plot with pgfplots two horizontal labels

Question

I want to produce the following plot:

Is a Lorentzian function, centered at x=408. But notice the upper label in the frame, that indicates a wave number associated to the coordinate measured in pixels (the bottom label).

I came across a few questions regarding plotting two x axes in pgfplots. (For example here and here), but they all are concerned about plotting two functions or curves on the same plot, and labeling them differently. I have only one function that I want to label twice.

What I have at the moment is this:

\documentclass{standalone}
\usepackage{pgfplots,tikz}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis} [
xlabel={CCD coordinate [px]},
ylabel={Intensity [A.U]},
xmin=0,xmax=1000,
ymajorgrids=true,
xmajorgrids=true,
]
\addplot[line width=1pt,samples=500,domain=0:1000]{4.278*10^(7)/((x-408.4)^2+54.25^2)};
\end{axis}
\end{tikzpicture}
\end{document}

I want the upper label to consist the following markers, written in the form

{{x₁,label₁},{x₂,label₂}, ... }

{80.15,639.892},{244.225,648.096},{408.3,656.3},{572.375,664.504},{736.45,672.708},{900.525,680.911}

What option should I add to my code to make it?

Answer 1

I also needed this plot in the past, so here is my result:

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{
    compat=1.17,
    % create a style for the plot, so you don't need to repeat yourself
    % in both axis environments.
    Lorentzian plot style/.style={
        every tick label/.append style={font=\small},
        scaled y ticks=false,
        xmin=0,
        xmax=1000,
        % keep domain limits in sync with the x-axis limits
        domain=\pgfkeysvalueof{/pgfplots/xmin}:\pgfkeysvalueof{/pgfplots/xmax},
    },
}
\begin{document}
    \begin{tikzpicture}
        \begin{axis} [
            % load the above created style
            Lorentzian plot style,
            xlabel={CCD coordinate [px]},
            ylabel={Intensity [a.u.]},
            axis x line*=left,
            ymajorgrids=true,
            xmajorgrids=true,
            ]
            \addplot[
            line width=1pt,
            samples=501,
            ] {4.278e7/((x - 408.4)^2 + 54.25^2)};
        \end{axis}
    % produce top x-axis
    \begin{axis}[
        % load the above created style here too
        Lorentzian plot style,
        xlabel={Wavelength [nm]},
        axis x line*=right,
        xtick={80.15,244.225,408.3,572.375,736.45,900.525},
        xticklabels={639.9,648.1,656.3,664.5,672.7,680.9},
        ytick=\empty,
        ]
        \addplot[
        draw=none,
        % for dummy use minimum number of `samples`
        samples=2 
        % dummy function to make it as less computational expensive as possible
        ]{0};
    \end{axis}
\end{tikzpicture}

\end{document}

First, I removed the right x axis of the main plot using axis x line*=left and then I added the same plot, but did not draw it with draw=none, added the right x axis using axis x line*=right and your labels with xtick={...} and xticklabels={...}, and at the end removed the y axis and labels of the empty plot using ytick=\empty.

Then, I recognised some overlap of the y label scaling factor, so I removed it using scaled y ticks=false and also decreased the size of the x axis labels using every tick label/.append style={font=\small}.

Hopefully, it suits your needs.

EDIT

I added @Stefan Pinnows excellent suggestions for improving the workflow and placed some of his comments for better understanding the changes.