File:InterferenceGrating.gif

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InterferenceGrating.gif ‎(683 × 446 pixels, file size: 827 KB, MIME type: image/gif, looped, 31 frames, 16 s)

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Summary[edit]

Description
English: Spectroscopy with an optical grating
Deutsch: Optisches Gitter: Beugungsordnungen und Spektroskopie
Date
Source Own work
Author And1mu

Similar graphics[edit]

Source Code[edit]

created with LaTeX and PGF/TikZ

Script to create the animation: 

#!/bin/bash

set -eu
DIR="animate"
FILE="Spektrum"

NUM=0
rm -f ${DIR}/frame???.png

for ANG in $(seq 400 10 700) ; do
#    POS=$(echo "30*c($ANG/45*a(1))" | bc -l)
    echo $ANG
    sed -i "s/\\\def\\\wavelength{.\+}/\\\def\\\wavelength{$ANG}/" $FILE.tex
#    echo "Creating frame $NUM for $ANG ..."
    pdflatex -shell-escape $FILE.tex 1> /dev/null
    echo "Convert to png ..."
    NUMSTR=$(printf "%03d" $NUM)
    convert -density 100 ${FILE}01.svg -shave 3 ${DIR}/frame${NUMSTR}.png
    NUM=$(($NUM+1))
done
cd $DIR
#convert -delay 40 -loop 1000 frame*.png  ${FILE}.gif
convert -set delay '%[fx:(t<n-1)?20:1000]' -loop 100 frame*.png  ${FILE}.gif
cd -

The code to create a single frame: 

\documentclass[crop,border=5,tikz,convert={outext=,
  command=\unexpanded{pdf2svg \infile\space\outfile\%02d.svg
    all}},multi=false]{standalone}
\usetikzlibrary{math,calc,through,shapes,patterns,decorations.pathmorphing}
\usepackage{ifthen}
\usepackage{bm}

\def\static{1} % 1: for static graphic

\def\lpmm{625}
\def\wavelength{700}

\newcommand{\markangle}[6][0.25]{
  \begin{scope}
    \clip (#2)--(#3)--(#4);
    \node (ANG) [draw, circle, minimum size=#5] at (#3){};
  \end{scope}
  \coordinate (E1) at (intersection 0 of ANG and #3--#2);
  \coordinate (E2) at (intersection 0 of ANG and #3--#4);
  %\draw[thick] (E1) to [bend right=50] (E2);
  \coordinate (EM) at ($ (E1)!0.5!(E2) $);
  \coordinate (EM) at ($ (EM)!#1!(#3) $);
  \node[fill=white, inner sep=2] at (EM) {#6};
}

\newcommand{\rainbow}[1]{
  %% #1 = 0: circle, #1 = 1: rectangle
  \foreach \n in {1,...,10}{
    \foreach \swl in {400,403,...,\wavelength}{
      \pgfmathsetmacro{\myarg}{ \n*\swl/1000.*\lpmm/1000 }
      \pgfmathsetmacro{\myarg}{ \myarg < 0.98 ? \myarg : 0}
      \ifthenelse{\lengthtest{ \myarg pt = 0 pt}}{}{
        \LAMBDAtoRGB{\swl}
        \tikzmath{ \myalpha = asin(\myarg);}
        \tikzmath{ \mx = 7*tan(\myalpha);}
        \tikzmath{ \mn = \n*\n;}
        \ifthenelse{ #1 = 0 }{
          \coordinate (A+) at (90-\myalpha:6+0.075*\mn);
          \coordinate (B+) at (90-\myalpha:8-0.075*\mn);
          \coordinate (A-) at (90+\myalpha:6+0.075*\mn);
          \coordinate (B-) at (90+\myalpha:8-0.075*\mn);
          \pgfmathsetmacro{\mywidth}%
          {0.14*\n*\lpmm/100/sqrt(1-\myarg*\myarg)}
        }{
          \coordinate (A+) at (-\mx,6.05+0.05*\mn);
          \coordinate (B+) at (-\mx,7.95-0.05*\mn);
          \coordinate (A-) at (\mx,6.05+0.05*\mn);
          \coordinate (B-) at (\mx,7.95-0.05*\mn);
          \pgfmathsetmacro{\mywidth}{\myarg < 0.92 ?%
            0.4*\n*3/10*\lpmm/100/(1-\myarg*\myarg)^(3/2)%
            : 0}
        }
        \draw[beamcolor,line width=\mywidth] (A+)--(B+);
        \draw[beamcolor,line width=\mywidth] (A-)--(B-);
        \ifthenelse{ \static = 1 }{
          \ifthenelse{ \swl = 502 }{
            \ifthenelse{ #1 = 0 }{
              \node[] at (90+\myalpha:8.3){$+\n$};
              \node[] at (90-\myalpha:8.3){$-\n$};
            }{
              \pgfmathsetmacro{\mxm}{\mx > 12 ? 11 : \mx}
              \node[] at (-\mxm,8.3){$+\n$};
              \node[] at (\mxm,8.3){$-\n$};
            }
          }{}
        }{}
      }{}
    }
  }
}

