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authorEugeniy Mikhailov <evgmik@gmail.com>2011-11-03 11:44:14 -0400
committerEugeniy Mikhailov <evgmik@gmail.com>2011-11-03 11:45:30 -0400
commit8a38fa851ce826a9be05b50838bc1472cb94f434 (patch)
treec524cceb703031772139e1f35acbe6bf0ac523cb /xmds2
parent2f6cfe4a53d69a44ab2594385f634c3f18347f57 (diff)
downloadNresonances-8a38fa851ce826a9be05b50838bc1472cb94f434.tar.gz
Nresonances-8a38fa851ce826a9be05b50838bc1472cb94f434.zip
Draft of report on perturbative approach
Diffstat (limited to 'xmds2')
-rw-r--r--xmds2/reports/4wm_with_perturbation_and_exact_analusis/4wm_with_perturbation_and_exact_analusis.tex120
-rw-r--r--xmds2/reports/4wm_with_perturbation_and_exact_analusis/Makefile34
-rw-r--r--xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/Makefile25
-rw-r--r--xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/fields_after_the_cell.eps9507
-rw-r--r--xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/Makefile25
-rw-r--r--xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/fields_after_the_cell.eps9487
6 files changed, 19198 insertions, 0 deletions
diff --git a/xmds2/reports/4wm_with_perturbation_and_exact_analusis/4wm_with_perturbation_and_exact_analusis.tex b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/4wm_with_perturbation_and_exact_analusis.tex
new file mode 100644
index 0000000..cb537a8
--- /dev/null
+++ b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/4wm_with_perturbation_and_exact_analusis.tex
@@ -0,0 +1,120 @@
+% -*- latex -*-
+\documentclass[aps,pra,twocolumn,groupedaddress,amsmath,amssymb]{revtex4}
+\usepackage{graphicx}
+\usepackage[normalem]{ulem} % needed by strike
+\usepackage[urlcolor=blue,colorlinks=true]{hyperref}
+
+\begin{document}
+\title{N-level system: four wave mixing with exact and perturbative
+approach}
+\author{E. E. Mikhailov}
+\date{2011/11/03}
+\maketitle
+%\clearpage
+
+We consider the following system
+
+\begin{verbatim}
+ -------- |4>
+ \
+ \ E3 -------- |3>
+ \ / \
+ \ E2 / \
+ \ / \ E1
+ ------- |2> \
+ \
+ ------- |1>
+\end{verbatim}
+
+Such system can exhibit slow and fast light behavior for the cases when
+field 2 connecting $|$2$>$-$|$3$>$$|$is weak and treated as a probe field, field 1
+is strong and field 3 serve as a switch toggling slow (field 3 is off),
+fast (field 3 is on and strong) light, and situations in between.
+
+Below the examples of fast and slow propagation for the following set of parameters:
+
+\begin{verbatim}
+G3=3.4e7 // decay rate of level |3> in 1/s
+G4=3.8e7 // decay rate of level |4> in 1/s
+gt=3.1416e+04 // repopulation rate in 1/s
+z=1.5e-2 // cell length in m
+N=1e10*(1e6); // number of particles per cubic m
+delta1=0; // field 1 one photon detuning
+delta2=0; // field 2 --------//---------
+delta3=0; // field 3 --------//---------
+\end{verbatim}
+
+\begin{figure}[h]
+ \begin{center}
+ \includegraphics[width=1.00\columnwidth]{slow_light/fields_propagation.pdf}
+ \end{center}
+ \caption{Propagation of the fields under slow light condition}
+ \label{fig:3fields_slow}
+\end{figure}
+
+Slow light behavior is observed for the 1 $\backslash$mu S long Gaussian pulse and
+the following fields parameters
+\begin{verbatim}
+E1=7.5e7; // field 1 Rabi frequency in 1/s
+E2=1; // field 2 --------//-----------
+E3=0; // field 3 --------//-----------
+\end{verbatim}
+fields 1 and 3 have no time dependence at the input of the cell.
+
+Propagation of all 3 fields is depicted at Fig.\ref{fig:3fields_slow}
+and output beam fields profiles in comparison with input are shown at
+Fig.\ref{fig:3fields_in_out_slow}
+where it easy to see delayed pulse for the field 2 in the middle.
