In situ color-to-depth calibration: toward practical three-dimensional color particle tracking velocimetry

We propose a seeding particle-based color-to-depth calibration methodology for three-dimensional color particle tracking velocimetry (3D color PTV) using a single camera and volumetric rainbow gradient illumination. The use of sheet-color illumination from a liquid crystal display projector enables in situ calibration, namely the color-to-depth relationships of particles seeded in a fluid are determined without inserting any calibration equipment or taking a different optical setup. That is, in this methodology, the calibration and application can be performed using the same optical configuration, and only the digital illumination patterns need to be changed. Adopting this calibration allows evaluating actual color-to-depth relationships of the particles in measurements. The calibration is conducted regarding the relationship between spatially distributed particle colors and their depth coordinates by support of an artificial neural network. By combining conventional PTV with the depth estimated by the color, particle trajectories in 3D real space can be reconstructed from the calibration. The performance of the proposed method was evaluated using a rotating flow in a cylindrical tank by comparing its results with the flow fields measured by conventional particle image velocimetry. Good accordance in the comparison at the highly 3D flow suggests the applicability of the present methodology for various flow configurations.