George C. Papen, William M. Pfenninger, and Dale M. Simonich, "Sensitivity analysis of Na narrowband wind–temperature lidar systems," Appl. Opt. 34, 480-498 (1995)
The performance and measurement accuracy of Na narrowband wind–temperature lidar systems are characterized. Error budgets are derived that include several effects not previously reported, such as power-dependent spectral characteristics in the frequency reference, magnetic-field-dependent oscillator line strengths (Hanle effect), saturation, and optical pumping. It is shown that the overall system uncertainty is dependent on the power, pulse temporal characteristics, and beam divergence of the laser transmitter. Results indicate that even systems with significant saturation can produce accurate measurements, which implies the prospect of continuous daytime wind and temperature measurements on semidiurnal and diurnal time periods.
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rms Jitter Measurements at fa for the University of Illinois Wind-Temperature Lidar for the Night of 17 January 1993
Location
f (MHz)
σj (MHz)
f−
−1238
1.22
fa
−638
1.48
f+
−38
1.45
fc
232
1.41
Table 2
Ratio Ra Calculated with Eqs. (7) and (10)–(12), Measurement Errors, and Derivativesb Calculated with Eq. (13) for Wind and Temperature Differentials
Temperature Differentials
Wind Differentials
W1
W2
Ratio R
RT= 0.281
RW1 = 1.07
RW = 0.460
Calculated with
Nfc/Nfa
Nf+/Nf−
Nf+ /Nfa
Error
Derivatives
For an operating point Q with T = 200 K, vR = 0 m/s, fa = −638 MHz, fc = 232 MHz, f− = −1238 MHz, f+ = 38 MHz, and σrms = 60 MHz.
Magnitudes of derivatives with respect to the other system parameters.
Table 3
Magnitude of Wind- and Temperature-Measurement Errors for Each System Parameter and Measurement Techniquea
Blank entries occur because only two frequencies are used to determine each system's measurement.
Calculated with Δf = (σj2 + σc2)1/2 σj jitter error (see Table 1) and a σc calibation error of 2 MHz.
Calculated for Δt = 60 s with weighted averaging through the use of ωc = 5 min for columns 1 and 2 (see Appendix C for details) and Δt ∼ 1 s, causing negligible error, for column 3.
Table 4
Total System Error for Each Measurement Technique and the Number of Photons Required to Produce the Same Error as the Total System Errora
Pulse Characteristics
Temperature Uncertainty
Wind Uncertainty
Error in T (K)
Nfa
Error in W1 (m/s)
Nfa
Error in W2 (m/s)
Nfa
35 mJ and 1 mrad
0.53
∼226,000
1.01
∼12,400
2.01
∼53,900
35 mJ and 0.5 mrad
0.54
∼226,000
1.01
∼12,400
2.01
∼53,900
100 mJ and 1 mrad
0.53
∼226,000
1.01
∼12,400
2.01
∼53,900
100 mJ and 0.1 mrad
1.22
∼43,000
1.2
∼9,300
2.51
∼34,600
Calculated for 7-ns pulses at 92 km with Δt = 60 s.
Table 5
Relative Oscillator Strengths for a Beam Traveling West through the Vapor Cell
Transition
Horizontal
Vertical
Ratio (H/V)
1
5
5
1
2
5.76
5.19
1.11
3
2
2
1
4
16.55
14.62
1.13
5
5
5
1
6
0.97
0.99
0.98
Table 6
Magnitude of the Percent Relative Density Errora as a Function of z and the Time Between Profiles Δt
Δt
z
84 km
88 km
92 km
96 km
100 km
10 s
1.60
0.968
0.333
0.301
0.936
30 s
4.81
2.90
1.00
0.904
2.81
60 s
9.62
5.81
2.00
1.81
5.62
Relative density error [ΔR′(Δt)]2 calculated with Eq. (C9) for parameter values σ0 = 4.2 km, H = 6 km, z0 = 92 km, γ = 1.4, Trms = 44 min, and (〈ra2〉)1/2 = 5.6%.
Tables (6)
Table 1
rms Jitter Measurements at fa for the University of Illinois Wind-Temperature Lidar for the Night of 17 January 1993
Location
f (MHz)
σj (MHz)
f−
−1238
1.22
fa
−638
1.48
f+
−38
1.45
fc
232
1.41
Table 2
Ratio Ra Calculated with Eqs. (7) and (10)–(12), Measurement Errors, and Derivativesb Calculated with Eq. (13) for Wind and Temperature Differentials
Temperature Differentials
Wind Differentials
W1
W2
Ratio R
RT= 0.281
RW1 = 1.07
RW = 0.460
Calculated with
Nfc/Nfa
Nf+/Nf−
Nf+ /Nfa
Error
Derivatives
For an operating point Q with T = 200 K, vR = 0 m/s, fa = −638 MHz, fc = 232 MHz, f− = −1238 MHz, f+ = 38 MHz, and σrms = 60 MHz.
Magnitudes of derivatives with respect to the other system parameters.
Table 3
Magnitude of Wind- and Temperature-Measurement Errors for Each System Parameter and Measurement Techniquea
Blank entries occur because only two frequencies are used to determine each system's measurement.
Calculated with Δf = (σj2 + σc2)1/2 σj jitter error (see Table 1) and a σc calibation error of 2 MHz.
Calculated for Δt = 60 s with weighted averaging through the use of ωc = 5 min for columns 1 and 2 (see Appendix C for details) and Δt ∼ 1 s, causing negligible error, for column 3.
Table 4
Total System Error for Each Measurement Technique and the Number of Photons Required to Produce the Same Error as the Total System Errora
Pulse Characteristics
Temperature Uncertainty
Wind Uncertainty
Error in T (K)
Nfa
Error in W1 (m/s)
Nfa
Error in W2 (m/s)
Nfa
35 mJ and 1 mrad
0.53
∼226,000
1.01
∼12,400
2.01
∼53,900
35 mJ and 0.5 mrad
0.54
∼226,000
1.01
∼12,400
2.01
∼53,900
100 mJ and 1 mrad
0.53
∼226,000
1.01
∼12,400
2.01
∼53,900
100 mJ and 0.1 mrad
1.22
∼43,000
1.2
∼9,300
2.51
∼34,600
Calculated for 7-ns pulses at 92 km with Δt = 60 s.
Table 5
Relative Oscillator Strengths for a Beam Traveling West through the Vapor Cell
Transition
Horizontal
Vertical
Ratio (H/V)
1
5
5
1
2
5.76
5.19
1.11
3
2
2
1
4
16.55
14.62
1.13
5
5
5
1
6
0.97
0.99
0.98
Table 6
Magnitude of the Percent Relative Density Errora as a Function of z and the Time Between Profiles Δt
Δt
z
84 km
88 km
92 km
96 km
100 km
10 s
1.60
0.968
0.333
0.301
0.936
30 s
4.81
2.90
1.00
0.904
2.81
60 s
9.62
5.81
2.00
1.81
5.62
Relative density error [ΔR′(Δt)]2 calculated with Eq. (C9) for parameter values σ0 = 4.2 km, H = 6 km, z0 = 92 km, γ = 1.4, Trms = 44 min, and (〈ra2〉)1/2 = 5.6%.
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