Customizing highlighting from soul

Question

I am using the following customization from make soul highlight span lines for the \hl from soul to get rid of the gaps between the highlighted zones:

\documentclass[a8paper, landscape]{scrartcl}
\usepackage{soul}

\usepackage[svgnames]{xcolor}

\sethlcolor{LightBlue}
\makeatletter
\def\SOUL@hlpreamble{%
\setul{\dp\strutbox}{\dimexpr\ht\strutbox+\dp\strutbox\relax}
\let\SOUL@stcolor\SOUL@hlcolor
\SOUL@stpreamble
}
\makeatother

\begin{document}
This is some \hl{highlighted text with a formula $q=\frac{p}{r}$. 
Notice how nicely it is highlighted.} 

Writting something more fancy, say, \hl{$|a|=\inf_{\overline{f}=a}|f|$, 
gives an obvious gap problem.}
\end{document}

Which produces

However, if there are symbols that extend below/above too much, the \hl does not fully highlight the gap, as the above example shows. I tried to fiddle with the \setul part but nothing seems to give a good result. I also tried to \smash the inf construction, but then the line below just overlaps with the one above.

What would be the right setup to highlight that gap?

Answer 1

Add some more to the depth (and the thickness), also setting \lineskip to zero. Note that this changes the interline space, but there's no way that I know for convincing soul and \hl to cover something that exceeds the stated depth for the underline (the background color is realized as underlining with a very thick rule).

\documentclass[a8paper, landscape]{scrartcl}
\usepackage{soul}

\usepackage[svgnames]{xcolor}

\sethlcolor{LightBlue}
\makeatletter
\def\SOUL@hlpreamble{%
\setul{\dimexpr\dp\strutbox+2pt}{\dimexpr\ht\strutbox+\dp\strutbox+2pt\relax}
\let\SOUL@stcolor\SOUL@hlcolor
\SOUL@stpreamble
}
\makeatother

\begin{document}
\setlength{\lineskip}{0pt}

This is some \hl{highlighted text with a formula $q=\frac{p}{r}$.
Notice how nicely it is highlighted.}

Writting something more fancy, say, \hl{$|a|=\inf_{\overline{f}=a}|f|$,
gives an obvious gap problem.}

\end{document}

Don't use \hl in your final document.