Abstract

Thanks to wavelength flexibility, interferometric filters such as Fabry–Perot interferometers (FPIs) and field-widened Michelson interferometers (FWMIs) have shown great convenience for spectrally separating the molecule and aerosol scattering components in the high-spectral-resolution lidar (HSRL) return signal. In this paper, performance comparisons between the FPI and FWMI as a spectroscopic discrimination filter in HSRL are performed. We first present a theoretical method for spectral transmission analysis and quantitative evaluation on the spectral discrimination. Then the process in determining the parameters of the FPI and FWMI for the performance comparisons is described. The influences from the incident field of view (FOV), the cumulative wavefront error induced by practical imperfections, and the frequency locking error on the spectral discrimination performance of the two filters are discussed in detail. Quantitative analyses demonstrate that FPI can produce higher transmittance while the remarkable spectral discrimination is one of the most appealing advantages of FWMI. As a result of the field-widened design, the FWMI still performs well even under the illumination with large FOV while the FPI is only qualified for a small incident angle. The cumulative wavefront error attaches a great effect on the spectral discrimination performance of the interferometric filters. We suggest if a cumulative wavefront error is less than 0.05 waves RMS, it is beneficial to employ the FWMI; otherwise, FPI may be more proper. Although the FWMI shows much more sensitivity to the frequency locking error, it can outperform the FPI given a locking error less than 0.1 GHz is achieved. In summary, the FWMI is very competent in HSRL applications if these practical engineering and control problems can be solved, theoretically. Some other estimations neglected in this paper can also be carried out through the analytical method illustrated herein.

© 2013 Optical Society of America

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References

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  1. E. Eloranta, “High spectral resolution lidar,” in Lidar, C. Weitkamp, ed. (Springer, 2005), pp. 143–163.
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    [CrossRef]
  3. 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]
  4. 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]
  5. 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]
  6. 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).
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  9. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
    [CrossRef]
  10. 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]
  11. H. Shimizu, S. A. Lee, and C. Y. She, “High spectral resolution lidar system with atomic blocking filters for measuring atmospheric parameters,” Appl. Opt. 22, 1373–1381 (1983).
    [CrossRef]
  12. 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]
  13. 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]
  14. P. B. Hays and R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
    [CrossRef]
  15. H. Jahn, G. Fellberg, B. Gladitz, and M. Scheele, “Maximum-likelihood optimization of a Fabry-Perot interferometer for thermospheric temperature and wind measurements,” J. Opt. Soc. Am. 72, 386–391 (1982).
    [CrossRef]
  16. M. J. McGill, W. R. Skinner, and T. D. Irgang, “Analysis techniques for the recovery of winds and backscatter coefficients from a multiple-channel incoherent Doppler lidar,” Appl. Opt. 36, 1253–1268 (1997).
    [CrossRef]
  17. G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. W. Kendall, and J. R. Wimperis, “WAMDII: wide-angle Michelson Doppler imaging interferometer for Spacelab,” Appl. Opt. 24, 1571–1584 (1985).
    [CrossRef]
  18. G. G. Shepherd, “Application of Doppler Michelson imaging to upper atmospheric wind measurement: WINDII and beyond,” Appl. Opt. 35, 2764–2773 (1996).
    [CrossRef]
  19. W. A. Gault, S. F. Johnston, and D. J. W. Kendall, “Optimization of a field-widened Michelson interferometer,” Appl. Opt. 24, 1604–1608 (1985).
    [CrossRef]
  20. G. Thuillier and M. Hersé, “Thermally stable field compensated Michelson interferometer for measurement of temperature and wind of the planetary atmospheres,” Appl. Opt. 30, 1210–1220 (1991).
    [CrossRef]
  21. R. Hilliard and G. Shepherd, “Wide-angle Michelson interferometer for measuring Doppler line widths,” J. Opt. Soc. Am. 56, 362–369 (1966).
    [CrossRef]
  22. 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]
  23. 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]
  24. G. Hernandez, “Analytical description of a Fabry-Perot photoelectric spectrometer,” Appl. Opt. 5, 1745–1748 (1966).
    [CrossRef]
  25. B.-Y. Liu, M. Esselborn, M. Wirth, A. Fix, D.-C. Bi, and G. Ehret, “Influence of molecular scattering models on aerosol optical properties measured by high spectral resolution lidar,” Appl. Opt. 48, 5143–5154 (2009).
    [CrossRef]
  26. C. Flesia and C. L. Korb, “Theory of the double-edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. 38, 432–440 (1999).
    [CrossRef]
  27. D. Bruneau, “Mach-Zehnder interferometer as a spectral analyzer for molecular Doppler wind lidar,” Appl. Opt. 40, 391–399 (2001).
    [CrossRef]
  28. D. Bruneau, A. Garnier, A. Hertzog, and J. Porteneuve, “Wind-velocity lidar measurements by use of a Mach-Zehnder interferometer, comparison with a Fabry-Perot interferometer,” Appl. Opt. 43, 173–182 (2004).
    [CrossRef]
  29. G. Thuillier and G. G. Shepherd, “Fully compensated Michelson interferometer of fixed-path difference,” Appl. Opt. 24, 1599–1603 (1985).
    [CrossRef]
  30. Matlab Peaks Function, (The Mathworks), http://www.mathworks.com/help/techdoc/ref/peaks.html .