\newcommand{\drawbeam}[2]{
  \pgfmathsetmacro{\myarg}{ \n*#1/1000.*\lpmm/1000 }
  \pgfmathsetmacro{\myarg}{ \myarg < 0.98 ? \myarg : 0 }
  \ifthenelse{\lengthtest{\myarg pt = 0 pt}}{}{
    \tikzmath{ \myalpha = asin(\myarg); }
    \LAMBDAtoRGB{#1}
    \ifthenelse{ #2 = 0 }{
      \coordinate (A+) at (90+\myalpha:8);
      \coordinate (A-) at (90-\myalpha:8);
    }{
      \tikzmath{ \mx = 7*tan(\myalpha); }
      \coordinate (A+) at (-\mx,7);
      \coordinate (A-) at (\mx,7);
      \draw[beamcolor,thick] (\mx,6)--(\mx,8);
      \draw[beamcolor,thick] (-\mx,6)--(-\mx,8);
    }
    \draw[beamcolor,thick] (A+) -- (0,0) -- (A-);
    \ifthenelse{ \static = 0 }{
      \node[beamcolor,fill=white] at (90+\myalpha:5) {$+\n$};
      \node[beamcolor,fill=white] at (90-\myalpha:5) {$-\n$};
      \node[anchor=west,beamcolor] at (0.7,-1.2){
        \Large $\bm{\lambda=#1\;\mathrm{nm}}$};
      \ifthenelse{\n < 3}{
        \markangle[0.1]{A+}{0,0}{0,6}{220-50*\n}{$\alpha_\n$}
        \pgfmathprintnumberto[precision=2]{\myalpha}{\roundedalpha}
        \node[anchor=west,beamcolor] at (4,-0.3-0.6*\n){
          $\bm{\alpha_\n=\roundedalpha^\circ}$};
      }{}
    }{
      \ifthenelse{ \n = 1 \AND #1 = 430 }{
        \markangle[0.1]{A+}{0,0}{0,6}{220-50*\n}{$\alpha_\n$}
      }{}
    }
  }
}

\newcommand{\info}[2]{
  \LAMBDAtoRGB{#1}
  \node[anchor=west,beamcolor,fill=white] at (0.7,-0.3-#2*0.5){
    \Large $\bm{\lambda=#1\;\mathrm{nm}}$};
  \draw[beamcolor,fill=beamcolor]
  (-0.4,-0.1-0.5*#2)rectangle(0.4,-0.6-0.5*#2);
}

\newcommand{\laser}{
  \LAMBDAtoRGB{\wavelength}
  \draw[white,line width=1.4mm] (0,6.2)--(0,7.8);
  \draw[beamcolor,thick] (0,0) -- (0,8);
  \ifthenelse{ \static = 0 }{
    \fill[beamcolor] (-0.4,-2)rectangle(0.4,-0.6);
    \node[beamcolor,fill=white] at (0,5){$0$};
  }{
    \node[] at (0,8.3){$0$};
  }
  \draw[beamcolor,ultra thick] (0,-0.6) -- (0,0);
  \draw[black,ultra thick,opacity=0.6] (-1,0)--(1,0)
  node[right]{\LARGE $g=\frac{1}{\lpmm}\;\mathrm{mm}$};
  \node[anchor=east,draw,text width=3.5cm,text centered] at
  (-1.5,-0.4){
    \LARGE $\sin\alpha_n=\frac{n\cdot\lambda}{g}$\\
    \normalsize $n=0,\pm 1,\pm 2,\dots$};
}

