单光子模式激光测高探测概率模型与精度分析

Detection Probability Model of Single-Photon Laser Altimetry and Its Range Accuracy

单光子模式激光测高仪具有灵敏度高、重复频率高、重量轻、体积小等诸多优势,其代表着新一代天基激光雷达的未来发展趋势。对常见的高斯回波波形,基于激光雷达方程、单光子探测器统计特性,建立了单光子回波探测概率模型,基于该模型进一步推导了测距误差的量化关系式,并利用蒙特卡罗方法对所建模型进行了仿真验证。理论分析和仿真计算表明:回波脉宽越窄,测距的系统误差和随机误差越小;回波强度越大,测距的随机误差减小,但系统误差增大。以均方根脉宽为1.5ns的高斯回波为例,忽略噪声影响,当平均信号光子数为1时,单次测距系统误差约6cm,随机误差约22cm。

Single-photon laser altimetry represents the future space-based lidar＇s development trends. It has many advantages, such as high sensitivity, high repetition rate, light weight and small volume. For normal Gaussian echo signal, this work establishes the detection probablity model based on the lidar equation and the statistical property of single-photon detector. Then the quantitative relationship of ranging error is obtained. The model is simulated by Monte Carlo method. Results show that narrower pulse width can result in better accuracy and precision. Higher echo signal intensity can also lead to better precision, but it will bring about worse accuracy. Take the case of a Gaussian echo whose root-mean-square width is about 1.5 ns, when the mean number of signal photons is 1, the range accuracy is about 6 cm and the range precision is approximately 22 cm with a single shoot regardless of the noise.