Abstract

This paper presents detailed analysis about the effects of spectral discrimination on the retrieval errors for atmospheric aerosol optical properties in high-spectral-resolution lidar (HSRL). To the best of our knowledge, this is the first study that focuses on this topic comprehensively, and our goal is to provide some heuristic guidelines for the design of the spectral discrimination filter in HSRL. We first introduce a theoretical model for retrieval error evaluation of an HSRL instrument with a general three-channel configuration. The model only takes the error sources related to the spectral discrimination parameters into account, while other error sources not associated with these focused parameters are excluded on purpose. Monte Carlo (MC) simulations are performed to validate the correctness of the theoretical model. Results from both the model and MC simulations agree very well, and they illustrate one important, although not well realized, fact: a large molecular transmittance and a large spectral discrimination ratio (SDR, i.e., ratio of the molecular transmittance to the aerosol transmittance) are beneficial to promote the retrieval accuracy. More specifically, we find that a large SDR can reduce retrieval errors conspicuously for atmosphere at low altitudes, while its effect on the retrieval for high altitudes is very limited. A large molecular transmittance contributes to good retrieval accuracy everywhere, particularly at high altitudes, where the signal-to-noise ratio is small. Since the molecular transmittance and SDR are often trade-offs, we suggest considering a suitable SDR for higher molecular transmittance instead of using unnecessarily high SDR when designing the spectral discrimination filter. These conclusions are expected to be applicable to most of the HSRL instruments, which have similar configurations as the one discussed here.

© 2014 Optical Society of America

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References

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  1. U. Wandinger, “Introduction to lidar,” in Lidar, C. Weitkamp, ed. (Springer, 2005), pp. 1–18.
  2. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
    [CrossRef]
  3. S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, and J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
    [CrossRef]
  4. J. T. Sroga, E. W. Eloranta, S. T. Shipley, F. L. Roesler, and P. J. Tryon, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: calibration and data analysis,” Appl. Opt. 22, 3725–3732 (1983).
    [CrossRef]
  5. C. Y. She, R. J. Alvarez Ii, L. M. Caldwell, and D. A. Krueger, “High-spectral-resolution Rayleigh-Mie lidar measurement of aerosol and atmospheric profiles,” Opt. Lett. 17, 541–543 (1992).
    [CrossRef]
  6. P. Piironen and E. W. Eloranta, “Demonstration of a high-spectral-resolution lidar based on an iodine absorption filter,” Opt. Lett. 19, 234–236 (1994).
    [CrossRef]
  7. Z. Liu, I. Matsui, and N. Sugimoto, “High-spectral-resolution lidar using an iodine absorption filter for atmospheric measurements,” Opt. Eng. 38, 1661–1670 (1999).
    [CrossRef]
  8. D. S. Hoffman, K. S. Repasky, J. A. Reagan, and J. L. Carlsten, “Development of a high spectral resolution lidar based on confocal Fabry-Perot spectral filters,” Appl. Opt. 51, 6233–6244 (2012).
    [CrossRef]
  9. D. Liu, C. Hostetler, I. Miller, A. Cook, and J. Hair, “System analysis of a tilted field-widened Michelson interferometer for high spectral resolution lidar,” Opt. Express 20, 1406–1420 (2012).
    [CrossRef]
  10. D. Liu, Y. Yang, Z. Cheng, H. Huang, B. Zhang, T. Ling, and Y. Shen, “Retrieval and analysis of a polarized high-spectral-resolution lidar for profiling aerosol optical properties,” Opt. Express 21, 13084–13093 (2013).
    [CrossRef]
  11. P. B. Russell, T. J. Swissler, and M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
  12. F. Rocadenbosch, M. N. Md. Reba, M. Sicard, and A. Comerón, “Practical analytical backscatter error bars for elastic one-component lidar inversion algorithm,” Appl. Opt. 49, 3380–3393 (2010).
    [CrossRef]
  13. D. Bruneau and J. Pelon, “Simultaneous measurements of particle backscattering and extinction coefficients and wind velocity by lidar with a Mach-Zehnder interferometer: principle of operation and performance assessment,” Appl. Opt. 42, 1101–1114 (2003).
    [CrossRef]
  14. C.-Y. She, J. Yue, Z.-A. Yan, J. W. Hair, J.-J. Guo, S.-H. Wu, and Z.-S. Liu, “Direct-detection Doppler wind measurements with a Cabannes–Mie lidar: A. Comparison between iodine vapor filter and Fabry–Perot interferometer methods,” Appl. Opt. 46, 4434–4443 (2007).
    [CrossRef]
  15. Z. Cheng, D. Liu, Y. Yang, L. Yang, and H. Huang, “Interferometric filters for spectral discrimination in high-spectral-resolution lidar: performance comparisons between Fabry-Perot interferometer and field-widened Michelson interferometer,” Appl. Opt. 52, 7838–7850 (2013).
    [CrossRef]
  16. A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995).
    [CrossRef]
  17. J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Electron. 31, 48–55 (1993).
  18. Z. Liu, P. Voelger, and N. Sugimoto, “Simulations of the observation of clouds and aerosols with the experimental lidar in space equipment system,” Appl. Opt. 39, 3120–3137 (2000).
    [CrossRef]
  19. M. Esselborn, M. Wirth, A. Fix, M. Tesche, and G. Ehret, “Airborne high spectral resolution lidar for measuring aerosol extinction and backscatter coefficients,” Appl. Opt. 47, 346–358 (2008).
    [CrossRef]
  20. J. W. Hair, C. A. Hostetler, A. L. Cook, D. B. Harper, R. A. Ferrare, T. L. Mack, W. Welch, L. R. Izquierdo, and F. E. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47, 6734–6752 (2008).
    [CrossRef]

