In this work, collinear laser spectroscopy on stable and neutron-rich Pd isotopeswas performed. This led to the first determination of changes in mean-squarecharge radii of ^{112,114,116,118}Pd, using atomic factors calibrated during extensivetesting on the stable Pd isotopes. The results were compared to nuclear densityfunctional theory, consisting of calculations using Skyrme-type energy densityfunctionals, and new calculations using two Fayans energy density functionals,Fy(std) and Fy(Δr, HFB). The recently developed Fayans functionals have beenshown to be particularly good at reproducing charge radii in spherical nuclei,and are applied to deformed nuclei for the first time in this work. Fy(Δr, HFB)agrees well with the measured charge radii, which show a smooth parabolic trendwith increasing neutron number. Technical developments related to frequencystabilisation, crucial for collinear laser spectroscopy, have been conducted andapplied for the experiments in this thesis. In parallel, techniques for frequencydetermination were investigated, with the characterisation of Fabry-Pérot interferometersand an in-depth analysis of a commercial wavemeter. This is importantfor (high-resolution) laser spectroscopy techniques whereby the laser frequency isscanned rather than stabilised, for example in-source resonant laser ionisation andin-gas-jet laser spectroscopy.Keywords: Collinear laser spectroscopy, frequency determination, nuclear chargeradii, IGISOL, palladium