High-resolution single-camera photogrammetry: incorporation of refraction at a fluid interface

Abstract: Photogrammetry uses images of a three-dimensional structure to derive information about its shape and position. In this work, a photogrammetric technique is implemented with a single camera and a digital projector to measure changes in an underwater sediment bed. This implementation incorporates refraction at an interface allowing for measurements through a deformed or changing water surface. The digital projector provides flexibility in choosing projected patterns and has a high frame rate, which allows to easily increase the spatial and temporal resolution of the measurements. The technique requires first for both the camera and the projector to be calibrated using triangulation. With the calibration, we construct lines in three-dimensional space that originate from the projector and the camera, and intersect on the surface to be measured. To correctly incorporate refraction due to a change of medium, each line in space is recalculated from its intersection with the interface using Snell’s law. This has the benefit that only one calibration for measurements is needed if the location and shape of the interface are known. The technique is validated by measuring a submerged undulated surface, plastic objects and a sediment bed. In particular, the undulated plate is reconstructed under a flat and a parabolic water surface. Finally, the technique is used in combination with particle image velocimetry to dynamically measure a changing sediment bed under an oscillating flow and the flow velocity at the free surface. Graphic abstract: [Figure not available: see fulltext.]