[Tex/LaTex] Fit sidewaysfigure to page width including caption and source

Question

I'm trying to add a sidewaysfigure to my document, but when I set the width to \textwidth it comes out too wide.

This is my code:

\usepackage{rotating}

\begin{sidewaysfigure}
   \centering
   \begin{minipage}{\textwidth}
      \caption{The caption}
      \includegraphics[width=\textwidth]{img/diagramm_hs.png}\\
      \source{The source}
      \label{fig:diagramm_hs}
   \end{minipage}
\end{sidewaysfigure}

And here is the result:

As you can see, the image is wider than the textwidth (textwidth is as wide as the line in the header), especially with the caption and source.

How can I make the image as large as possible on the page while everything, including caption and source, remain in the textarea?

EDIT: The image dimensions are 1327×960 px.
This is my documentclass:

\documentclass[
paper=A4,
fontsize=12pt,
BCOR12mm,
DIV14,
parskip=half*,
headsepline,
listof=totoc,
footinclude=false,
headinclude=true,
final
]{scrartcl}

Answer 1

First, the original \textwidth is lost using sidewaysfigure. Second, I needed to test if the total figure was too big. Finally, I needed the image height using [width=\textwidth] in order to determine what [height=] should be to compensate.

I tested \listoffigures to make sure only one caption showed up.

\documentclass{article}
\usepackage{showframe}
\usepackage[Export]{adjustbox}
\usepackage{rotating}
\usepackage{caption}
\captionsetup{justification=raggedright,
               singlelinecheck=false}

\newcommand{\source}[1]{\ttfamily #1}

\newsavebox{\tempbox}
\newlength{\tempdima}
\newlength{\tempdimb}
\newlength{\tempdimc}

\begin{document}
  \tempdima=\textwidth% inside \textwidth=\linewidth=\textheight
  \begin{sidewaysfigure}
  \textheight=\tempdima
  \settoheight{\tempdimb}{\includegraphics[width=\textwidth]{example-image-a}}% default height
  \savebox{\tempbox}{\begin{minipage}{\textwidth}
    \caption{The caption}
    \addtocounter{figure}{-1}% reset
    \rule{\textwidth}{\tempdimb}% same size but faster
    \par\source{The source}
    \end{minipage}}%
  \tempdima=\ht\tempbox\relax% can't get \dimexpr to work
  \advance\tempdima by \dp\tempbox\relax
  \tempdimc=\tempdimb
  \ifdim\textheight<\tempdima
    \advance\tempdimb by \textheight
    \advance\tempdimb by -\tempdima
  \fi
  \tempdima=\dimexpr \tempdimb*\textwidth/\tempdimc\relax% compute scaled width
  \hfil\begin{minipage}{\tempdima}
  \caption{The caption}
  \includegraphics[width=\textwidth]{example-image-a}\par
  \source{The source}
  \end{minipage}
  \end{sidewaysfigure}
\end{document}