Utilizing the ball lens effect for astigmatism particle tracking velocimetry

In the present study, a simple method is developed to apply astigmatism particle tracking velocimetry (APTV) to transparent particles utilizing backlight illumination. Here, a particle acts as ball lens and bundles the light to a focal point, which is used to determine the particle’s out-of-plane position. Due to the distance between focal point and particle, additional features have to be considered in ball lens astigmatism particle tracking velocimetry (BLAPTV) compared to conventional APTV. We describe required calibration steps and perform parameter studies to show how the autocorrelation coefficient and the light exposure affect the accuracy of the method. It is found that the accuracy and robustness of the Euclidean calibration approach as also used in conventional APTV (Cierpka et al. in Meas Sci Technol 22(1):015401, 2010a) can be increased if an additional calibration curve for the light intensity of the particle’s focal point is considered. In addition, we study the influence of the particle diameter and the refractive index jump between liquid and particles on the calibration curves and the accuracy. In this way, particles of the same size, but different material, can be distinguished by their calibration curve. Furthermore, an approach is presented to account for shape changes of the calibration curve along the depth of the measurement volume. Overall, BLAPTV provides high out-of-plane particle reconstruction accuracies with respect to the particle diameter. In test cases, position uncertainties down to 1.8% of the particle diameter are achieved for particles of dp = 124 μm . The measurement technique is validated for a laminar flow in a straight rectangular channel with a cross-sectional area of 2.3 × 30 mm2 . Uncertainties of 0.75% for the in-plane and 2.29% for out-of-plane velocity with respect to the maximum streamwise velocity are achieved.