采用两路光子时间到达点构建光纤式光子计数伪随机码深度获取系统.为了研究降低深度误差的方法, 以高斯函数为激光回波脉冲, 计算瞬时概率密度函数, 引入”时间行走“效应数学模型, 推导深度误差克拉美罗下限.随着激光回波能量的增大, 深度误差先降低再增大, 并且码长越长, 深度误差越小.采用理论推导的累积分布函数, 生成光子时间到达点, 蒙特卡洛仿真伪随机序列光子探测过程, 结果大于理论数值模拟, 符合克拉美罗下界原理.17组标定实验表明: 由于目标表面特性的不同而导致探测到激光回波中光子数的浮动, 该浮动引发光子”时间行走”效应, 并带来伪随机码深度获取系统的互相关函数的整体偏移.采用数值拟合方程拟合不同光子计数比例值下的深度误差, 测量得到的光子计数比例值, 代入拟合的矫正方程, 矫正后的深度均方误差下降至1 cm.

Two channels of photon arrivals are applied to construct fiber pseudo-random depth acquisition photon counting system. In order to find the method to diminish the depth error, Gauss function is used to model laser echo pulse. By calculating the probability density function,the time walk effect is introduced and the Cramer-Rao lower boundary is modeled. The theory model proves that with the growing signal energy, the depth error decreases sharply firstly and then rises and the longer code length can bring smaller depth error. From the theoretical part, using the cumulative distribution function to generate photon arrivals and simulate the pseudo-random depth acquisition photon counting system, Monte Carlo simulation results are larger than the numerical modelling,which agree with Cramer-Rao lower boundary. 17 experimental tests also converge to the presented boundary model in this paper. It has been proven that fluctuation of the number of detected photon counts in the laser echo pulse caused by different target reflection leads to the depth drift of Correlation Function on pseudo-random depth acquisition photon detection process. Finally, numerical fitting function is used to determine the relationship between the depth error and the photon counting ratio. Depth error is calibrated by substituting the measured photon counting ratio into numerical fitting function. The corrected depth RMSE is decreased to 1 cm.