The main background $K^+ \rightarrow \mu^+ \nu_{\mu}$ should be suppressed by a factor $10^{-13}$ in order to achieve a signal-to-background ratio of the order of 10\% for the $K^+ \rightarrow \pi^+ \nu \bar{\nu}$ decay \cite{2008NIM-rich}. This task will be fulfilled by a combination of kinematic cuts and direct muon rejection at trigger level.\\

The \textbf{Ring Imaging \v{C}erenkov} (RICH) sub-detector in the NA62 setup will be able to separate pions from muons in the momentum range comprised between 15 and 35~\si{\giga\electronvolt/\textit{c}} up to a level of $5 \times 10^{-3}$; moreover, it will also provide a level 0 trigger primitive for charged tracks. Since this detector is central to the work described in this thesis, it is here discussed in more detail.\\

Let us describe the functioning of a RICH detector in general terms, before discussing the one devised for the NA62 setup.\\