2013 (1)

2012 (2)

2009 (1)

2008 (2)

2004 (1)

2003 (1)

2001 (1)

1999 (2)

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]

C. Flesia and C. L. Korb, “Theory of the double-edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. 38, 432–440 (1999).
[CrossRef]

1997 (1)

1996 (1)

1994 (1)

1992 (1)

1991 (1)

1985 (3)

1984 (1)

1983 (3)

1982 (1)

1981 (1)

1971 (1)

1966 (2)

Alvarez Ii, R. J.

Bi, D.-C.

Bruneau, D.

Caldwell, L. M.

Carlsten, J. L.

Cheng, Z.

Cook, A.

Cook, A. L.

Ehret, G.

Eloranta, E.

E. Eloranta, “High spectral resolution lidar,” in Lidar, C. Weitkamp, ed. (Springer, 2005), pp. 143–163.

Eloranta, E. W.

Esselborn, M.

Fellberg, G.

Fernald, F. G.

Ferrare, R. A.

Fix, A.

Flesia, C.

Garnier, A.

Gault, W. A.

Gladitz, B.

Hair, J.

Hair, J. W.

Harper, D. B.

Haslett, J. W.

Hays, P. B.

Hernandez, G.

Hersé, M.

Hertzog, A.

Hilliard, R.

Hoffman, D. S.

Hostetler, C.

Hostetler, C. A.

Hovis, F. E.

Huang, H.

Irgang, T. D.

Izquierdo, L. R.

Jahn, H.

Johnston, S. F.

Kendall, D. J. W.

Klett, J. D.

Korb, C. L.

Kosteniuk, P. R.

Krueger, D. A.

Lee, S. A.

Ling, T.

Liu, B.-Y.

Liu, D.

Liu, Z.

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]

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]

McGill, M. J.

Miller, D. W.

Miller, I.

Pasturczyk, Z.

Pelon, J.

Piironen, P.

Porteneuve, J.

Reagan, J. A.

Repasky, K. S.

Roble, R. G.

Roesler, F. L.

Scheele, M.

She, C. Y.

Shen, Y.

Shepherd, G.

Shepherd, G. G.

Shimizu, H.

Shipley, S. T.

Skinner, W. R.

Sroga, J. T.

Sugimoto, N.

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]

Tesche, M.

Thuillier, G.

Tracy, D. H.

Trauger, J. T.

Tryon, P. J.

Weinman, J. A.

Welch, W.

Wimperis, J. R.

Wirth, M.

Yang, Y.

Zhang, B.

Appl. Opt. (21)

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]

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]

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[CrossRef]

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

H. Shimizu, S. A. Lee, and C. Y. She, “High spectral resolution lidar system with atomic blocking filters for measuring atmospheric parameters,” Appl. Opt. 22, 1373–1381 (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]

M. J. McGill, W. R. Skinner, and T. D. Irgang, “Analysis techniques for the recovery of winds and backscatter coefficients from a multiple-channel incoherent Doppler lidar,” Appl. Opt. 36, 1253–1268 (1997).
[CrossRef]

G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. W. Kendall, and J. R. Wimperis, “WAMDII: wide-angle Michelson Doppler imaging interferometer for Spacelab,” Appl. Opt. 24, 1571–1584 (1985).
[CrossRef]

G. G. Shepherd, “Application of Doppler Michelson imaging to upper atmospheric wind measurement: WINDII and beyond,” Appl. Opt. 35, 2764–2773 (1996).
[CrossRef]

W. A. Gault, S. F. Johnston, and D. J. W. Kendall, “Optimization of a field-widened Michelson interferometer,” Appl. Opt. 24, 1604–1608 (1985).
[CrossRef]

G. Thuillier and M. Hersé, “Thermally stable field compensated Michelson interferometer for measurement of temperature and wind of the planetary atmospheres,” Appl. Opt. 30, 1210–1220 (1991).
[CrossRef]

P. B. Hays and R. G. Roble, “A technique for recovering Doppler line profiles from Fabry-Perot interferometer fringes of very low intensity,” Appl. Opt. 10, 193–200 (1971).
[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]

G. Hernandez, “Analytical description of a Fabry-Perot photoelectric spectrometer,” Appl. Opt. 5, 1745–1748 (1966).
[CrossRef]

B.-Y. Liu, M. Esselborn, M. Wirth, A. Fix, D.-C. Bi, and G. Ehret, “Influence of molecular scattering models on aerosol optical properties measured by high spectral resolution lidar,” Appl. Opt. 48, 5143–5154 (2009).
[CrossRef]

C. Flesia and C. L. Korb, “Theory of the double-edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. 38, 432–440 (1999).
[CrossRef]

D. Bruneau, “Mach-Zehnder interferometer as a spectral analyzer for molecular Doppler wind lidar,” Appl. Opt. 40, 391–399 (2001).
[CrossRef]

D. Bruneau, A. Garnier, A. Hertzog, and J. Porteneuve, “Wind-velocity lidar measurements by use of a Mach-Zehnder interferometer, comparison with a Fabry-Perot interferometer,” Appl. Opt. 43, 173–182 (2004).
[CrossRef]

G. Thuillier and G. G. Shepherd, “Fully compensated Michelson interferometer of fixed-path difference,” Appl. Opt. 24, 1599–1603 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

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 (2)

Matlab Peaks Function, (The Mathworks), http://www.mathworks.com/help/techdoc/ref/peaks.html .

