A method combining half width of point spread function with maximum gradient of image gray for single-camera three-dimensional spray velocity detection

When a defocus image is obtained by direct imaging, it is hard to determine whether the detected object is in the front or rear of the focal plane. This is called the ambiguity problem and it causes great trouble in the 3D-particle tracking velocimetry (PTV) defocus method, which obtains the defocus location by directly obtaining depth information from the intensity along the radial direction of particles. This study proposes a method to obtain the true position of a particle based on the asymmetry feature of the defocus image with respect to the focal plane. The method distinguishes two ambiguous positions with equal width of point spread function (PSF) width by introducing a parameter derived from the maximum gradient of image gray. The method also derives a mathematical expression for the half width of PSF(& chi;) considering aberration. The method is validated by a calibration technique, which shows that in 19 out of 20 experimental conditions correct results are obtained. We apply the method to measure the 3D velocity of an airflow jet with 3D-PTV and compare it with computational fluid dynamics results, which show a maximum error of 8.8 %. Furthermore, the method is used to measure a real spray as an example, and obtains a 3D vector map and velocity cumulative distribution of the measured area.