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<p>This paper describes photogrammetric reconstruction of a three-dimensional (3D) velocity field from multiple particle images taken by cameras with different positions and orientations based on integration of the multiple-camera photogrammetry and the optical flow method. The main technical aspects include photogrammetric camera calibration to establish the local object-space frame associated with a camera and the point-correspondence between particle images taken by multiple cameras. The least-squares solution of an overdetermined linear system of the projection equations gives an explicit linear transform from the optical flow in the image plane to a 3D velocity in the object space for reconstruction of a 3D velocity field from the optical flow fields. The error analysis of the proposed method is given and the major error sources are identified. The use of this method is demonstrated in simulations of a vortex jet and a vortex ring to evaluate the effects of the measurement domain depth, particle density, particle size and overlapped particles on the total error of the reconstructed 3D velocity fields. Further, this method is applied to experiments to reconstruct the 3D time-averaged velocity fields of an underwater jet and an air flow over a delta wing.</p>

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Photogrammetry for three-dimensional particle image velocimetry

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Tianshu Liu,
  • David M. Salazar,
  • Yun Liu,
  • Zhenyu Zang,
  • Shizhao Wang

摘要

This paper describes photogrammetric reconstruction of a three-dimensional (3D) velocity field from multiple particle images taken by cameras with different positions and orientations based on integration of the multiple-camera photogrammetry and the optical flow method. The main technical aspects include photogrammetric camera calibration to establish the local object-space frame associated with a camera and the point-correspondence between particle images taken by multiple cameras. The least-squares solution of an overdetermined linear system of the projection equations gives an explicit linear transform from the optical flow in the image plane to a 3D velocity in the object space for reconstruction of a 3D velocity field from the optical flow fields. The error analysis of the proposed method is given and the major error sources are identified. The use of this method is demonstrated in simulations of a vortex jet and a vortex ring to evaluate the effects of the measurement domain depth, particle density, particle size and overlapped particles on the total error of the reconstructed 3D velocity fields. Further, this method is applied to experiments to reconstruct the 3D time-averaged velocity fields of an underwater jet and an air flow over a delta wing.