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We demonstrate the use of tone-burst excitation and time-gated spectral analysis for photoacoustic Doppler mapping of flow in an unperturbed vessel phantom and in a vessel with a spatially varying lumen. The method, which mimics pulsed Doppler ultrasound, enables simultaneous measurement of axial position and flow as well as complete characterization of the Doppler spectrum over a wide range of mean velocities (3.5 to 200 mm/s). To generate the required optical excitation, a continuous cw laser source followed by an external electro-optic modulator is used. Stenoses at various levels are emulated in a C-flex tube with a flowing suspension of micrometer-scale carbon particles. Two-dimensional maps of spectral content versus axial position at different points along the vessel and for various levels of perturbations demonstrate the potential use of the method for characterization of flow irregularities.