Analytical model of a laser rangefinder for measuring distances to objects with poorly predictable motion dynamics

Abstract

Subject of study. A pulsed laser rangefinder for measuring distances to distant small-sized objects whose movements are characterized by poorly predictable space-time evolutions is studied. Aim of study. The aim of this study is to develop a computational analytical model of a pulsed laser rangefinder considering the probabilistic nature of laser pulses hitting the location object. Main result. An analytical model of a rangefinder that satisfies the required probability of at least one laser pulse hitting the location object during a single range measurement is developed. Half-widths of the directivity pattern and energy of the probing laser radiation are calculated based on the obtained equations as functions of the root-mean-square deviation of the directivity pattern axis from the direction to the object and the number of laser pulses required for radiation to hit the location object with at least one pulse with a given probability. The study demonstrates that, for the energy density distribution in the beam of the far field described by the Airy distribution, an optimal diameter of the emitter aperture exists at which the energy of the probing pulses required to detect the reflected radiation with a photodetector is the minimum compared with the energy required for the same outcome at different diameters of the emitter aperture. Practical significance. The results of this study complement and improve the existing models and methods for calculating the characteristics of a pulsed laser rangefinder.