Simulation of 3d laser scanning with phase-based EDM for the prediction of systematic deviations

摘要

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