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None-tactile metrology systems for inner radius measurements of cylindrical objects with large diameters are often based on the triangulation principle, using a laser source as illumination unit and a camera as detection unit. Different approaches have been presented in the past in order to generate a complete profile section of the measurement object’s inner radius. A standard light-section sensor cannot provide a 360° view of the radius without sensor rotation around the cylinder axis. The additional rotation axis needs to be calibrated and the captured point clouds registered in the same coordinate frame. To spare the necessity of a rotational axis, we developed a prototype sensor based on the hardware approach suggested by Yoshizawa et al.,1 using a cylinder cone mirror and a laser illumination unit in order to generate a line circle projected onto the inner radius. In combination with a wide-angle camera, the laser line can be captured in one shot. Unlike the approach by Yoshizawa et al. , we present a model-based calibration routine for the triangulation sensor by mathematically describing the laser light path. The cone mirror expands the laser light into a disc (plane) or into a cone – depending on the incidence angle between laser and mirror. In our model, the light cone is parametrized by the right circular cone equation to reduce the number of unknowns in regression calculus. The necessary 3D support points to approximate the model parameter are gained by recording planar calibration pattern poses with and without laser line. The intersection calculation between the camera’s line-of-sight and the projected laser light geometry is derived, and the mathematical ambiguity in the line-cone intersection successfully solved. We present first experimental calibration and measurement data of a cylinder. By intentionally misaligning sensor and cylinder axes with arbitrarily chosen angles, the robustness of the suggested procedure is demonstrated.
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