Abstract

A technique that uses a single effective frequency to represent the effects of finite spectral bandwidth for active and passive measurements centered on an absorption line, a trough region, or a slowly varying spectral feature is described. For Gaussian and rectangular instrumental line shapes, the effective frequency is shown to have a simple form that depends only on the instrumental line shape and bandwidth and not on the absorption line profile. The technique is applicable to a large class of active and passive measurements and simulations in both the laboratory and the atmosphere. Simulations show that the technique yields accuracies better than 0.1% for bandwidths less than 0.2 times the atmospheric linewidth for a rectangular line shape or better than 0.2% for a Gaussian.

© 2004 Optical Society of America

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References

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  1. H. J. Kostkowski, A. M. Bass, “Slit function effects in the direct measurement of absorption line half-widths and intensities,” J. Opt. Soc. Am. 46, 1060–1064 (1956).
    [CrossRef]
  2. P. A. Jansson, “Method for determining the response function of a high-resolution infrared spectrometer,” J. Opt. Soc. Am. 60, 184–191 (1970).
    [CrossRef]
  3. C. L. Korb, C. Y. Weng, “A theoretical study of a two-wavelength lidar technique for the measurement of atmospheric temperature profiles,” J. Appl. Meteorol. 21, 1346–1355 (1982).
    [CrossRef]
  4. C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quantum Spectrosc. Radiat. Transfer 25, 151–157 (1981).
    [CrossRef]
  5. C. L. Korb, C. Y. Weng, “The theory and correction of finite laser bandwidth effects in DIAL experiments,” in Proceedings of the 11th International Laser Radar Conference, J. A. Weinman, ed., NASA Conf. Publ.2228, 78–81 (1982).
  6. R. C. Buck, E. F. Buck, Advanced Calculus (McGraw-Hill, New York, 1965), p. 106.
  7. C. L. Korb, C. Y. Weng, “Differential absorption lidar technique for measurement of the atmospheric pressure profile,” Appl. Opt. 22, 3759–3770 (1983).
    [CrossRef] [PubMed]
  8. R. T. H. Collis, “Lidar,” Adv. Geophys. 13, 113–139 (1969).
    [CrossRef]
  9. S. S. Penner, R. W. Kavanagh, “Radiation from isolated spectral lines with combined Doppler and Lorentz broadening,” J. Opt. Soc. Am. 43, 385–388 (1953).
    [CrossRef]
  10. J. J. Olivero, R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quantum Spectrosc. Radiat. Transfer 17, 233–236 (1977).
    [CrossRef]

1983 (1)

1982 (1)

C. L. Korb, C. Y. Weng, “A theoretical study of a two-wavelength lidar technique for the measurement of atmospheric temperature profiles,” J. Appl. Meteorol. 21, 1346–1355 (1982).
[CrossRef]

1981 (1)

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quantum Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

1977 (1)

J. J. Olivero, R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quantum Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

1970 (1)

1969 (1)

R. T. H. Collis, “Lidar,” Adv. Geophys. 13, 113–139 (1969).
[CrossRef]

1956 (1)

1953 (1)

Bass, A. M.

Buck, E. F.

R. C. Buck, E. F. Buck, Advanced Calculus (McGraw-Hill, New York, 1965), p. 106.

Buck, R. C.

R. C. Buck, E. F. Buck, Advanced Calculus (McGraw-Hill, New York, 1965), p. 106.

Cahen, C.

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quantum Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

Collis, R. T. H.

R. T. H. Collis, “Lidar,” Adv. Geophys. 13, 113–139 (1969).
[CrossRef]

Jansson, P. A.

Kavanagh, R. W.

Korb, C. L.

C. L. Korb, C. Y. Weng, “Differential absorption lidar technique for measurement of the atmospheric pressure profile,” Appl. Opt. 22, 3759–3770 (1983).
[CrossRef] [PubMed]

C. L. Korb, C. Y. Weng, “A theoretical study of a two-wavelength lidar technique for the measurement of atmospheric temperature profiles,” J. Appl. Meteorol. 21, 1346–1355 (1982).
[CrossRef]

C. L. Korb, C. Y. Weng, “The theory and correction of finite laser bandwidth effects in DIAL experiments,” in Proceedings of the 11th International Laser Radar Conference, J. A. Weinman, ed., NASA Conf. Publ.2228, 78–81 (1982).

Kostkowski, H. J.