2013 (2)

2012 (2)

2010 (1)

2008 (2)

2007 (1)

2003 (1)

2000 (1)

1999 (1)

Z. Liu, I. Matsui, and N. Sugimoto, “High-spectral-resolution lidar using an iodine absorption filter for atmospheric measurements,” Opt. Eng. 38, 1661–1670 (1999).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Electron. 31, 48–55 (1993).

1992 (1)

1984 (1)

1983 (2)

1979 (1)

Alvarez Ii, R. J.

Bruneau, D.

Bucholtz, A.

Caldwell, L. M.

Carlsten, J. L.

Cheng, Z.

Comerón, A.

Cook, A.

Cook, A. L.

Ehret, G.

Eloranta, E. W.

Esselborn, M.

Fernald, F. G.

Ferrare, R. A.

Fix, A.

Guo, J.-J.

Hair, J.

Hair, J. W.

Harper, D. B.

Hoffman, D. S.

Hostetler, C.

Hostetler, C. A.

Hovis, F. E.

Huang, H.

Izquierdo, L. R.

Krueger, D. A.

Ling, T.

Liu, D.

Liu, Z.

Z. Liu, P. Voelger, and N. Sugimoto, “Simulations of the observation of clouds and aerosols with the experimental lidar in space equipment system,” Appl. Opt. 39, 3120–3137 (2000).
[CrossRef]

Z. Liu, I. Matsui, and N. Sugimoto, “High-spectral-resolution lidar using an iodine absorption filter for atmospheric measurements,” Opt. Eng. 38, 1661–1670 (1999).
[CrossRef]

Liu, Z.-S.

Mack, T. L.

Matsui, I.

Z. Liu, I. Matsui, and N. Sugimoto, “High-spectral-resolution lidar using an iodine absorption filter for atmospheric measurements,” Opt. Eng. 38, 1661–1670 (1999).
[CrossRef]

McCormick, M. P.

Md. Reba, M. N.

Miller, I.

Pelon, J.

Piironen, P.

Reagan, J. A.

Repasky, K. S.

Rocadenbosch, F.

Roesler, F. L.

Russell, P. B.

She, C. Y.

She, C.-Y.

Shen, Y.

Shipley, S. T.

Sicard, M.

Spinhirne, J. D.

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Electron. 31, 48–55 (1993).

Sroga, J. T.

Sugimoto, N.