+
+\begin{figure}[h]
+ \begin{center}
+ \includegraphics[width=1.00\columnwidth]{slow_light/fields_before_after_cell.pdf}
+ \end{center}
+ \caption{Propagation of the fields under slow light condition}
+ \label{fig:3fields_in_out_slow}
+\end{figure}
+
+
+Fast light or negative group delay is observed for the similar conditions
+but with field 3 switched on
+\begin{verbatim}
+E1=7.5e7; // field 1 Rabi frequency in 1/s
+E2=1; // field 2 --------//-----------
+E3=1.5e8; // field 3 --------//-----------
+\end{verbatim}
+
+Propagation of all 3 fields is depicted at Fig.\ref{fig:3fields_fast}
+and output beam fields profiles in comparison with input are shown at
+Fig.\ref{fig:3fields_in_out_fast}.
+
+\begin{figure}[h]
+ \begin{center}
+ \includegraphics[width=1.00\columnwidth]{fast_light/fields_propagation.pdf}
+ \end{center}
+ \caption{Propagation of the fields under fast light condition}
+ \label{fig:3fields_fast}
+\end{figure}
+
+\begin{figure}[h]
+ \begin{center}
+ \includegraphics[width=1.00\columnwidth]{fast_light/fields_before_after_cell.pdf}
+ \end{center}
+ \caption{Propagation of the fields under fast light condition}
+ \label{fig:3fields_in_out_fast}
+\end{figure}
+
+The advancement of the pulse is very small but it could be seen on zoomed
+in Fig.\ref{fig:field2_in_out_fast}.
+
+\begin{figure}[h]
+ \begin{center}
+ \includegraphics[width=1.00\columnwidth]{fast_light/probe_before_after_cell.pdf}
+ \end{center}
+ \caption{Propagation of the fields under fast light condition}
+ \label{fig:field2_in_out_fast}
+\end{figure}
+
+% LaTeX2e code generated by txt2tags 2.5 (http://txt2tags.sf.net)
+% cmdline: txt2tags --target=tex report.t2t
+\end{document}
+
diff --git a/xmds2/reports/4wm_with_perturbation_and_exact_analusis/Makefile b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/Makefile
new file mode 100644
index 0000000..a1d036c
--- /dev/null
+++ b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/Makefile
@@ -0,0 +1,34 @@
+# -*- make -*-
+# FILE: "/home/evmik/src/my_src/Nresonances/xmds2/Nlevels_no_dopler_with_z_fast_and_slow_light/report/Makefile"
+# LAST MODIFICATION: "Wed, 28 Sep 2011 17:35:55 -0400 (evmik)"
+# (C) 2007 by Eugeniy Mikhailov, <evgmik@gmail.com>
+# $Id:$
+
+make = make
+
+includes =
+tex_targets = $(wildcard *.tex)
+pdf_targets = $(tex_targets:%.tex=%.pdf)
+
+dest_dir = ./
+
+all: pdf
+ make clean
+
+
+pdf: $(pdf_targets)
+
+$(pdf_targets): %.pdf : %.tex $(includes)
+ rubber --pdf $<
+
+
+clean_latex_tmp:
+ rm -f *.aux
+ rm -f *.log
+ rm -f *.out
+
+clean: clean_latex_tmp
+
+
+real_clean: clean
+ rm -f $(pdf_targets)
diff --git a/xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/Makefile b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/Makefile
new file mode 100644
index 0000000..26b1451
--- /dev/null
+++ b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/Makefile
@@ -0,0 +1,25 @@
+# -*- make -*-
+
+
+eps_targets = $(wildcard *.eps)
+pdf_targets = $(eps_targets:%.eps=%.pdf)
+png_targets = $(eps_targets:%.eps=%.png)
+
+default: pdf
+pdf: $(pdf_targets)
+png: $(png_targets)
+
+
+$(pdf_targets): %.pdf : %.eps
+ epspdf $< $@
+
+$(png_targets): %.png : %.eps
+ convert $< $@
+
+clean:
+
+
+real_clean: clean
+ rm -f $(pdf_targets)
+ rm -f $(png_targets)
+
diff --git a/xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/fields_after_the_cell.eps b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/fields_after_the_cell.eps
new file mode 100644
index 0000000..37d7a96
--- /dev/null
+++ b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/fast_light_compared/fields_after_the_cell.eps
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+>> matrix makepattern
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+<< Tile8x8
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+>> matrix makepattern
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+} def
+%
+%
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+%
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+} def
+%
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+%
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+/Pattern4 {0.125 Density} bind def
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+/Pattern6 {0.625 Density} bind def
+/Pattern7 {0.875 Density} bind def
+} def
+%
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+ {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt}
+ {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv}
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+ {/dgdxval dgdx def redvalue greenvalue bluevalue} ifelse} def
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+ }{
