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We present the optical tomography of the probability density of quasiparticles, the microcavity polaritons, confined in three dimensions by cylindrical traps. Collecting the photoluminescence emitted by the quasimodes under continuous nonresonant laser excitation, we reconstruct a three-dimensional mapping of the photoluminescence, from which we can extract the spatial distribution of the confined states at any energy. We discuss the impact of the confinement geometry on the wave function patterns and give an intuitive understanding in terms of a light-matter quasiparticle confined in a box.