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

Zhijian Li; Jiancheng Lai; Chunyong Wang; Wei Yan; Zhenhua Li

doi:10.1364/AO.57.007415

Applied Optics
Vol. 57,
Issue 26,
pp. 7415-7426
(2018)
•https://doi.org/10.1364/AO.57.007415

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

Zhijian Li, Jiancheng Lai, Chunyong Wang, Wei Yan, and Zhenhua Li

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Zhijian Li, Jiancheng Lai, Chunyong Wang, Wei Yan, and Zhenhua Li, "Research on the optimal optical attenuation in a laser radar using a Geiger-mode APD," Appl. Opt. 57, 7415-7426 (2018)

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Abstract

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

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		Noise Rate M Counts Per Second
		0.5	1	2	3	4	5
PEs Per Echo	1	0	0	0	0	0	0
	2	0	0	0.03	0.06	0.09	0.11
	3	0	0.07	0.15	0.20	0.23	0.25
	4	0	0.16	0.24	0.29	0.33	0.35
	5	0	0.23	0.31	0.36	0.40	0.42
	6	0.05	0.28	0.37	0.42	0.45	0.48
	7	0.11	0.33	0.42	0.47	0.50	0.53
	8	0.15	0.38	0.46	0.51	0.54	0.57
	9	0.20	0.42	0.49	0.55	0.58	0.61
	10	0.23	0.45	0.53	0.58	0.61	0.64
	12	0.30	0.51	0.59	0.63	0.67	0.70
	14	0.36	0.56	0.63	0.68	0.72	0.74
	16	0.41	0.61	0.68	0.72	0.76	0.79
	18	0.45	0.65	0.72	0.76	0.80	0.82
	20	0.49	0.68	0.75	0.80	0.83	0.86

		Noise Rate M Counts Per Second
		6	7	8	9	10
PEs/Echo	1	0	0.04	0.08	0.12	0.15
	2	0.14	0.16	0.19	0.22	0.25
	3	0.26	0.28	0.30	0.31	0.33
	4	0.36	0.38	0.39	0.40	0.41
	5	0.44	0.46	0.47	0.48	0.49
	6	0.50	0.52	0.53	0.54	0.55
	7	0.55	0.57	0.58	0.59	0.60
	8	0.59	0.61	0.63	0.64	0.65
	9	0.63	0.65	0.67	0.68	0.69
	10	0.66	0.68	0.70	0.71	0.72
	12	0.72	0.74	0.76	0.77	0.78
	14	0.77	0.79	0.80	0.82	0.83
	16	0.81	0.83	0.84	0.86	0.87
	18	0.84	0.87	0.88	0.90	0.91
	20	0.88	0.90	0.91	0.93	0.94

		Noise Rate M Counts Per Second
		0.5	1	2	3	4	5
PEs/Echo	1	0	0	0.17	0.30	0.41	0.49
	2	0	0.10	0.27	0.38	0.47	0.54
	3	0	0.20	0.34	0.45	0.53	0.59
	4	0	0.27	0.40	0.50	0.57	0.63
	5	0	0.33	0.45	0.54	0.61	0.67
	6	0.05	0.38	0.50	0.58	0.65	0.70
	7	0.11	0.42	0.54	0.62	0.68	0.73
	8	0.15	0.46	0.57	0.65	0.71	0.75
	9	0.20	0.50	0.60	0.68	0.73	0.78
	10	0.23	0.53	0.63	0.70	0.76	0.80
	12	0.30	0.58	0.68	0.75	0.80	0.84
	14	0.36	0.63	0.72	0.79	0.84	0.88
	16	0.41	0.67	0.76	0.82	0.87	0.91
	18	0.45	0.71	0.80	0.86	0.90	0.94
	20	0.49	0.74	0.83	0.89	0.93	0.97

		Noise Rate M Counts Per Second
		6	7	8	9	10
PEs/Echo	1	0.56	0.62	0.67	0.72	0.76
	2	0.61	0.66	0.71	0.75	0.79
	3	0.65	0.70	0.74	0.78	0.82
	4	0.68	0.73	0.77	0.81	0.84
	5	0.72	0.76	0.80	0.84	0.87
	6	0.75	0.79	0.83	0.86	0.89
	7	0.77	0.82	0.85	0.88	0.91
	8	0.80	0.84	0.87	0.90	0.93
	9	0.82	0.86	0.89	0.92	0.95
	10	0.84	0.88	0.91	0.94	0.97
	12	0.88	0.92	0.95	0.97	1.00
	14	0.92	0.95	0.98	1.00	1.03
	16	0.95	0.98	1.01	1.03	1.06
	18	0.97	1.00	1.03	1.06	1.08
	20	1.00	1.03	1.06	1.08	1.10

		Noise Rate M Counts Per Second
		0.5	1	2	3	4	5
PEs Per Echo	1	0	0	0	0	0	0
	2	0	0	0.03	0.06	0.09	0.11
	3	0	0.07	0.15	0.20	0.23	0.25
	4	0	0.16	0.24	0.29	0.33	0.35
	5	0	0.23	0.31	0.36	0.40	0.42
	6	0.05	0.28	0.37	0.42	0.45	0.48
	7	0.11	0.33	0.42	0.47	0.50	0.53
	8	0.15	0.38	0.46	0.51	0.54	0.57
	9	0.20	0.42	0.49	0.55	0.58	0.61
	10	0.23	0.45	0.53	0.58	0.61	0.64
	12	0.30	0.51	0.59	0.63	0.67	0.70
	14	0.36	0.56	0.63	0.68	0.72	0.74
	16	0.41	0.61	0.68	0.72	0.76	0.79
	18	0.45	0.65	0.72	0.76	0.80	0.82
	20	0.49	0.68	0.75	0.80	0.83	0.86

Abstract

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Figures (11)

Tables (4)

Equations (30)

Applied Optics