Z. Liu, P. Voelger, and N. Sugimoto, “Simulations of the observation of clouds and aerosols with the experimental lidar in space equipment system,” Appl. Opt. 39, 3120–3137 (2000).
[CrossRef]

Z. Liu, I. Matsui, and N. Sugimoto, “High-spectral-resolution lidar using an iodine absorption filter for atmospheric measurements,” Opt. Eng. 38, 1661–1670 (1999).
[CrossRef]

Swissler, T. J.

Tesche, M.

Tracy, D. H.

Trauger, J. T.

Tryon, P. J.

Voelger, P.

Wandinger, U.

U. Wandinger, “Introduction to lidar,” in Lidar, C. Weitkamp, ed. (Springer, 2005), pp. 1–18.

Weinman, J. A.

Welch, W.

Wirth, M.

Wu, S.-H.

Yan, Z.-A.

Yang, L.

Yang, Y.

Yue, J.

Zhang, B.

Appl. Opt. (13)

F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
[CrossRef]

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, and J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
[CrossRef]

J. T. Sroga, E. W. Eloranta, S. T. Shipley, F. L. Roesler, and P. J. Tryon, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: calibration and data analysis,” Appl. Opt. 22, 3725–3732 (1983).
[CrossRef]

D. S. Hoffman, K. S. Repasky, J. A. Reagan, and J. L. Carlsten, “Development of a high spectral resolution lidar based on confocal Fabry-Perot spectral filters,” Appl. Opt. 51, 6233–6244 (2012).
[CrossRef]

P. B. Russell, T. J. Swissler, and M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).

F. Rocadenbosch, M. N. Md. Reba, M. Sicard, and A. Comerón, “Practical analytical backscatter error bars for elastic one-component lidar inversion algorithm,” Appl. Opt. 49, 3380–3393 (2010).
[CrossRef]

D. Bruneau and J. Pelon, “Simultaneous measurements of particle backscattering and extinction coefficients and wind velocity by lidar with a Mach-Zehnder interferometer: principle of operation and performance assessment,” Appl. Opt. 42, 1101–1114 (2003).
[CrossRef]

C.-Y. She, J. Yue, Z.-A. Yan, J. W. Hair, J.-J. Guo, S.-H. Wu, and Z.-S. Liu, “Direct-detection Doppler wind measurements with a Cabannes–Mie lidar: A. Comparison between iodine vapor filter and Fabry–Perot interferometer methods,” Appl. Opt. 46, 4434–4443 (2007).
[CrossRef]

Z. Cheng, D. Liu, Y. Yang, L. Yang, and H. Huang, “Interferometric filters for spectral discrimination in high-spectral-resolution lidar: performance comparisons between Fabry-Perot interferometer and field-widened Michelson interferometer,” Appl. Opt. 52, 7838–7850 (2013).
[CrossRef]

A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995).
[CrossRef]

Z. Liu, P. Voelger, and N. Sugimoto, “Simulations of the observation of clouds and aerosols with the experimental lidar in space equipment system,” Appl. Opt. 39, 3120–3137 (2000).
[CrossRef]

M. Esselborn, M. Wirth, A. Fix, M. Tesche, and G. Ehret, “Airborne high spectral resolution lidar for measuring aerosol extinction and backscatter coefficients,” Appl. Opt. 47, 346–358 (2008).
[CrossRef]

J. W. Hair, C. A. Hostetler, A. L. Cook, D. B. Harper, R. A. Ferrare, T. L. Mack, W. Welch, L. R. Izquierdo, and F. E. Hovis, “Airborne high spectral resolution lidar for profiling aerosol optical properties,” Appl. Opt. 47, 6734–6752 (2008).
[CrossRef]

IEEE Trans. Geosci. Electron. (1)

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans. Geosci. Electron. 31, 48–55 (1993).

Opt. Eng. (1)

Z. Liu, I. Matsui, and N. Sugimoto, “High-spectral-resolution lidar using an iodine absorption filter for atmospheric measurements,” Opt. Eng. 38, 1661–1670 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Other (1)

U. Wandinger, “Introduction to lidar,” in Lidar, C. Weitkamp, ed. (Springer, 2005), pp. 1–18.

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Figures (8)

Fig. 1.
Fig. 1.

