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<head><title>Fan Beam Angle</title></head>
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<H3>Fan Beam Angle</H3>
For these divergent beam geometries, the <EM>fan beam angle</EM>
needs to be calculated. For real-world CT scanners, this is fixed
at the time of manufacture. <TT>CTSim</TT>, however, calculates the
<EM>fan beam angle</EM>, alpha, from the <EM>scan diameter</EM> and
the <EM>focal length</EM> as
<CENTER><EM>alpha = 2 x asin (
(Sd / 2) / f)</EM></CENTER>
<CENTER><img src="alphacalc.gif"></CENTER>
<P>
Empiric testing with <TT>CTSim</TT> shows that for very large <EM>fan beam angles</EM>,
greater than approximately
120 degrees,
there are significant artifacts. The primary way to manage the
<EM>fan beam angle</EM> is by varying the <EM>focal length</EM> since the
<EM>scan diameter</EM> is usually fixed at the size of the phantom.<P>
To illustrate, the <EM>scan diameter</EM> can be defined as
<BR>
<CENTER><EM>Sd = Sr x Vr x Pd</EM></CENTER><BR>
<P>
Further, the <EM>focal length</EM> can be defined as
<BR>
<CENTER><EM>F = FR x (VR x Pd)<CENTER></CENTER><BR>
</EM></CENTER><P>
Substituting these equations into the above
equation, We have,
<BR>
<CENTER><EM>alpha = 2 sin (Sr / Fr)</EM></CENTER><BR>
<P>
Since in normal scanning s_r = 1, alpha depends only upon the
<EM>focal length ratio</EM> in normal scanning.<P>
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