Longbothum, R. L.

J. J. Olivero, R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quantum Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Megie, G.

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quantum Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

Olivero, J. J.

J. J. Olivero, R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quantum Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Penner, S. S.

Weng, C. Y.

C. L. Korb, C. Y. Weng, “Differential absorption lidar technique for measurement of the atmospheric pressure profile,” Appl. Opt. 22, 3759–3770 (1983).
[CrossRef] [PubMed]

C. L. Korb, C. Y. Weng, “A theoretical study of a two-wavelength lidar technique for the measurement of atmospheric temperature profiles,” J. Appl. Meteorol. 21, 1346–1355 (1982).
[CrossRef]

C. L. Korb, C. Y. Weng, “The theory and correction of finite laser bandwidth effects in DIAL experiments,” in Proceedings of the 11th International Laser Radar Conference, J. A. Weinman, ed., NASA Conf. Publ.2228, 78–81 (1982).

Adv. Geophys. (1)

R. T. H. Collis, “Lidar,” Adv. Geophys. 13, 113–139 (1969).
[CrossRef]

Appl. Opt. (1)

J. Appl. Meteorol. (1)

C. L. Korb, C. Y. Weng, “A theoretical study of a two-wavelength lidar technique for the measurement of atmospheric temperature profiles,” J. Appl. Meteorol. 21, 1346–1355 (1982).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Quantum Spectrosc. Radiat. Transfer (2)

J. J. Olivero, R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quantum Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quantum Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

Other (2)

C. L. Korb, C. Y. Weng, “The theory and correction of finite laser bandwidth effects in DIAL experiments,” in Proceedings of the 11th International Laser Radar Conference, J. A. Weinman, ed., NASA Conf. Publ.2228, 78–81 (1982).

R. C. Buck, E. F. Buck, Advanced Calculus (McGraw-Hill, New York, 1965), p. 106.

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Figures (1)

Fig. 1
Fig. 1

Percentage error in the differential absorption coefficient as a function of the instrumental bandwidth to the half-width at half-height of the Voigt line profile, where a monochromatic calculation at an effective frequency has been used to represent the effects of finite instrumental bandwidth. (A) and (B) are for Gaussian and rectangular laser line shapes, respectively, for a downward-viewing experiment from space to an altitude (pressure) in the atmosphere defined by the Voigt parameter a = (bc0 p/ b d )ln 2.

Equations (23)

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τ¯ν0, R=- hνexp-2 0R Kν, xdxdν,
Kν, x=a1x-a2xν-ν02+0ν-ν04,
hν=2Δνln 2π1/2 exp-ln2ν-ν0/Δν/22,
τ¯ν0, R=bπ1/2 exp-2 0R a1xdx-exp-ν-ν02b-2 0R a2xdxdν,
2 0R a2xdx/b  1,
τ¯ν0, R=exp-2 0Ra1x-a2x/2b×1+0R a2xdx/bdx,
τ¯ν0, R=exp-2 0R Kν¯e, xdx,
ν¯e=ν0±Δν/22 ln21+Δν24 ln20R a2xdx1/2.
hν=1/Δν |ν-ν0|Δν/2=0 |ν-ν0|>Δν/2,
τ¯ν0, R=1/Δν-Δν/2Δν/2exp-2 0Ra1x-a2xν-ν02dxdν.
ν¯e=ν0±Δν/23.
Kν, x=ax+bxν-νr.
2ν-νr0R bxdx  1,
τ¯r0, R=exp-2 0R axdx- hν1-2ν-νr0R bxdxdν.
τ¯r0, R=exp-2 0R Kνr, xdx, ν¯e=νr.
R=τ¯ν0, R2/τ¯r0, R2τ¯ν0, R1/τ¯r0, R1,
R=ενR2/εrR2ενR1/εrR1
R=- hνexp-2 0R2Kν, x-Kνr, xdxdν- hνexp-2 0R1Kν, x-Kνr, xdxdν,
R=exp-2 R1R2Kν¯e, x-Kνr, xdx.
Kν=qnp, TSTfν-ν0,
fν-ν0=faπ-exp-y2dya2+ξ-y2,
f=ln 2/π1/2bd,a=ln 21/2bc/bd,ξ=ln 21/2ν-ν0/bd,
bcp, T=bc0T0p/p0T0/Tm,bdT=2kT ln 2/M0c21/2ν0,

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