We experimentally demonstrate background-free, hyperfine-level-selective measurements of individual Cs atoms by simultaneous cooling to $5.3\mathrm{\mu }\mathrm{K}$ and imaging on the $6s_{1/2}\to 5d_{5/2}$ electric-quadrupole transition. We achieve hyperfine-resolved detection with fidelity 0.9993(4) and atom retention of 0.9954(5), limited primarily by vacuum lifetime. Performing state measurements in a 3D cooling configuration enables repeated low loss measurements. A theoretical analysis of an extension of the demonstrated approach, based on quenching of the excited state with an auxiliary field, identifies parameters for hyperfine-resolved measurements with a projected fidelity of $\sim 0.9995$ in $\sim 60\mathrm{\mu }\mathrm{s}$.

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• Cooling & trapping
• Quantum computation
• Atoms
• Atom & ion cooling