After measurement, a wave-function is postulated to collapse on a predetermined set of states—the measurement basis. Using quantum process tomography, we show how a measurement basis emerges in the evolution of the electronic spin of a single trapped atomic ion after spontaneous photon scattering and detection. This basis is determined by the excitation laser polarization and the direction along which the photon was detected. Quantum tomography of the combined spin-photon state reveals that although photon scattering entangles all superpositions of the measurement-basis states with the scattered photon polarization, the measurement-basis states themselves remain classically correlated with it. Our findings shed light on the process of quantum measurement in atom-photon interactions.