X-Git-Url: http://git.kpe.io/?a=blobdiff_plain;f=doc%2Fctsim-concepts.tex;h=32d60c83bd67b2f180637f1be1c3c09e93c9538b;hb=512a128ce9bc1d4a4477df791d2a1e63148752af;hp=f8c0da1d7eae57288758b15059be6bf1ad0facea;hpb=05c48981f4eacfe8a79f01a49cbddde10a94dda4;p=ctsim.git

diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex
index f8c0da1..32d60c8 100644
--- a/doc/ctsim-concepts.tex
+++ b/doc/ctsim-concepts.tex
@@ -215,7 +215,7 @@ to be calculated. For real-world CT scanners, this is fixed at the
 time of manufacture. \ctsim, however, calculates the \emph{fan beam angle},
 \latexonly{$\alpha$,}\latexignore{\emph{alpha},} 
 from the diameter of the \emph{scan diameter} and the \emph{focal length}
-\latexignore{\\$$\emph{alpha = 2 x asin ( (Sd / 2) / F)}$$\\}
+\latexignore{\\$$\emph{alpha = 2 x asin ( (Sd / 2) / f)}$$\\}
 \latexonly{$$\alpha = 2 \sin^{-1} ((s_d / 2) / f)$$}
 This is illustrated in figure 2.3.
 \begin{figure}
@@ -231,6 +231,14 @@ there are significant artifacts. The primary way to manage the
 \emph{fan beam angle} is by varying the \emph{focal length} since the
 \emph{scan diameter} by the size of the phantom.
 
+$$s_d = p_d v_R s_R$$
+If $v_r = 1$ and $s_R = 1$, then $s_d = p_d$. Further, $f = f_R v_R (p_d / 2)$
+Plugging these equations into the above equation,
+$$\alpha = 2\,\sin^{-1} \frac{p_d / 2}{f_R (p_d / 2)}$$
+$$\alpha = 2\,\sin^{-1} (1 / f_R)$$
+
+Thus, $\alpha$ depends only upon the \emph{focal length ratio}.
+
 \subsubsection{Detector Array Size}
 In general, you do not need to be concerned with the detector array
 size. It is automatically calculated by \ctsim.  The size of the