Digital micromirror device enriched nearly single-pixel 3D calibration framework for particle-based velocimetry techniques

Abstract This paper introduces a high-precision and nearly single-pixel three-dimensional (3D) calibration framework for the camera system and optical transfer function (OTF); using a digital micromirror device (DMD) to generate a large number of 3D calibration points, precise 3D reconstruction and 2D reprojection for particle-based velocimetry techniques is achieved. Additionally, a line-of-sight (LOS) calibration approach, which utilizes an extensive number of LOSs from 3D points to 2D centers, leverages accurate 2D reprojection and 3D reconstruction—even in the presence of curved interfaces with significant refractive index variations. In camera calibration, the high-frequency DMD can efficiently generate 240 000 3D volume points for a single Z -plane at −15 mm or +15 mm, which can be captured by a 400 Hz camera in just 6.25 s; as well as a massive dataset of 3072 000 calibration points in 80 planes can be obtained quickly. This extensive calibration dataset defining projection of 3D to 2D points enhances the performance of both pinhole Tsai camera model and polynomial model in the presence of a planar refractive interface. As for the planar or curved refractive interfaces, such LOS calibration proves to be more effective, significantly improving 3D reconstruction and 2D reprojection accuracy compared to the pinhole Tsai camera and polynomial models. Using this large calibration dataset, the averaging OTF strategy (with a reprojection similarity of about 0.92) is feasible for efficiency-first measurement applications, as a coarser OTF grid enhances computational efficiency. While the higher resolution OTF grid can further improve projection quality (maximal similarity of over 0.94) through interpolation from the OTF grid. This strategy is highly beneficial for 2D reprojection in simultaneous multiplicative algebraic reconstruction techniques or iterative particle reconstruction procedures, ultimately leading to improved 3D reconstruction in particle-based velocimetry techniques.