Weight Coefficient Calculation through Equivalent Ray Tracing Method for Light Field Particle Image Velocimetry

Light field particle image velocimetry (LF-PIV) can measure three-dimensional (3D) flow velocity from a single snapshot of a light field camera based on the 3D reconstruction of tracer particles of light field images. However, it requires light field intensity calibrations to calculate accurate weight coefficients. Conventionally, the weight coefficients are calculated through in-situ calibration approaches whereas the translation of the calibration board within the entire measurement area is required. Therefore, these approaches are inapplicable for internal industrial flows and space-constrained applications. This study presents an equivalent ray tracing method for the weight coefficients calculation. With a light field snapshot of a smart calibration board, a mapping relationship is established to relate the target points sampled in the flow field with their equivalent points in the air. The weight coefficients are then calculated through the ray tracing method by changing the starting points of ray tracing from the target points to their equivalent points. The calculated weight coefficients are employed to reconstruct the feature marks of the calibration board. Results show that the spatial locations of the marks can be reconstructed accurately with a mean lateral and depth error of 0.63 and 5.6, respectively. Experiments were also carried out on a low-speed laminar flow. The result indicates that the equivalent ray tracing method provides a similar measurement accuracy with the in-situ calibration method. The overall error of 6.77 is achieved for the velocity measurement. It is demonstrated that the proposed method is capable of measuring the 3D flow velocity for internal industrial and space-constrained applications without translating the calibration board within the entire measurement area.