The maximum measurement range of a laser altimeter can be extended by averaging the measurements from multiple laser shots at the same target. We present the principles of operation and design of such a multishot laser altimeter, which uses a Si avalanche photodiode detector. As an example, the performance of a spaceborne multishot altimeter containing components similar to those of the single-shot Mars Observer Laser Altimeter are given under operating conditions that would be encountered near Saturn. With 100-shot averages, we show that the multishot laser altimeter is capable of accurate ranging at fly-by distances of 10,000 km from an icy satellite. With 100-shot averages, the minimum optical signal level at a 90% correct-measurement probability under nighttime background is 9.8 detected signal photons per pulse as compared with 76 photons per pulse with a single shot.
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Laser Altimeter and Target Parameter Values Used in the Numerical Example
Parameter
Value
Laser altimeter parameters
Laser wavelength
λ = 1.064 μm
Laser-pulse energy
Et = 40 mJ
Laser-pulse width
τ = 20 ns
Laser beam divergence angle
θD = 0.25 mrad
Receiver telescope diameter
ϕ = 0.5 m
Receiver telescope FOV
θFOV = 0.85 mrad
Receiver optical bandwidth
Δλ = 2 nm
Optics transmission throughput
ηs = 50%
Target parameters
Target surface reflectivity
rdiff = 0.5 (ice), 0.2 (terrain)
Daytime solar illumination intensity
Isolr = 7.965 (mW m−2 nm−1)
Day-night solar illumination ratio
1000:1
Reflected laser-pulse width
Tp = 180 ns
Range-gate interval
TRG = 667 μs (100 km)
Si APD parameters
Ionization coefficient ratio
keff = 0.0065
Average APD Gain
G = 100 to 600
APD load resistance
RL = 100 kΩ
Equivalent noise temperature
Tn = 750 K
Quantum efficiency
ηq = 30% (enhanced for λ = 1.064 μm)
ηq = 5% (RCA-C30902S)
Bulk leakage current
Ib = 50 pA (enhanced for λ = 1.064 μm)
Ib = 0.5 pA (RCA-C30902S)
Surface leakage current
Is = 12 nA
Table 2
Miss Probabilities 1—PD and Measurement Probabilities Pmeas for a Multishot Laser Altimeter with the Threshold Setting nthre as a Parametera
nthre Pfa Kfa
170 0.363 1300
180 0.188 700
190 0.0782 290
200 0.0255 96
Range (km)
λsTp
1 − PD
Pmeas
1 − PD
Pmeas
1 − PD
Pmeas
1 − PD
Pmeas
N = 10 shots
3500
79.6
0.00544
1.000
0.0161
1.000
0.0410
1.000
4000
61.0
0.0294
0.990
0.0716
1.000
0.150
0.999
4500
48.2
0.0809
0.928
0.169
0.975
0.304
0.976
5000
39.0
0.153
0.758
0.285
0.848
0.456
0.841
5500
32.2
0.232
0.525
0.396
0.609
0.580
0.591
N = 30 shots
5000
39.0
0.0693
1.000
0.153
1.000
0.285
1.000
5500
32.2
0.115
0.993
0.232
0.999
0.396
0.999
6000
27.1
0.164
0.950
0.308
0.982
0.490
0.977
6500
23.2
0.212
0.834
0.376
0.908
0.567
0.880
7000
19.9
0.257
0.656
0.435
0.754
0.628
0.695
N = 100 shots
7500
17.3
0.297
0.999
0.485
1.000
0.676
0.997
8000
15.2
0.333
0.990
0.527
0.992
0.714
0.973
8500
13.5
0.364
0.956
0.561
0.960
0.744
0.901
9000
12.0
0.391
0.877
0.591
0.881
0.769
0.771
9500
10.8
0.415
0.755
0.615
0.757
0.789
0.611
Number of laser firings are (a) N = 10 shots, (b) N = 30 shots, and (c) N = 100 shots. The photodetector used was assumed to be a Si APD enhanced for operating at λ = 1.064 μm. The APD gain was G = 200, target reflectivity rdiff = 0.50 (icy surface), and background noise λ0Tp = 39.7 (under daytime background light). Other parameter values are listed in Table 1.
Table 3
Maximum Operational Range of the Multistat Laser Altimeter Under Pmeas > 0.90 with the Enhanced Si APD, and RCA-C30902S Si APD, and a Hypothetical Intermediate APD for Day and Night Target Background Lighta
η(%)
Ib (pA)
Rmax (km) (Day/Night)
10 Shots
30 Shots
100 Shots
30
50
4500/5000
6500/7000
8500/10,000
15
5
4000/5500
5500/8000
7000/11,000
5
0.5
3000/5000
4000/7000
6000/10,000
Other parameter values used are listed in Table 1. Optimal average APD gains were used in each case.
