Li Zhijian, Lai Jiancheng, Wang Chunyong, Yan Wei, Li Zhenhua
Appl Opt. 2018 Sep 10;57(26):7415-7426. doi: 10.1364/AO.57.007415.
For a laser radar (LADAR) system using a Geiger-mode avalanche photodiode (GmAPD), attenuating echo and background noise simultaneously affect the original data output from the GmAPD and eventually affect detection performance. In this study, we established a model that applies to the GmAPD-based LADAR with optical attenuation and also applies to any typical single photon detector that has a dead time (e.g., the photomultiplier tube); thus, a comprehensive and fundamental study is performed for the mathematical expectation of the number of signal detections (E), the mathematical expectation of the number of noise detections (E), the signal-to-noise ratio (SNR), and the range bias (absolute error, R) and precision (standard deviation, R) under various attenuation levels with different dead times and signal noise conditions. We observed the following: on the one hand, there exists an optimum attenuation level at which E and SNR are maximized; on the other hand, there exists another optimum attenuation level for shorter dead times, at which R is minimized. The phenomenon of the maximum E, SNR, or minimum R disappears gradually as the echo or noise decreases from high levels (e.g., 10 photoelectrons/echo or an equivalent background noise of 10 photoelectrons/range gate). Further, higher attenuation, which shows advantages under strong echo or noise conditions, yields a larger improvement in E for longer dead times; and, with the reduction of the dead time or the noise, the maximum E gradually increases, and the corresponding optimum attenuation level becomes slighter. Additionally, we found that, as the optical attenuation increases, E decreases to 0, R changes from a negative value to 0, and R is minimized, becomes slightly worse, and reaches a constant. Moreover, the shorter dead times, which show advantages when they are shorter than the end time of the echo, lead to a larger E, better R, and slightly worse R than the longer ones.
对于使用盖革模式雪崩光电二极管（GmAPD）的激光雷达（LADAR）系统，衰减回波和背景噪声会同时影响GmAPD输出的原始数据，并最终影响检测性能。在本研究中，我们建立了一个模型，该模型适用于具有光学衰减的基于GmAPD的LADAR，也适用于任何具有死区时间的典型单光子探测器（例如光电倍增管）；因此，针对不同死区时间和信号噪声条件下各种衰减水平下的信号检测数的数学期望（E）、噪声检测数的数学期望（E）、信噪比（SNR）以及距离偏差（绝对误差，R）和精度（标准差，R）进行了全面而基础的研究。我们观察到：一方面，存在一个最佳衰减水平，在该水平下E和SNR最大化；另一方面，对于较短的死区时间存在另一个最佳衰减水平，在该水平下R最小化。随着回波或噪声从高水平（例如10个光电子/回波或10个光电子/距离门的等效背景噪声）降低，E、SNR最大或R最小的现象逐渐消失。此外，更高的衰减在强回波或噪声条件下显示出优势，对于较长的死区时间，E的提升更大；并且，随着死区时间或噪声的减小，最大E逐渐增加，相应的最佳衰减水平变得更轻微。此外，我们发现，随着光学衰减增加，E减小到0，R从负值变为0，并且R最小化，变得稍差，然后达到一个常数。而且，当死区时间短于回波结束时间时显示出优势的较短死区时间，会导致比长死区时间更大的E、更好的R和稍差的R。
