Abstract

Criteria for optimizing system parameters in the lidar measurement of atmospheric temperature profiles from simultaneous Raman and elastic returns by use of a three-channel system are discussed and summarized. It is shown that the filter constraints of earlier techniques are removed thereby eliminating the need for the high rejection capability of spectrometers in this type of measurement. Also, SNR is improved, and a greater freedom in the choice of optimum Raman filters is demonstrated.

© 1976 Optical Society of America

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References

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  1. J. Cooney, J. Appl. Meteor. 11, 108 (1972).
  2. J. Cooney, M. Pina, Appl. Opt. 15, 602 (1976).
  3. G. Herzberg, Molecular Spectra and Molecular Structure. 1: Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1950).

1976 (1)

1972 (1)

J. Cooney, J. Appl. Meteor. 11, 108 (1972).

Cooney, J.

J. Cooney, M. Pina, Appl. Opt. 15, 602 (1976).

J. Cooney, J. Appl. Meteor. 11, 108 (1972).

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure. 1: Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1950).

Pina, M.

Appl. Opt. (1)

J. Appl. Meteor. (1)

J. Cooney, J. Appl. Meteor. 11, 108 (1972).

Other (1)

G. Herzberg, Molecular Spectra and Molecular Structure. 1: Spectra of Diatomic Molecules (Van Nostrand, Princeton, 1950).

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Figures (4)

Fig. 1
Fig. 1

Filter integrated RRS spectrum from air excited by 6943 Å at T = 220 K, 260 K, and 300 K. Here, Gaussian filter functions with FWHM of 5 Å (a) and 10 Å (b) are used to generate the spectra.

Fig. 2
Fig. 2

Derivative with respect to temperature of the filter integrated RRS spectrum from air at T = 220 K, 260 K, and 300 K. Here, Gaussian functions with FWHM of 5 Å (a) and 10 Å (b) are used to generate the derivative spectrum.

Fig. 3
Fig. 3

Isometric plot of the system performance parameter (ΔT/T)−1 as a function of central filter wavelengths λ1 and λ2. This result is for the 10-Å filter integrated anti-Stokes RRS spectrum from air at T = 260 K.

Fig. 4
Fig. 4

Uncertainty in the measured ratio R as a function of central filter transmission for several values of rejection for the near filter number 1. The rejection of the far filter number 2 is 106.

Tables (4)

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Table I Central Filter Wavelengths for Optimum System Performance at λ0 = 6943 Å for the 10 Å (FWHM) Single Gaussian Filter and the Special Case R = 1

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Table II Optimum Wavelengths for a Single Component Atmosphere Excited by λ0 = 6943 Å

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Table III Central Filter Wavelengths for Optimum System Performance at λ0 = 6943 Å for the 10 Å (FWHM) Single Gaussian Filter Spectrum

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Table IV Values of the Relative RRS Intensity at the Design Wavelengths of λ1 = 6927 Å and λ2 = 6899 Å for a 10-Å FWHM Single Gaussian Filter Function and the Resulting Values of the Ratio R

Equations (23)

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P ν J , K = P 0 N K Δ r τ ( ν 0 ) F J , K ( T ) σ k ( ν J ) τ ( ν J ) A 4 π r 2 ,
F J , K ( T ) = Q K - 1 g J , K ( 2 J + 1 ) exp ( - E J , K / k T ) ,
J F J , K = 1.
Q K = ( 2 I K + 1 ) 2 k T / 2 h c B 0 , K ,
P 1 , K = J γ 1 ( ν J ) P ν J , K ,
P 1 = K J γ 1 ( ν J ) P ν J , K .
R = P 1 P 2 = K J γ 1 ( ν J ) P ν J , K K J γ 2 ( ν J ) P ν J , K = K J γ 1 ( ν J ) F J , K ( T ) σ K ( ν J ) τ ( ν J ) K J γ 2 ( ν J ) F J , K ( T ) σ K ( ν J ) τ ( ν J ) .
Δ R = R ( P 1 ) 1 / 2 ( 1 + R ) 1 / 2 .
d R d T = R | 1 P 1 d P 1 d T - 1 P 2 d P 2 d T | .
Δ T T = Δ R T ( d R d T ) = ( 1 + R ) 1 / 2 ( P 1 ) 1 / 2 | T P 1 d P 1 d T - T P 2 d P 2 d T | .
1 P d P d T = 1 T ( E J k T - 1 ) .
Δ T T = 1 ( P 1 ) 1 / 2 ( 1 + R ) 1 / 2 1 - 2 ,
T P d P d T = K J γ ( ν J ) F J , K ( T ) ( J , K - 1 ) σ K ( ν J ) τ ( ν J ) K J γ ( ν J ) F J , K ( T ) σ K ( ν J ) τ ( ν J )
S 1 , i = G 1 P 0 , i [ P 1 RRS + γ 1 ( ν 0 ) P 0 el ] ,
S 2 , i = G 2 P 0 , i [ P 2 RRB + γ 2 ( ν 0 ) P 0 el ] .
s 1 , j = G 1 γ 0 ( ν 0 ) γ 1 ( ν 0 ) P 0 , j P 0 el
S 2 , j = G 2 γ 0 ( ν 0 ) γ 2 ( ν 0 ) P 0 , j P 0 el .
R = S 1 , i - P 0 , i P 0 , j 1 γ 0 ( ν 0 ) s 1 , j S 2 , i - P 0 , i P 0 , j 1 γ 0 ( ν 0 ) s 2 , j × G 2 G 1 .
R = S 1 , k - P 0 , k P 0 , l 1 γ 0 ( ν 0 ) s 1 , l S 2 , k - P 0 , k P 0 , l 1 γ 0 ( ν 0 ) s 2 , l × G 1 G 2 .
R = S 1 , i - G 1 G 0 γ 1 ( ν 0 ) γ 0 ( ν 0 ) s 0 , i S 2 , i - G 2 G 0 γ 1 ( ν 0 ) γ 0 ( ν 0 ) s 0 , i × G 2 G 1 ,
Δ R R = 1 ( S 1 , i - s 1 , j ) 1 / 2 × [ 1 + 2 s 1 , j S 1 , i - s i , j + R ( 1 + 2 s 1 , j S 2 , i - s 2 , j ) ] 1 / 2 .
s 1 , j S 1 , i - s 1 , j = γ 1 ( ν 0 ) P 0 el P 1 RRS = γ 1 ( ν 0 ) ( 1 + x ) σ Rayleigh J γ 1 ( ν J ) σ RRS ( ν J ) ,
Δ R R const . 1 [ γ 1 ( ν 1 ) ] 1 / 2 { 1 + σ Rayleigh σ RRS ( ν 1 ) ( 1 + x ) γ 1 ( ν 0 ) γ 1 ( ν 1 ) + R [ 1 + 2 σ Rayleigh σ RRS ( ν 1 ) ( 1 + x ) γ 2 ( ν 0 ) γ 2 ( ν 2 ) ] } 1 / 2 .

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