We discuss the application of synthetic aperture particle image velocimetry for measuring the flow around human swimmers using small bubbles as tracer. We quantify the two-dimensional projection of the velocity field in planes perpendicular to the viewing direction of an array of six cameras. With help of simulations, modelled after the experiment, we address questions about depth selectivity and occlusion in dense bubble fields. Using vortex rings in the swimming pool, we provide a proof of principle of the method. It is further illustrated by the vorticity field produced by a human swimmer.