How to have linked axes on plots?

Question

I plot infrared spectra in many reports and I display the energy units in two ways, wavenumbers $cm^{-1}$ on the bottom x-axis and wavelength (nm) on the upper x-axis. The relationship is X(nm)=1e7/Y(cm^{-1}).

for example a spectra running from 4000$cm^{-1}$-400$cm^{-1}$ on the bottom x-axis (a linear scale) corresponds to a wavelength range of 2500nm - 25,000nm a non-linear scale. Is there a way to have this done in pgf, tikz etc? I use Origin to do this and then export as pdf and use \includegraphics{linked-axis-plot.pdf}

Answer 1

You could use PGFplots for this. To get a second x-axis, you have to overlay the original plot with a second one of equal dimension that contains only the secondary axis. I've written a style called master axis that calculates and saves the equivalent horizontal dimensions needed for the secondary axis, which in turn uses the style secondary axis to read and set the dimensions.

\documentclass{article}
\usepackage{pgfplots}
\usepackage{siunitx} % For typesetting of units

\pgfplotsset{compat=newest}
\pgfkeys{/pgfplots/.cd,master axis/.style={
    scale only axis,
    enlarge x limits=false,
    x dir=reverse,axis x line*=bottom,
    xticklabel shift=3pt,
    after end axis/.code={
      \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed}
      \pgfmathparse{\pgfkeysvalueof{/pgfplots/xmin}}
      \global\let\masterxmin=\pgfmathresult
      \pgfmathparse{\pgfkeysvalueof{/pgfplots/xmax}}
      \global\let\masterxmax=\pgfmathresult
      \pgfkeys{/pgf/fpu=false}
    }
  },
  slave axis/.style={
    scale only axis,enlarge x limits=false,
     x dir=reverse,
    axis x line*=top,
    axis y line=none,
    xmin=\masterxmin,xmax=\masterxmax,ymin=0,ymax=1,
    scaled x ticks=false,
    xtick={100,400,1000,2000,4000,10000},
    xticklabel={
      \pgfkeys{/pgf/fpu}
      \pgfmathparse{1e7/\tick}
      \pgfmathprintnumber{\pgfmathresult}
    }
  }
}
\begin{document}
\begin{tikzpicture}

\begin{axis}[master axis,
  ymin=0,ymax=100,
  xmin=400,xmax=4000,
  enlarge x limits=false, yticklabel={\SI[round-mode=places,round-precision=0]{\tick}{\percent}}, xlabel=Wavenumber / \si{\per\centi\metre},
  ylabel=Transmissivity
]
\addplot[domain=400:4000,samples=100,thick]{-(abs(tan(x/10))-2*rnd)+90};
\end{axis}

\begin{axis}[slave axis,xlabel=Wavelength / \si{\nano\metre}]\end{axis}

\end{tikzpicture}
\end{document}