Waveform model of a laser altimeter for an elliptical Gaussian beam

Ma Yue; Wang Mingwei; Li Guoyuan; Lu Xiushan; Yang Fanlin

doi:10.1364/AO.55.001957

Applied Optics
Vol. 55,
Issue 8,
pp. 1957-1965
(2016)
•https://doi.org/10.1364/AO.55.001957

Waveform model of a laser altimeter for an elliptical Gaussian beam

Ma Yue, Wang Mingwei, Li Guoyuan, Lu Xiushan, and Yang Fanlin

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Ma Yue, Wang Mingwei, Li Guoyuan, Lu Xiushan, and Yang Fanlin, "Waveform model of a laser altimeter for an elliptical Gaussian beam," Appl. Opt. 55, 1957-1965 (2016)

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Abstract

The current waveform model of a laser altimeter is based on the Gaussian laser beam of the fundamental mode, whose cross section is a circular spot, whereas some of the cross sections of Geoscience Laser Altimeter System lasers are closer to elliptical spots. Based on the expression of the elliptical Gaussian beam and the waveform theory of laser altimeters, the primary parameters of an echo waveform were derived. In order to examine the deduced expressions, a laser altimetry waveform simulator and waveform processing software were programmed and improved under the circumstance of an elliptical Gaussian beam. The result shows that all the biases between the theoretical and simulated waveforms were less than 0.5%, and the derived model of an elliptical spot is universal and can also be used for the conventional circular spot. The shape of the waveforms is influenced by the ellipticity of the laser spot, the target slope, and the “azimuth angle” between the major axis and the slope direction. This article provides the waveform theoretical basis of a laser altimeter under an elliptical Gaussian beam.

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Group	Laser Mode	Slope	Roughness (m)	Azimuth Angle (°)	Theoretical Width (ns)	Simulated Width (ns)	Bias (ns)
1	Circular	0	0	Arbitrary	2.37	2.37	0.00
1	Elliptical $R = 2$	0	0	Arbitrary	2.37	2.37	0.00
2	Circular	0	0.1	Arbitrary	2.47	2.47	0.00
2	Elliptical $R = 2$	0	0.1	Arbitrary	2.47	2.47	0.00
3	Circular	0.01	0	Arbitrary	5.00	5.00	0.00
	Elliptical $R = 2$			0	6.66	6.66	0.00
				30	6.09	6.07	$+ 0.02$
				45	5.46	5.44	$+ 0.02$
				60	4.75	4.73	$+ 0.02$
				90	3.91	3.91	0.00
4	Circular	0.01	0.1	Arbitrary	5.04	5.04	0.00
	Elliptical $R = 2$			0	6.69	6.68	$+ 0.01$
	Elliptical $R = 2$			90	3.97	3.97	0.00
5	Circular	0.01	0.3	Arbitrary	5.38	5.39	−0.01
	Elliptical $R = 2$			0	6.95	6.93	$+ 0.02$
				45	5.82	5.80	$+ 0.02$
				90	4.39	4.38	$+ 0.01$
6	Circular	0.1	0	Arbitrary	44.06	44.06	0.00
	Elliptical $R = 2$			0	62.27	62.21	$+ 0.00$
				30	56.14	56.05	$+ 0.09$
				45	49.25	49.14	$+ 0.11$
				60	41.23	41.07	$+ 0.16$
				90	31.20	31.20	0.00
7	Circular	0.1	0.3	Arbitrary	44.11	44.12	−0.01
	Elliptical $R = 2$			0	62.30	62.30	0.00
				45	49.29	49.19	$+ 0.10$
				90	31.27	31.25	$+ 0.02$
8	Circular	0.01	0	Arbitrary	5.00	5.00	0.00
	Elliptical $R = 1.5$			0	5.89	5.89	0.00
	Elliptical $R = 1.5$			90	4.31	4.31	0.00
9	Circular	0.01	0	Arbitrary	5.00	5.00	0.00
	Elliptical $R = 1.2$			0	5.37	5.37	0.00
	Elliptical $R = 1.2$			90	4.67	4.67	0.00