Table 4
Maximum Range of the Multishot Laser Altimeter Versus Pulse Width with the Enhanced Si APD Under Pmeas ≥ 0.90a
Tp(ns)
Rmas (km) (Day/Night)
10 Shots
30 Shots
100 Shots
90
5500/6000
7000/8000
10,000/11,000
180
4500/5000
6500/7000
8500/10,000
360
4000/4500
5500/6000
7500/8500
720
3500/4000
4500/5000
6500/7500
Other parameter values used are listed in Table 1. Optimal average APD gains were used in each case.
Tables (4)
Table 1
Laser Altimeter and Target Parameter Values Used in the Numerical Example
Parameter
Value
Laser altimeter parameters
Laser wavelength
λ = 1.064 μm
Laser-pulse energy
Et = 40 mJ
Laser-pulse width
τ = 20 ns
Laser beam divergence angle
θD = 0.25 mrad
Receiver telescope diameter
ϕ = 0.5 m
Receiver telescope FOV
θFOV = 0.85 mrad
Receiver optical bandwidth
Δλ = 2 nm
Optics transmission throughput
ηs = 50%
Target parameters
Target surface reflectivity
rdiff = 0.5 (ice), 0.2 (terrain)
Daytime solar illumination intensity
Isolr = 7.965 (mW m−2 nm−1)
Day-night solar illumination ratio
1000:1
Reflected laser-pulse width
Tp = 180 ns
Range-gate interval
TRG = 667 μs (100 km)
Si APD parameters
Ionization coefficient ratio
keff = 0.0065
Average APD Gain
G = 100 to 600
APD load resistance
RL = 100 kΩ
Equivalent noise temperature
Tn = 750 K
Quantum efficiency
ηq = 30% (enhanced for λ = 1.064 μm)
ηq = 5% (RCA-C30902S)
Bulk leakage current
Ib = 50 pA (enhanced for λ = 1.064 μm)
Ib = 0.5 pA (RCA-C30902S)
Surface leakage current
Is = 12 nA
Table 2
Miss Probabilities 1—PD and Measurement Probabilities Pmeas for a Multishot Laser Altimeter with the Threshold Setting nthre as a Parametera
nthre Pfa Kfa
170 0.363 1300
180 0.188 700
190 0.0782 290
200 0.0255 96
Range (km)
λsTp
1 − PD
Pmeas
1 − PD
Pmeas
1 − PD
Pmeas
1 − PD
Pmeas
N = 10 shots
3500
79.6
0.00544
1.000
0.0161
1.000
0.0410
1.000
4000
61.0
0.0294
0.990
0.0716
1.000
0.150
0.999
4500
48.2
0.0809
0.928
0.169
0.975
0.304
0.976
5000
39.0
0.153
0.758
0.285
0.848
0.456
0.841
5500
32.2
0.232
0.525
0.396
0.609
0.580
0.591
N = 30 shots
5000
39.0
0.0693
1.000
0.153
1.000
0.285
1.000
5500
32.2
0.115
0.993
0.232
0.999
0.396
0.999
6000
27.1
0.164
0.950
0.308
0.982
0.490
0.977
6500
23.2
0.212
0.834
0.376
0.908
0.567
0.880
7000
19.9
0.257
0.656
0.435
0.754
0.628
0.695
N = 100 shots
7500
17.3
0.297
0.999
0.485
1.000
0.676
0.997
8000
15.2
0.333
0.990
0.527
0.992
0.714
0.973
8500
13.5
0.364
0.956
0.561
0.960
0.744
0.901
9000
12.0
0.391
0.877
0.591
0.881
0.769
0.771
9500
10.8
0.415
0.755
0.615
0.757
0.789
0.611
Number of laser firings are (a) N = 10 shots, (b) N = 30 shots, and (c) N = 100 shots. The photodetector used was assumed to be a Si APD enhanced for operating at λ = 1.064 μm. The APD gain was G = 200, target reflectivity rdiff = 0.50 (icy surface), and background noise λ0Tp = 39.7 (under daytime background light). Other parameter values are listed in Table 1.
Table 3
Maximum Operational Range of the Multistat Laser Altimeter Under Pmeas > 0.90 with the Enhanced Si APD, and RCA-C30902S Si APD, and a Hypothetical Intermediate APD for Day and Night Target Background Lighta
η(%)
Ib (pA)
Rmax (km) (Day/Night)
10 Shots
30 Shots
100 Shots
30
50
4500/5000
6500/7000
8500/10,000
15
5
4000/5500
5500/8000
7000/11,000
5
0.5
3000/5000
4000/7000
6000/10,000
Other parameter values used are listed in Table 1. Optimal average APD gains were used in each case.
Table 4
Maximum Range of the Multishot Laser Altimeter Versus Pulse Width with the Enhanced Si APD Under Pmeas ≥ 0.90a
Tp(ns)
Rmas (km) (Day/Night)
10 Shots
30 Shots
100 Shots
90
5500/6000
7000/8000
10,000/11,000
180
4500/5000
6500/7000
8500/10,000
360
4000/4500
5500/6000
7500/8500
720
3500/4000
4500/5000
6500/7500
Other parameter values used are listed in Table 1. Optimal average APD gains were used in each case.