Optical triangulation metrology is an essential part of modern industrial quality assurance. Due to their robustness and cost-effectiveness Laser Light Section Sensors have become a widespread solution for geometry inspections. The configuration of a measurement system involves balancing the size of the measurement volume against the accuracy to be achieved. Therefore, in order to provide accurate measurements on a larger scale, it is required to combine several individual measurements of different configurations. This study thus investigates the identification of parameters of a focus-adjustable triangulation sensor. Adaptability of the working distance is achieved by automatic focusing of the camera and repositionability of the laser with a piezo rotation stage and a mirror. The movement of the projected laser plane has to be identified with regard to the tilting angle. This ensures accurate calibration of the measuring system while the working distance being adjustable. Two general approaches are suitable for solving this task: One is based on a simplified identification of the rotational axis of the tilted laser plane. However, this does not take into account the deviations resulting from the offset of the reflection axis on the mirror surface and the rotational axis. This paper extends conventional models by deriving the position of the projected plane from the complete set of all rigid body transformations with regard to the rotation angles. The position of the laser source, the rotation axis and the mirror surface are described in the camera coordinate system. The validity of the extended model is assessed in comparison with a simplified model. Furthermore, the influence of the focusable camera on the calibration of the laser rotation axis is further investigated.
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