Abstracted systematic layout of a general three-channel HSRL.

Fig. 2.
Fig. 2.

Simplified exercise to test the tendencies of the error terms ε2 with respect to R.

Fig. 3.
Fig. 3.

Modeled atmospheric optical properties inputted into the MC simulations: (a) backscatter coefficient and optical depth and (b) depolarization ratio.

Fig. 4.
Fig. 4.

100 inverted backscatter profiles from the MC method (red points) along with the true values inputted into simulations (green line) and calculated 3σ error limits by our theoretical model (blue lines). (a) is the result for the backscatter coefficient and (b) is for the optical depth. (c) Equivalent SNRs in this simulation are presented for reference.

Fig. 5.
Fig. 5.

Statistical error RMSs from the MC simulation along with the straightforwardly calculated errors from the theoretical model for the backscatter coefficient and optical depth retrieval (the top figure), as well as the aerosol-loading index R (the bottom figure).

Fig. 6.
Fig. 6.

Inversion errors in different SDRs for a given molecular transmittance. (a) and (b) are for the errors of backscatter coefficient and optical depth, respectively.

Fig. 7.
Fig. 7.

Same as Fig. 6 except that plots are drawn with different molecular transmittances and a given SDR.

Fig. 8.
Fig. 8.

Inversion errors in different combinations of SDRs and molecular transmittances.

Tables (1)

Tables Icon

Table 1. HSRL System Specifications Employed by MC Simulations

Equations (28)

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BC=(βm+βa)exp(2τ),BC=(βm+βa)exp(2τ),BM=(Tmβm+Taβa)exp(2τ),
β=βm(1+δ)(1+δm)(TmTa)K1TaK,
δ=BC/BC.
K=BC/BM.
τ=12ln[(1KTa)(1+δm)BM(TmTa)βm].
εt2=(σββ)2=(ββδ)2(σδ)2+(ββK)2(σK)2+(ββTa)2(σTa)2+(ββTm)2(σTm)2,
ε12=δ¯2(1+δ¯)2[1SNRC2+1SNRC2],
ε22=1(1Ta¯K¯)2[1SNRC2+1SNRM2],
R=βa+βmβm.
R=(TmTa)K1TaK.
ε12=[(R1)δa+δmR+(R1)δa+δm]21SNRCC2,
ε22=[1+RTm¯/Ta¯1]21SNRCM2,
ε32=[R1Tm¯Ta¯]2(σTa)2
ε42=1(Tm¯Ta¯)2(σTm)2.
(στ)2=14[(1+RTm/Ta1)21SNRM2+(RTm/Ta1)21SNRC2+ε32+ε42].
SDR=Tm/Ta.
ε12=(ββδ)2·σδ2=11+δ¯·σδ2.
σδ=E[(δδ¯)2],
δδ¯=1BC¯(BCBC¯)+BC¯BC¯2(BCBC¯).
(σδ)2=(σBC)2BC¯2+(σBC)2·BC¯2BC¯4.
(σδ)2=δ¯2[(σBC)2BC¯2+(σBC)2BC¯2]=δ¯2[1SNRC2+1SNRC2].
δ=βa+βmβa+βm=βaδa+βmδmβa+βm=(R1)δa+δmR.
SNRMTmβm+Taβa.
ε22(1+RSDR1)2(1SNRC2+1Tmβm+Tmβa/SDR).
ε22Tm(1+RSDR1)2(βm+βa/SDR)(Tmβm+Tmβa/SDR)2<0.
ε22SDR(1+RSDR1)2TmβaSDR2(Tmβm+Tmβa/SDR)2(1+RSDR1)2R(SDR1)2[1SNRC2+1Tmβm+Tmβa/SDR].
A=(R+SDR1)Tmβa(TmβmSDR+Tmβa)22RSDR(SDR1)(TmβmSDR+Tmβa)=1TmβmSDR+Tmβa[(R1+SDR)βa/βmSDR+βa/βm2RSDRSDR1]<0.
A=1TmβmSDR+Tmβa[R12RSDRSDR1]<1TmβmSDR+Tmβa[R12R]<0.

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