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We report on observations of thermal motion of a single, Doppler-cooled ionalong the axis of a linear radio-frequency quadrupole trap. We show that for aharmonic potential the thermal occupation of energy levels leads to Gaussiandistribution of the ion's axial position. The dependence of the spatial thermalspread on the trap potential is used for precise calibration of our imagingsystem's point spread function and sub-milliKelvin thermometry. We employ thistechnique to investigate the laser detuning dependence of the Dopplertemperature.

Sub-milliKelvin spatial thermometry of a single Doppler cooled ion in a Paul trap