Single camera volumetric shadowgraphy system for simultaneous droplet sizing and depth location, including empirical determination of the effective optical aperture

The proposed approach is tested on real opaque images of a calibrated target. The proposal includes a practical procedure to double-check relevant optical parameters like the effective aperture of the lens setup. The empirical determination of the effective optical aperture is essential as it may significantly deviate from the nominal expected value, depending on the optical setup. Results obtained are satisfactory, allowing for an accurate volumetric measurement with displacements up to 30 particle diameters away in the out of focus direction (less than 20% error in particle sizing and 2 mm in particle depth location). Extension of these results to the measurement of transparent water droplets generated by an injector is also proposed and the coherence of results is checked. In this case, the size of the background stage and its location are important issues. Following the indications detailed in the paper, satisfactory results are obtained for measurements of transparent water droplets with displacements up to 10 particle diameters away in the out of focus direction.