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Research on the optimal optical attenuation in a laser radar using a Geiger-mode APD.

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 (ES), the mathematical expectation of the number of noise detections (EN), the signal-to-noise ratio (SNR), and the range bias (absolute error, Rb) and precision (standard deviation, Rp) 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 ES and SNR are maximized; on the other hand, there exists another optimum attenuation level for shorter dead times, at which Rp is minimized. The phenomenon of the maximum ES, SNR, or minimum Rp 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 ES for longer dead times; and, with the reduction of the dead time or the noise, the maximum ES gradually increases, and the corresponding optimum attenuation level becomes slighter. Additionally, we found that, as the optical attenuation increases, EN decreases to 0, Rb changes from a negative value to 0, and Rp 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 ES, better Rb, and slightly worse Rp than the longer ones.