Group	Laser Mode	Azimuth angle (°)	Inversion Slope	Bias	Bias Percentage (%)
1	Circular	Arbitrary	0.1000	0.0000	—
	Elliptical $R = 1.2$	0	0.1095	0.0095	9.5
	Elliptical $R = 1.2$	90	0.0913	−0.0087	8.7
2	Circular	Arbitrary	0.0100	0.0000	—
	Elliptical $R = 1.5$	0	0.1225	0.0225	22.5
	Elliptical $R = 1.5$	90	0.0816	−0.0184	18.4
4	Circular	Arbitrary	0.1000	0.0000	—
	Elliptical $R = 2$	0	0.1414	0.0414	41.4
	Elliptical $R = 2$	90	0.0707	−0.0293	29.3

Group	Laser Mode	Slope	Roughness (m)	Azimuth Angle (°)	Theoretical Width (ns)	Simulated Width (ns)	Bias (ns)
1	Circular	0	0	Arbitrary	2.37	2.37	0.00
1	Elliptical $R = 2$	0	0	Arbitrary	2.37	2.37	0.00
2	Circular	0	0.1	Arbitrary	2.47	2.47	0.00
2	Elliptical $R = 2$	0	0.1	Arbitrary	2.47	2.47	0.00
3	Circular	0.01	0	Arbitrary	5.00	5.00	0.00
	Elliptical $R = 2$			0	6.66	6.66	0.00
				30	6.09	6.07	$+ 0.02$
				45	5.46	5.44	$+ 0.02$
				60	4.75	4.73	$+ 0.02$
				90	3.91	3.91	0.00
4	Circular	0.01	0.1	Arbitrary	5.04	5.04	0.00
	Elliptical $R = 2$			0	6.69	6.68	$+ 0.01$
	Elliptical $R = 2$			90	3.97	3.97	0.00
5	Circular	0.01	0.3	Arbitrary	5.38	5.39	−0.01
	Elliptical $R = 2$			0	6.95	6.93	$+ 0.02$
				45	5.82	5.80	$+ 0.02$
				90	4.39	4.38	$+ 0.01$
6	Circular	0.1	0	Arbitrary	44.06	44.06	0.00
	Elliptical $R = 2$			0	62.27	62.21	$+ 0.00$
				30	56.14	56.05	$+ 0.09$
				45	49.25	49.14	$+ 0.11$
				60	41.23	41.07	$+ 0.16$
				90	31.20	31.20	0.00
7	Circular	0.1	0.3	Arbitrary	44.11	44.12	−0.01
	Elliptical $R = 2$			0	62.30	62.30	0.00
				45	49.29	49.19	$+ 0.10$
				90	31.27	31.25	$+ 0.02$
8	Circular	0.01	0	Arbitrary	5.00	5.00	0.00
	Elliptical $R = 1.5$			0	5.89	5.89	0.00
	Elliptical $R = 1.5$			90	4.31	4.31	0.00
9	Circular	0.01	0	Arbitrary	5.00	5.00	0.00
	Elliptical $R = 1.2$			0	5.37	5.37	0.00
	Elliptical $R = 1.2$			90	4.67	4.67	0.00

Group	Laser Mode	Azimuth angle (°)	Inversion Slope	Bias	Bias Percentage (%)
1	Circular	Arbitrary	0.1000	0.0000	—
	Elliptical $R = 1.2$	0	0.1095	0.0095	9.5
	Elliptical $R = 1.2$	90	0.0913	−0.0087	8.7
2	Circular	Arbitrary	0.0100	0.0000	—
	Elliptical $R = 1.5$	0	0.1225	0.0225	22.5
	Elliptical $R = 1.5$	90	0.0816	−0.0184	18.4
4	Circular	Arbitrary	0.1000	0.0000	—
	Elliptical $R = 2$	0	0.1414	0.0414	41.4
	Elliptical $R = 2$	90	0.0707	−0.0293	29.3

Abstract

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Equations (25)

Applied Optics