\begin{document}

\include{LaserColor}

\begin{tikzpicture}[>=latex,scale=1]
  \clip(-8.4,-2.4)rectangle(8.4,8.5);
  \begin{scope}
    \clip (168.8:8)arc(168.8:11.2:8)--(11.2:6)arc(11.2:168.8:6)--cycle;
    \fill[black] (0,0) circle (8);
    \fill[white] (0,0) circle (6.0);
  \end{scope}
  \foreach \n in {1,...,10}{
    \ifthenelse{ \static = 0 }{
      \drawbeam{\wavelength}{0}
    }{
      \foreach \wl/\s in {430/1,532/2,633/3}{
        \drawbeam{\wl}{0}
        \info{\wl}{\s}
      }
    }
  }
  \rainbow{0}
  \laser
\end{tikzpicture}

\begin{tikzpicture}[>=latex,scale=1]
  \clip(-12.4,-2.4)rectangle(12.4,8.5);
  \fill[black](-12.4,6)rectangle(12.4,8);
  \rainbow{1}
  \foreach \n in {1,...,10}{
    \ifthenelse{ \static = 0 }{
      \drawbeam{\wavelength}{1}
    }{
      \foreach \wl/\s in {430/1,532/2,633/3}{
        \drawbeam{\wl}{1}
        \info{\wl}{\s}
      }
    }
  }
  \laser
\end{tikzpicture}

\end{document}

The code to find RGB from wavelenght [1] (slightly modified) LaserColor.tex: 

\newcommand{\LAMBDAtoRGB}[1]{
  \def\locallambda{#1}

  \def\red{0.0}
  \def\green{0.0}
  \def\blue{0.0}

  \def\t{0.0}

  \tikzmath{
    if ( \locallambda >= 400.0 && \locallambda < 410.0 ) then {
      \t = (\locallambda-400.0)/(410.0-400.0);
      \red = (0.345*\t)-(0.20*\t*\t);
    } else {
      if ( \locallambda >= 410.0 && \locallambda < 475.0) then {
        \t = (\locallambda-410.0)/(475.0-410.0);
        \red = 0.15-(0.15*\t*\t);
      } else {
        if ( \locallambda >= 545.0 && \locallambda < 595.0 ) then {
          \t = (\locallambda-545.0)/(595.0-545.0);
          \red = +(1.98*\t)-(\t*\t);
        } else {
          if ( \locallambda >= 595.0 && \locallambda < 650.0 ) then {
            \t = (\locallambda-595.0)/(650.0-595.0);
            \red = 0.98+(0.06*\t)-(0.40*\t*\t);
          } else {
            if ( \locallambda >= 650.0 && \locallambda < 700.0 ) then {
              \t = (\locallambda-650.0)/(700.0-650.0);
              \red = 0.64-(0.84*\t)+(0.20*\t*\t);
            };
          };
        };
      };
    };
  }

  \tikzmath{
    if ( \locallambda >= 415.0 && \locallambda < 475.0 ) then {
      \t = (\locallambda-415.0)/(475.0-415.0);
      \green = +(0.80*\t*\t);
    } else {
      if ( \locallambda >= 475.0 && \locallambda < 590.0 ) then {
        \t = (\locallambda-475.0)/(590.0-475.0);
        \green = 0.8 +(0.76*\t)-(0.80*\t*\t);
      } else {
        if ( \locallambda >= 590.0 && \locallambda < 639.0 ) then {
          \t = (\locallambda-590.0)/(639.0-590.0);
          \green = 0.76-(0.76*\t);
        };
      };
    };
  }

  \tikzmath{
    if ( \locallambda >= 400.0 && \locallambda < 475.0 ) then {
      \t = (\locallambda-400.0)/(475.0-400.0);
      \blue = +(2.20*\t)-(1.50*\t*\t);
    } else {
      if ( \locallambda >= 475.0 && \locallambda < 560.0 ) then {
        \t = (\locallambda-475.0)/(560.0-475.0);
        \blue = 0.7 -(\t)+(0.30*\t*\t);
      };
    };
  }
  \definecolor{beamcolor}{rgb}{\red,\green,\blue}
}

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:29, 29 October 2017Thumbnail for version as of 15:29, 29 October 2017683 × 446 (827 KB)And1mu (talk | contribs)many small improvements
16:01, 23 October 2017Thumbnail for version as of 16:01, 23 October 2017652 × 439 (839 KB)And1mu (talk | contribs)minor cosmetic optimizations
21:22, 21 October 2017Thumbnail for version as of 21:22, 21 October 2017653 × 439 (841 KB)And1mu (talk | contribs)show angles
13:19, 21 October 2017Thumbnail for version as of 13:19, 21 October 2017652 × 437 (784 KB)And1mu (talk | contribs)User created page with UploadWizard

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