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diff --git a/xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/Makefile b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/Makefile
new file mode 100644
index 0000000..26b1451
--- /dev/null
+++ b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/Makefile
@@ -0,0 +1,25 @@
+# -*- make -*-
+
+
+eps_targets = $(wildcard *.eps)
+pdf_targets = $(eps_targets:%.eps=%.pdf)
+png_targets = $(eps_targets:%.eps=%.png)
+
+default: pdf
+pdf: $(pdf_targets)
+png: $(png_targets)
+
+
+$(pdf_targets): %.pdf : %.eps
+ epspdf $< $@
+
+$(png_targets): %.png : %.eps
+ convert $< $@
+
+clean:
+
+
+real_clean: clean
+ rm -f $(pdf_targets)
+ rm -f $(png_targets)
+
diff --git a/xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/fields_after_the_cell.eps b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/fields_after_the_cell.eps
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index 0000000..e77052b
--- /dev/null
+++ b/xmds2/reports/4wm_with_perturbation_and_exact_analusis/slow_light_compared/fields_after_the_cell.eps
@@ -0,0 +1,9487 @@
+%!PS-Adobe-2.0 EPSF-2.0
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+ /Title (fields_after_the_cell.eps)
+ /Subject (gnuplot plot)
+ /Creator (gnuplot 4.4 patchlevel 0)
+ /Author (evmik)
+% /Producer (gnuplot)
+% /Keywords ()
+ /CreationDate (Thu Nov 3 11:31:37 2011)
+ /DOCINFO pdfmark
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+/hpt2 hpt 2 mul def
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+ Blacktext {gsave 0 setgray show grestore} {show} ifelse} def
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+ Blacktext {gsave 0 setgray show grestore} {show} ifelse} def
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+ Blacktext {gsave 0 setgray show grestore} {show} ifelse} def
+/UP {dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
+ /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def} def
+/DL {Color {setrgbcolor Solid {pop []} if 0 setdash}
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+ Rounded {1 setlinejoin 1 setlinecap} if} def
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+ Rounded {1 setlinejoin 1 setlinecap} if} def
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+ dup 1 lt {pop 1} if 10 mul /udl exch def} def
+/PL {stroke userlinewidth setlinewidth
+ Rounded {1 setlinejoin 1 setlinecap} if} def
+% Default Line colors
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+/LC7 {1 0.3 0} def
+/LC8 {0.5 0.5 0.5} def
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+ hpt vpt V hpt neg vpt V closepath stroke
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+ currentpoint stroke M
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+ } def
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+ hpt2 neg 0 V closepath stroke
+ Pnt} def
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+ hpt2 vpt2 neg V currentpoint stroke M
+ hpt2 neg 0 R hpt2 vpt2 V stroke} def
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+ hpt 2 mul 0 V
+ hpt neg vpt 1.62 mul V closepath stroke
+ Pnt} def
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+ closepath stroke grestore Pnt} def
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+ 2 copy vpt 180 270 arc closepath fill
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+ 2 copy vpt 0 90 arc
+ 2 copy moveto
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+ 2 copy vpt 270 450 arc closepath fill
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+ 2 copy moveto
+ 2 copy vpt 90 180 arc closepath fill
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+ 2 copy vpt 0 180 arc closepath fill
+ 2 copy moveto
+ 2 copy vpt 270 360 arc closepath fill
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+ 2 copy vpt 180 360 arc closepath fill
+ vpt 0 360 arc closepath} bind def
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+ 2 copy vpt 0 90 arc closepath fill
+ 2 copy moveto
+ 2 copy vpt 180 360 arc closepath fill
+ vpt 0 360 arc closepath} bind def
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+ 2 copy vpt 90 360 arc closepath fill
+ vpt 0 360 arc} bind def
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+ vpt 0 360 arc closepath} bind def
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+ Bsquare} bind def
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+ Bsquare} bind def
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+ 2 copy vpt Square fill Bsquare} bind def
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+ 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
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+ closepath stroke grestore} def
