From 54d83ac5be392640ae8d65f3398e445c61741aaf Mon Sep 17 00:00:00 2001 From: "Kevin M. Rosenberg" Date: Thu, 8 Feb 2001 16:19:42 +0000 Subject: [PATCH] r503: no message --- doc/ctsim-concepts.tex | 43 ++++++++++++++++++++++++----------------- doc/ctsim.hlp | Bin 57955 -> 58296 bytes doc/ctsim.tex | 2 +- doc/tex2rtf.ini | 4 +++- 4 files changed, 29 insertions(+), 20 deletions(-) diff --git a/doc/ctsim-concepts.tex b/doc/ctsim-concepts.tex index 32d60c8..e8de343 100644 --- a/doc/ctsim-concepts.tex +++ b/doc/ctsim-concepts.tex @@ -125,28 +125,28 @@ used to define the square that completely surrounds the phantom. Let \latexonly{$p_l$}\latexignore{\emph{Pl}} be the width and height of this square. The diameter of this boundary box, \latexonly{$p_d$,}\latexignore{\emph{Pd},} -is then +\rtfsp is then \latexignore{\\$$\emph{Pl x sqrt(2)}$$\\} \latexonly{$$p_d = p_l \sqrt{2}$$} CT scanners actually collect projections around a circle rather than a square. The diameter of this circle is also the diameter of the boundary square -\latexonly{$p_d$.}\latexignore{\emph{Pd}.} +\latexonly{$p_d$.}\latexignore{\rtfsp\emph{Pd}.} These relationships are diagrammed in figure 2.1. \subsubsection{View Diameter} The \emph{view diameter} is the area that is being processed during scanning of phantoms as well as during rasterization of phantoms. By default, the \emph{view diameter} -is set equal to the \emph{phantom diameter}. It may be useful, especially for +\rtfsp is set equal to the \emph{phantom diameter}. It may be useful, especially for experimental reasons, to process an area larger (and maybe even smaller) than the phantom. Thus, during rasterization or during projections, \ctsim\ will ask for a \emph{view ratio}, -\latexonly{$v_{R}$.}\latexignore{\emph{VR}.} +\latexonly{$v_r$.}\latexignore{\rtfsp \emph{VR}.} The \emph{view diameter} is then set as -\latexonly{$$v_d = p_d v_{R}$$}\latexignore{\\$$\emph{Vd = Pd x VR}$$} +\latexonly{$$v_d = p_d v_r$$}\latexignore{\\$$\emph{Vd = Pd x VR}$$} By using a -\latexonly{$v_{R}$}\latexignore{\emph{VR}} +\latexonly{$v_r$}\latexignore{\emph{VR}} less than 1, \ctsim\ will allow for a \emph{view diameter} less than \emph{phantom diameter}. @@ -158,11 +158,11 @@ scanner that is larger than the scanner itself! By default, the entire \emph{view diameter} is scanned. For experimental purposes, it may be desirable to scan an area either larger or smaller than the \emph{view diameter}. Thus, the concept of \emph{scan ratio} -\latexonly{$s_{R}$}\latexignore{\emph{SR}} +\latexonly{$s_r$}\latexignore{\emph{SR}} is born. The scan diameter \latexonly{$s_d$}\latexignore{\emph{Sd}} is the diameter over which x-rays are collected and is defined as -\latexonly{$$s_d = v_d s_{R}$$}\latexignore{\\$$\emph{Sd = Vd x SR}$$\\} +\latexonly{$$s_d = v_d s_r$$}\latexignore{\\$$\emph{Sd = Vd x SR}$$\\} By default and for all ordinary scanning, the \emph{scan ratio} is to \texttt{1}. If the \emph{scan ratio} is less than \texttt{1}, you can expect significant artifacts. @@ -172,10 +172,10 @@ The \emph{focal length}, \latexonly{$f$,}\latexignore{\emph{F},} is the distance of the X-ray source to the center of the phantom. The focal length is set as a ratio, -\latexonly{$f_{R}$,}\latexignore{\emph{FR},} +\latexonly{$f_r$,}\latexignore{\emph{FR},} of the view radius. Focal length is calculated as -\latexonly{$$f = (v_d / 2) f_R$$}\latexignore{\\$$\emph{F = (Vd / 2) x FR}$$} +\latexonly{$$f = (v_d / 2) f_r$$}\latexignore{\\$$\emph{F = (Vd / 2) x FR}$$} For parallel geometry scanning, the focal length doesn't matter. However, divergent geometry scanning (equilinear and equiangular), the \emph{focal @@ -213,10 +213,9 @@ See figure 2.2. For these divergent beam geometries, the \emph{fan beam angle} needs to be calculated. For real-world CT scanners, this is fixed at the time of manufacture. \ctsim, however, calculates the \emph{fan beam angle}, -\latexonly{$\alpha$,}\latexignore{\emph{alpha},} -from the diameter of the \emph{scan diameter} and the \emph{focal length} +$\alpha$ from the diameter of the \emph{scan diameter} and the \emph{focal length} \latexignore{\\$$\emph{alpha = 2 x asin ( (Sd / 2) / f)}$$\\} -\latexonly{$$\alpha = 2 \sin^{-1} ((s_d / 2) / f)$$} +\latexonly{\begin{equation}\label{alphacalc}\alpha = 2 \sin^{-1} ((s_d / 2) / f)\end{equation}} This is illustrated in figure 2.3. \begin{figure} \image{10cm;0cm}{alphacalc.eps} @@ -231,11 +230,19 @@ there are significant artifacts. The primary way to manage the \emph{fan beam angle} is by varying the \emph{focal length} since the \emph{scan diameter} by the size of the phantom. -$$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)$$ +To illustrate, the \emph{scan diameter} can be defined as +\latexonly{$$s_d = v_r s_r p_d$$}\latexignore{\\$$Sd = Vr x Sr x Pd$$\\} + +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 +\latexignore{the above equation,}\latexonly{equation~\ref{alphacalc},} +We have, +\latexonly{ +\begin{eqnarray} +\alpha &= 2\,\sin^{-1} \frac{p_d / 2}{f_r (p_d / 2)} \nonumber \\ +&= 2\,\sin^{-1} (1 / f_r) +\end{eqnarray} +} Thus, $\alpha$ depends only upon the \emph{focal length ratio}. diff --git a/doc/ctsim.hlp b/doc/ctsim.hlp index 4efe16970d9cb3f6005a6bc703ab072842e3ea45..299f5ee0d260c79b68ceb130dcb5aeb0643ed150 100644 GIT binary patch delta 31547 zcmYg2349Yp_ir}YOxm=~rdJ99vOOs+ZPKQkGER<{dNhX6DVCw>kT|V&7Ye zq|tK~;Ex8lf&ccM1*pU485@)8LUncrEb#fg^Cd@6aCtqYv0Zgi9ke^_Zb!4*4nfK3 zuzSi%q0}LHf|B0>F2BPqIlN6=(^LpJydH-HzM!ws?g@GmoBGFD{YLNvf&=}{GsGlY zpb|V1`1_Z6JuQ;IG&meuyzb`Pgfgqw>vy_5q50rg5;ZSSR$Jq0dIFZYnxe#7sVx{Q zazVAPE!f}D?0?