How to add secondary non linear scaled x-axis (1/x) for same data that does not align to linear scale (x) ticks

Question

I want to plot Wavelength and Wavenumbers of one Dataset to one tikzpicture. I found stackexchange: How to have linked axes on plots? but I DONT want to have both axis-ticks aligned to same position. See image: red is plotted but blue does not fit with buttom axes and is unfortunately not plotted.

Like Jakes code:

\documentclass{article}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}
\pgfkeys{/pgfplots/.cd,master axis/.style={
    scale only axis,
    enlarge x limits=false,
    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,
    axis x line*=top,
    axis y line=none,
    xmin=\masterxmin,xmax=\masterxmax,ymin=0,ymax=1,
    scaled x ticks=false,
    xtick={1,4,10,20,40,100},
    xticklabel={
      \pgfkeys{/pgf/fpu}
      \pgfmathparse{1/\tick}
      \pgfmathprintnumber{\pgfmathresult}
    }
  }
}
\begin{document}
\begin{tikzpicture}

\begin{axis}[master axis,
  ymin=0,ymax=100,
  xmin=7,xmax=16,
  enlarge x limits=false,
  xlabel={Wavelength $\lambda$},
  ylabel=Transmissivity
]
\addplot[domain=7:16,samples=100,thick]{-(abs(tan(x*10))-2*rnd)+90};
\end{axis}

\begin{axis}[slave axis,xlabel=Wavenumber 1/$\lambda$]\end{axis}

\end{tikzpicture}
\end{document}

so how to change the code? One posibility is to leave or change

xtick={1,4,10,20,40,100}

but this leads in badly brocken values align with bottom (see Image 2).

I also tried to set to

xmin=0.1428,xmax=0.0625,x dir=reverse %   1/7=0.1428   1/16=0.0625

but this destroys the axis.

I also found stackexchange:Use function to scale x axis but I don't know how to change this because of the reverse counting.

Thanks a lot :-)

Answer 1

You can change the xtick values to

% 8.33=1/0.12, 9.09=1/0.11, 1=1/0.1, 11.11=1/0.09, ...
xtick={8.33,9.09,10,11.11,12.5,14.29},

Then you get

\documentclass{article}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}
\pgfkeys{/pgfplots/.cd,master axis/.style={
    scale only axis,
    enlarge x limits=false,
    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,
    axis x line*=top,
    axis y line=none,
    xmin=\masterxmin,xmax=\masterxmax,
    ymin=0,ymax=1,
    scaled x ticks=false,
    xtick=\slavextick,
    xticklabel={%
      \pgfkeys{/pgf/fpu}%
      \pgfmathparse{1/\tick}%
      \pgfmathprintnumber{\pgfmathresult}%
    },
      xticklabel style={/pgf/number format/.cd,fixed,precision=2},
      xmajorgrids=true, % to show the tick position
      every axis x grid/.style={red,dashed,very thick},
  }
}
  % calculation of the xtick position
  \xdef\slavextick{}
  \foreach[count=\n][evaluate=\i as \j using 1/\i]%
    \i in {0.12,0.11,...,0.07} % xtick for the slave axis
    {\pgfmathparse{\n==1?"":","}\xdef\slavextick{\slavextick\pgfmathresult\j}
    }

\begin{document}
\begin{tikzpicture}

\begin{axis}[master axis,
  ymin=0,ymax=100,
  xmin=7,xmax=16,
  enlarge x limits=false,
  xlabel={Wavelength $\lambda$},
  ylabel=Transmissivity,
]
\addplot[domain=7:16,samples=100,thick]{-(abs(tan(x*10))-2*rnd)+90};
\end{axis}

\begin{axis}[slave axis,xlabel=Wavenumber 1/$\lambda$]\end{axis}

\end{tikzpicture}
\end{document}