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+/Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def
+/DiaW {stroke [] 0 setdash vpt add M
+ hpt neg vpt neg V hpt vpt neg V
+ hpt vpt V hpt neg vpt V Opaque stroke} def
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+/PentW {stroke [] 0 setdash gsave
+ translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
+ Opaque stroke grestore} def
+/CircW {stroke [] 0 setdash
+ hpt 0 360 arc Opaque stroke} def
+/BoxFill {gsave Rec 1 setgray fill grestore} def
+/Density {
+ /Fillden exch def
+ currentrgbcolor
+ /ColB exch def /ColG exch def /ColR exch def
+ /ColR ColR Fillden mul Fillden sub 1 add def
+ /ColG ColG Fillden mul Fillden sub 1 add def
+ /ColB ColB Fillden mul Fillden sub 1 add def
+ ColR ColG ColB setrgbcolor} def
+/BoxColFill {gsave Rec PolyFill} def
+/PolyFill {gsave Density fill grestore grestore} def
+/h {rlineto rlineto rlineto gsave closepath fill grestore} bind def
+%
+% PostScript Level 1 Pattern Fill routine for rectangles
+% Usage: x y w h s a XX PatternFill
+% x,y = lower left corner of box to be filled
+% w,h = width and height of box
+% a = angle in degrees between lines and x-axis
+% XX = 0/1 for no/yes cross-hatch
+%
+/PatternFill {gsave /PFa [ 9 2 roll ] def
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+ currentlinewidth 0.5 mul setlinewidth
+ /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def
+ 0 0 M PFa 5 get rotate PFs -2 div dup translate
+ 0 1 PFs PFa 4 get div 1 add floor cvi
+ {PFa 4 get mul 0 M 0 PFs V} for
+ 0 PFa 6 get ne {
+ 0 1 PFs PFa 4 get div 1 add floor cvi
+ {PFa 4 get mul 0 2 1 roll M PFs 0 V} for
+ } if
+ stroke grestore} def
+%
+/languagelevel where
+ {pop languagelevel} {1} ifelse
+ 2 lt
+ {/InterpretLevel1 true def}
+ {/InterpretLevel1 Level1 def}
+ ifelse
+%
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+%
+/Level2PatternFill {
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+ bind def
+/KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def
+<< Tile8x8
+ /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke}
+>> matrix makepattern
+/Pat1 exch def
+<< Tile8x8
+ /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke
+ 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke}
+>> matrix makepattern
+/Pat2 exch def
+<< Tile8x8
+ /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L
+ 8 8 L 8 0 L 0 0 L fill}
+>> matrix makepattern
+/Pat3 exch def
+<< Tile8x8
+ /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L
+ 0 12 M 12 0 L stroke}
+>> matrix makepattern
+/Pat4 exch def
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+ /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L
+ 0 -4 M 12 8 L stroke}
+>> matrix makepattern
+/Pat5 exch def
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+ /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L
+ 0 12 M 8 -4 L 4 12 M 10 0 L stroke}
+>> matrix makepattern
+/Pat6 exch def
+<< Tile8x8
+ /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L
+ 0 -4 M 8 12 L 4 -4 M 10 8 L stroke}
+>> matrix makepattern
+/Pat7 exch def
+<< Tile8x8
+ /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L
+ 12 0 M -4 8 L 12 4 M 0 10 L stroke}
+>> matrix makepattern
+/Pat8 exch def
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+ /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L
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+/Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def
+} def
+%
+%
+%End of PostScript Level 2 code
+%
+/PatternBgnd {
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+} def
+%
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+%
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+/Pattern3 {0.750 Density} bind def
+/Pattern4 {0.125 Density} bind def
+/Pattern5 {0.375 Density} bind def
+/Pattern6 {0.625 Density} bind def
+/Pattern7 {0.875 Density} bind def
+} def
+%
+% Now test for support of Level 2 code
+%
+Level1 {Level1PatternFill} {Level2PatternFill} ifelse
+%
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+ {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt}
+ {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv}
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+/ColorSpace (RGB) def
+Color InterpolatedColor or { % COLOUR vs. GRAY map
+ InterpolatedColor { %% Interpolation vs. RGB-Formula
+ /g {stroke pm3dround /grayv exch def interpolate
+ SelectSpace setrgbcolor} bind def
+ }{
+ /g {stroke pm3dround dup cF7 Constrain exch dup cF5 Constrain exch cF15 Constrain
+ SelectSpace setrgbcolor} bind def
+ } ifelse
+}{
+ /g {stroke pm3dround pm3dGamma exp setgray} bind def
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