We present a technique called photoacoustic vector-flow (PAVF) to quantify the speed and direction of flowing optical absorbers at each pixel from acoustic-resolution PA images. By varying the receiving angle at each pixel in post-processing, we obtain multiple estimates of the phase difference between consecutive frames. These are used to solve the overdetermined photoacoustic Doppler equation with a least-squares approach to estimate a velocity vector at each pixel. This technique is tested in bench-top experiments and compared to simultaneous pulse-echo ultrasound vector-flow (USVF) on whole rat blood at speeds on the order of 1 mm/s. Unlike USVF, PAVF can detect flow without stationary clutter filtering in this experiment, although the velocity estimates are highly underestimated. When applying spatio-temporal singular value decomposition clutter filtering, the flow speed can be accurately estimated with an error of 16.8% for USVF and −8.9% for PAVF for an average flow speed of 2.5 mm/s.

By changing the ultrasonic receiving angle in post-processing, we can obtain flow vectors from a photoacoustic experiment on a blood vessel phantom by solving the photoacoustic Doppler equation using a least-squares optimisation approach.