EM>view diameter</EM> is set equal
to the <EM>phantom diameter</EM>. 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, <TT>CTSim</TT> will ask for a <EM>view ratio</EM>,
<EM>VR</EM>. The <EM>view
diameter</EM> is then calculated as
<BR>
<CENTER><EM>Vd = Pd x VR</EM></CENTER><BR>
<P>
By using a
<EM>VR</EM>
less than 1, <TT>CTSim</TT> will allow
for a <EM>view diameter</EM> less than
<EM>phantom diameter</EM>.
This will lead to significant artifacts. Physically, this would
be impossible and is analogous to inserting an object into the CT
scanner that is larger than the scanner itself!<P>
<A HREF="ctsim19.html#topic13"><B>Scan Diameter</B></A><BR>
By default, the entire <EM>view diameter</EM> is scanned. For
experimental purposes, it may be desirable to scan an area either
larger or smaller than the <EM>view diameter</EM>. Thus, the concept
of <EM>scan ratio</EM>, <EM>SR</EM>,
arises. The scan diameter,
<EM>Sd</EM>, is the diameter over
which x-rays are collected and is defined as
<BR>
<CENTER><EM>Sd = Vd x SR</EM></CENTER><BR>
By default and
for all ordinary scanning, the <EM>scan ratio</EM> is to <TT>1</TT>.
If the <EM>scan ratio</EM> is less than <TT>1</TT>, you can expect
significant artifacts.<P>
<A HREF="ctsim20.html#topic14"><B>Focal Length</B></A><BR>
The <EM>focal length</EM>,
<EM>F</EM>,
is the distance of the X-ray source to the center of
the phantom. The focal length is set as a ratio,
<EM>FR</EM>,
of the view radius. Focal length is
calculated as
<BR>
<CENTER><EM>F = (Vd / 2) x FR</EM></CENTER><P>
For parallel geometry scanning, the focal length doesn't matter.
However, for divergent geometry scanning (equilinear and equiangular),
the <EM>focal length ratio</EM> should be set at <TT>2</TT> or more
to avoid artifacts. Moreover, a value of less than <TT>1</TT> is
physically impossible and it analagous to having the x-ray
source inside of the <EM>view diameter</EM>.<P>
<A HREF="ctsim21.html#topic15"><B>Center-Detector Length</B></A><BR>
The <EM>center-detector length</EM>,
<EM>C</EM>,
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,
<EM>CR</EM>,
of the view radius. The center-detector length is
calculated as
<BR>
<CENTER><EM>F = (Vd / 2) x CR</EM></CENTER><P>
For parallel geometry scanning, the center-detector length doesn't matter.
A value of less than <TT>1</TT> is physically impossible and it analagous to
having the detector array inside of the <EM>view diameter</EM>.<P>
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