^XFF2)Q2vz{KLZIAbcY7P0jV^mrFYw0#6)T`rTG;Hedm1V}##Rb$ zmq$-31(#c@SBP#Y(4dC%z?&s!Z>(Hj>Ww4yUVkMgG%NifS1S0uO%2j^?_7w5z?dj= zyUsd*&U3ncgoa_HeGS2mM9I?}fJt6|lilrFgra!s-q!KvK*+nQ-s}5N zXLnCtK*B99snuuqYYO@VY~lpH9L+){kgS0vE?SV_R=RR&!8c$?qrkX{Z1vi$-S zmX7cTGT|fN2SiQ$dxUCuG>&^T7$9z``gWba(L5$LUYGVW1f+(=qHA7*$5roY;;xZJ zYq3|zBJhPIMT<(G}oo6%h1J^-T>Z>PWZH z>IycdrNMyy*#q$3Ko~GQcVJ$Aem>03pJg(e^9!J$Am3atY)Fy1VAxO!LoJ1cTs{Yu z!u%pj5ey%0GL4)yYc>p=H9LQHXm;tKcs!nKT3Jp7s)-Px3T6U2Sg?_i5OgV7L0c z%^qjTBMBu?Q&v@F50*54AN1N4(4^p2D_mf0vAf*%y73`s0k6whXAekqf@E(hRY0BO zD6%)l3DS#-O0G@{yS=S-Qm|D3uJjg#zrA##tuE~KE~xVc8{Y;Jo7i6J_qGNkrN306 zaMm>kOP5?y1f;StRgPnd%7*!5qoU01YD{y)c-=h;n&@?V{l&kPk@CEfgji*04(AG- zjZseH+)~>aMUSOl;z_?pa$Zpc=fq!4pueZj5q@0i^|kw5zJ|u2W4n@9@}iT(m;(;K zHxS5s$hTSLPD|ITU1D8-IIm^qPEiT70sT|q3>g%cUnqBEKDgxE%(eor_ zl#l;5-pN}73(8%AUw1=$Km)&X6M@zWPR{wF!tHf9z0NIONAqn77t@{Idx2afE>F3) z)#C=Q-C6Fpw>nD{;Bhuf&UU3I1P#tMXM2U+ak+6B*C>6z zD(k6$q=AJma23BeXIrMc6)&~f_v!vc7)q{fSP#5;daU z?y0P-wbj=LTem9QnS8_N&HhrJ7bYYH1`irHNO4-ZTvzY%2SUO67*|^jKR&6_>y|Rw z>t}G@)?byClh;>&t~;Z=BD)T4F+ole7JXY}x-*6AF5CRP+{dQmD+=MY|o6Z^^5Uhd5>wI3TOLPVs z8|^Wuf0Dvap1`KNePgAl+jvjoi=5;i>#c2-K2$ZT%&x)l7G+iaJIeY3SAF4HSABWG z7fMgPm(LpWvFaAx5Lz{% z`Mu6J<_~er&XMEM9@+zg|t`6|DK~jqT$CQDK!3p() z|Hn^w2d*iU!eLjP&(knr(O{EaVHq+^ADH0sG`A^U=Q2_zcpL1Vi9(azzaUu`Y-~Di zZ=aGpQ!P24N?t|Pjb10NbxmI9bg9W3t=gt=6(~J0sl3b+k|gJ(Q(g~&AP15PmMgY- z0vie^HJ?}dD?rCXU~*-aAbCAk-R&(Z&xK?q?HT;@Ui;=D#70rW3hDVFXLLRN~{PB_o8K!c+vc{d0^eG&P1-WX=eFsj9MNE!Au*STGRMm@aQJV<@c;tIC^FAAaz zOZpdb&0FaR&hJ`uaB3*KI>wrjP@?P??M#d2+zKJD)$4aVTVGrG?&?qP^HlKPy>)$c z;E!r)SmsFe`~ef9yvm-c589Ov@d1BHV)btDMR)rf{9Xm02`b?c0c;ZkbDe>?{tr1$ zQkB+(6@g`n_UJ#iC~L~5YsFi8>jX#i{BgEGjWdv(Qxi%YUUS=3e*V}RI`7lu8sbh2 z{!kQMBMsq$yr2Swp#M%tgiAueLEP>dTchOjDaE`iX@RdBz0Gdty9pbC7v~;M&!R!n?luHg>yiw$=f+kfM7jJ)QAa>2#2Ta8n-#Hwx4EJ5 z`C4AYJysnfG!KJtlT_=i^)^k4Uvd!j+~;x>@M3LYk;*(IL9`^AE#n5qnuleJMT1o4 zp;HHogNB#~nazXJ%tQYOhWzKFUev3_i33fV*c=G9dV}pgsafzf`@C;QOH*t5R80Mh zdt0p#>YLq}vEct$9cUJkTIO2)Ep~S^PLqJS#qMcYsE+FuxFz3tHStJ{${Ls*(|*gC z%h3wqK=List$tDsC6j7rwAusH8l}2cPN;L{HW~Wov}T8Bt4h`QU1qCGiUrqd+B%K5 zYJ>ncZF2Oqs@k!Wr>>}-*;|O7HnDQrfP^La>8-7;ZPWAYu{vZteQsLR^tnEw6r1dA z)91D{b-6s#=e8z7s}?S`@t_rxpiL`KVQN%I+poRbS{?1}qL?!yOKi77I~6=maCDA~ zwuQP*11v6^JgK%~dM)UmWG}VTCr>P~!TJ^WQi%{)wj7_vPb;mhuBd?htK^sRlG+m3 z&#H`{#%e#xifxVlDrPQ$0Dr%EoKhP+5{GX!GiqupCPE#87S~R;Rh7YqI)HwQYilP& z2!G#&kh&%_RPL4^(3Uv8XZO8R6rooMz&=dC60Q}{g%8gn(HUsTvVTh_!ML--jSsDg zDGz(b2m+)Y5nou7m^Ss@1?Owy>(t9fKJn7Fx)m4Jm%HD%z2J2*vs@>=`RKq)%lE$& z81Ur0*moZ2bgAph>$5uQMKO)56W3EBaM zYMn)DZ8=hX`hIRh{KiLe=9|l3w;qdMJ8;>Xol~`z$){(p+ETV~YHN8#L3-`E6H7*# z%TA`8+PSTELH?W+MX|1z;n9LUcNXpsq!v2HOnB<4H_v$7IqRP|NV z?5%sqG{*#&D1Vfaaa2hr#{nrc@im=G6P_izI|~!DLg9Ewa0LTE$#U93NdZv4j6O

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