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Reflectorless electro-optical distance measurement (RL-EDM) relies on measuring the round-trip time of optical signals transmitted from the instrument and reflected by natural surfaces. It is the backbone of laser scanning technology, which allows easily digitizing the environment and obtaining 3d models that represent the geometry of the scanned objects. However, the measured distances do not refer to single, well-defined target points at the object surface but rather correspond to a weighted average of effective distances within the respective footprint of the laser beam. This increases the uncertainty of the measurements and may cause systematic deviations significantly exceeding the mm-or sub-mm level precision that would otherwise be attainable with EDM technology. In this paper we introduce a numerical simulation of the measurement process for phase-based RL-EDM with I/Q-demodulation assuming a Gaussian beam profile. The beam is discretized into a fixed number of rays for each of which the corresponding phase delay and attenuation are calculated. The I- and Q-components are obtained by integration over the footprint taking the beam profile into account. By deflection of the beam into incrementally changed spatial directions we extend the simulation to one of the 3d scanning process. The scanned surfaces are represented by triangular irregular meshes (TINs) with high spatial resolution. Each triangle is associated with a reflectivity, as a starting point for the modelling of surface properties. The simulation takes the interplay between the energy distribution within the laser footprint, the surface geometry and the surface reflectivity into account. Herein, we use the simulation framework to study the effects of the angle of incidence, of surface curvature and of mixed pixels in absence of measurement noise. The results indicate that the angle of incidence at a planar surface and the surface curvature within the footprint are on the order of 0.1 mm or less for small footprint and angles of incidence below about 60 deg. If the footprint and the angle of incidence are very large the biases may reach mm-level, however even then the impact of measurement noise and surface roughness will typically exceed these biases, such that they are negligible. On the other hand we show using simulations and real scans of a cylinder in front of a planar background, that the impact of mixed pixels or beams only partially hitting an object may introduce large biases and is practically relevant.
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