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The spontaneous emission of atoms can be controlled by placing them betweentwo mirrors that form an optical cavity. Rapid advances in material processingtechniques in the last 10 years have made it possible to fabricate microscopicoptical cavities that can be finely tuned into resonance with the emitter. Thishas enabled progress in single-photon sources, nano-lasers and spectroscopy ofnew nano-emitters such as semiconductor quantum dots and Nitrogen-vacancycentres in diamond. Here we introduce a step-by-step method for computing thePurcell factor of the latest generation of open tunable Fabry-Perotmicrocavities used in micro-photoluminescence studies. We discuss how thePurcell factor can be optimised as a function of the cavity's geometry and findthe conditions for resonance with the emitter. Subtleties such as the opticalproperties of the emitter and penetration depth of the electric field into thecavity mirrors are also considered.

Computation and optimization of the Purcell factor of an open tunable Fabry-Perot microcavity