Modeling the Deviations of the Reflectorless Distance Measurement due to the Laser Beam’s Incident Angle
E. Lambrou

Abstract
The reflectorless (RL) distance measurements provide exceptional possibilities to the modern surveying projects, so the reliability of the measured distances has major significance. However the reflectorless distance measurement is influenced by numerous parameters via a complex interaction, which add extra error to the measured value. Several studies were carried out in order to determine the magnitude of these errors by using different instruments. This study investigates the determination of a correction equation for the error in the reflectorless distance measurements that occurs outdoors at a distance of 100m due to the change of the incident angle of the laser beam. Three advanced total stations, 23 materials and 13 different incident angles are participated in the experiments for the data collection. Deviations up to 5cm are registered. Numerous of approximation equations are tested in order to estimate, which describes better the deviation of the distance from its correct value. The RMSE and R2 are used as criteria in order to ensure the reliability of the adaptations. It was fount that each total station has a different behaviour. Thus one general correction equation of 2nd order is determined, for each total station and for all the involved materials, which corrects all the measurements by an accuracy of ±3mm. Moreover individual equations of 1st, 2nd, 3rd and exponential order are determined for each material. The results certify that the modelling of the deviations of the reflectorless distance measurement due to the beam’s incident angle is feasible. This fact strengthens the possibility to incorporate such equations in total stations’ software in order to automatically correct their reflectorless distance measurements.

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