Lidar Essential Beam Model for Accurate Width Estimation of Thin Poles

While Lidar beams are often represented as rays, they actually have finite beam width and this width impacts the measured shape and size of objects in the scene. Here we investigate the effects of beam width on measurements of thin objects such as vertical poles. We propose a model for beam divergence and show how this can explain both object dilation and erosion. We develop a calibration method to estimate beam divergence angle. This calibration method uses one or more vertical poles observed from a Lidar on a moving platform. In addition, we derive an incremental method for using the calibrated beam angle to obtain accurate estimates of thin object diameters, observed from a Lidar on a moving platform. Our method achieves significantly more accurate diameter estimates than is obtained when beam divergence is ignored.