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Collinear laser spectroscopy is a well established tool for measuring model-independent properties of nuclear ground and isomeric states. With this spins, electromagnetic moments and root mean square charge radii can be extracted. These quantities probe nuclear structure with a high sensitivity - and by this the nuclear wave function - as well as macroscopic properties such as size or shape. In particular, the experimental input is of crucial importance near closed shells to improve nuclear models. We plan to study the chain of cadmium between the N=50 and N=82 shell closures with high-resolution laser spectroscopy for the first time. These data will contribute to a better understanding of the nuclear structure in the vicinity of the doubly-magic 100Sn and 132Sn. On the neutron-rich side this is expected to shed light on a shell-quenching hypothesis and consequently on the duration of the r-process along the waiting-point nuclei below 130Cd. The physics motivation will be presented in detail along with the experimental techniques needed to resolve the exotic species of cadmium.