Analytical waveform generation from small objects in lidar bathymetry

H. Michael Tulldahl; K. Ove Steinvall

doi:10.1364/AO.38.001021

Applied Optics
Vol. 38,
Issue 6,
pp. 1021-1039
(1999)
•https://doi.org/10.1364/AO.38.001021

Analytical waveform generation from small objects in lidar bathymetry

H. Michael Tulldahl and K. Ove Steinvall

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H. Michael Tulldahl and K. Ove Steinvall, "Analytical waveform generation from small objects in lidar bathymetry," Appl. Opt. 38, 1021-1039 (1999)

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Abstract

We present a model to simulate receiver waveforms from an airborne sea-depth-sounding lidar to compare the influence that is due to different shapes of objects placed on the sea bottom. The objects are of size 1 m³, and the bottom depths are 5–12 m. We use an existing analytical beam-propagation model and divide the bottom into squares. For each element on the bottom grid we create a transmitted and a reflected waveform. The waveforms are summed, yielding a total contribution from all bottom elements. We compare two object types, cylinder and cube, and find that the difference in the receiver waveform is small between these objects. Simulated waveforms are compared with experimental data from the Swedish Hawk Eye system and show good agreement.

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Element	Description
A	Horizontal, flat bottom with area 1 m × 1 m
B	Horizontal cube with side 1 m
C	Horizontal cylinder with radius 0.5 m and length 1 m

Laser system	Value	Unit	Atmosphere	Value		Unit
E ₀ (λ = 532 nm)	3	mJ	Two-way atmospheric loss (T _atm ²)	0.9
Laser spot e ^-1/2 minor axis on the water surface (σ_s)a	0.6	m	rms Scattering angle owing to maritime aerosols (σ_β)a	0.06		rad
Pulse length (FWHM) (t ₀)	7	ns
			Coastal Water Type	Clear	Average
Flight altitude (H)	300	m	Refractive index (n _w)	1.333	1.333
Beam off-nadir angle (θ₀)	20	°	Attenuation coefficient (c)	0.5	1	m^-1
Receiver system			Volume scattering function at π [β(π)]	0.0014	0.0025	m^-1 sr^-1
FOV	17	mrad	Scattering coefficient (b)	0.35	0.8	m^-1
Receiver area (A _R)	0.025	m²	Absorption coefficient (a)	0.15	0.2	m^-1
Optical efficiency (η_opt)	0.5		rms Single scattering angle (Θ_R)	0.39	0.40	rad
Water surface			Single scattering albedo (ω₀)	0.7	0.8
Water surface reflectivity (ρ_s)	0.02		Scattering probability for Θ > 45° (b̃₄₅)b	0.045	0.055
Standard deviations of the x and y wave-slope variations (σ_x, σ_y)a	0.2, 0.2	rad, rad	Variance of the scattering angle for Θ < 45° (〈Θ₄₅ ²〉)b	0.037	0.051	rad²
Bottom and objects			Small-angle scattering albedo [ω_sa = ω₀(1- b̃₄₅)]	0.67	0.76	m^-1
Object or bottom reflectivity (ρ_m; m means material)	0.10		Diffuse attenuation coefficient (K)	0.17	0.25	m^-1

Required Minimum Level of Relative Object Pulse Height	Necessary Shot-to-Shot Distance (m)
	Bottom Depth 7 m		Bottom Depth 10 m
	Cube	Cylinder	Cube	Cylinder
0.1	2.9	2.7	2.6	2.5
0.2	2.2	2.0	1.5	1.3

Estimate
Parameter	Element A, Flat	Element B, Cube	Element C, Cylinder
α	2.90	2.31	3.82
L ₁₀ (ns)	0.53	0.55	0.74
L ₁₁ (ns)	1.26	1.82	1.65
L ₁₂ (ns)	1.57	4.77	4.01 × sin² Φ_i
\|ε_σ\| (ns)	<0.25	<0.3	<0.4
L ₂₀	-5.855	-3.647	-4.061
L ₂₁	-1.188	-0.642	-0.753
L ₂₂	9.736	10.004	10.032
L ₂₃	1.089 × cos θ_i	0.687 × η̂_i · η̂_v	0.914 × η̂_i · η̂_v
L ₂₄	1.864 × cos θ_v	0	0
\|ε_ρ\|	<1%	<5%	<6%
L ₃₀ (ns)	-0.91	-0.94	-0.83
L ₃₁ (ns)	-4.98	-4.95	-6.84
L ₃₂ (ns)	-2.44	-2.54	-5.59 × sin² Φ_i
L ₃₃ (ns)	0	0	-0.27 × sin² Φ_i
\|ε_t\| (ns)	<0.25	<0.4	<0.6

Element	Description
A	Horizontal, flat bottom with area 1 m × 1 m
B	Horizontal cube with side 1 m
C	Horizontal cylinder with radius 0.5 m and length 1 m

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Applied Optics