E. Eloranta, “High spectral resolution lidar,” in Lidar, C. Weitkamp, ed. (Springer, 2005), pp. 143–163.

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Figures (7)

Fig. 1.
Fig. 1.

Schematics of the most common configurations of FPI and FWMI: (a) the configuration of FPI and (b) the configuration of FWMI.

Fig. 2.
Fig. 2.

Examples of the spectrum of lidar return signal and the spectral functions of FPI and FWMI, as well as the remaining spectrum through the filters in the working mode SAS.

Fig. 3.
Fig. 3.

Tendencies of Tm, Ta, SDR and PEF (which will be introduced later) of the FPI with coating refractivity from 0.8 to 1 and FSR from 1 to 50 GHz: (a) tendency of the molecular signal transmittance (%); (b) tendency of the aerosol signal transmittance (%); (c) tendency of the SDR; and (d) tendency of the PEF.

Fig. 4.
Fig. 4.

Spectral discrimination parameters of the FWMI with respect to its FSR: (a) profiles of aerosol and molecular transmittances and (b) SDRs and PEFs.

Fig. 5.
Fig. 5.

Comparisons of spectral discrimination parameters between the FPI and FWMI at different incident divergences: (a) the aerosol and molecular signal transmittances of the FPI and FWMI; (b) the SDRs of the FPI and FWMI; and (c) the PEFs of the FPI and FWMI.

Fig. 6.
Fig. 6.

Comparisons of spectral discrimination parameters between the FPI and FWMI under different cumulative wavefront error RMSs: (a) the aerosol signal and molecular signal transmittances of the FPI; (b) the aerosol signal and molecular signal transmittances of the FWMI; (c) the SDRs of the FPI and FWMI; and (d) the PEFs of the FPI and FWMI.

Fig. 7.
Fig. 7.

Same as Fig. 5 except with the frequency locking error.

Tables (2)

Tables Icon

Table 1. Technical Parameters of the FPI for This Comparative Study

Tables Icon

Table 2. Technical Parameters of the FWMI for This Comparative Study

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

Si(υυ0)=1γiπexp[(υυ0)2γi2],
i(θ)=Si(υυ0)F(θ,υ)dυSi(υυ0)dυ,
Ti=0θdi(θ)θdθ/0θdθdθ,
SDR=Tm/Ta.
F(θ,υ)=2R(1cosδ)1+R22Rcos(δ)=11R1+R{1+2k=1Rkcos(kδ)},
δ(θ,υ)=4πnhccos(θ)υ,
δ(θ,υ)=δ(θ,υ0)+4πnhcos(θ)c(υυ0),
δ(θ,υ0)=δ(0,υ0)+4πnh(cosθ1)cυ0.
δ(θ,υ)=δ(0,υ0)+4πnhc(υcosθυ0).
δ(θ,υ)δ(0,υ0)+4πnhc(υυ0)2πnhυ0θ2c.
FSR=c/2nh.
FWHMFSRπarccos[1(1R)22R].
F(υ,θ)=I1+I2+2I1I2cos(δ),
δ(θ,υ)=2πυcOPD(θ),
δ(θ,υ)δ(0,υ0)+2πOPD(0)c(υυ0)πυ0Mθ42c.
FSR=c/OPD(0)
FWHMFSR/2.
i(θ)=11R1+R{1+2k=1Rkexp[k2π2γi2FSR2]cos[kπυ0FSRθ2]}.
Ti=11R1+R{1+2k=1Rkexp[k2π2γi2FSR2]}.
PEF=(Tm)p(SDR)q,
i(θ)=12[1exp(π2γi2FSR2)cos(πMυ0θ42c)],
Ti=12[1exp(π2γi2FSR2)].
Ti=11R1+R{1+2k=1Rkexp[k2π2γi2FSR2]sinc[kθd2υ0FSR]},
Ti=12{1exp(π2γi2FSR2)C(πMυ02cθd2)/(πMυ02cθd2)},
C(x)=0xcos(t2)dt.
δ(0,υ)2mπ+4πnΔWυ0c+4πn(h+ΔW)c(υυ0),
δ(0,υ)(2m+1)π+2πυ0ΔWc+2πOPD(0)c(υυ0).
Ti(ΔW)=11R1+R{1+2k=1Rkexp[k2π2γi2FSR2]cos(k4πnΔWυ0c)},
Ti(ΔW)=12[1exp(π2γi2FSR2)cos(2πυ0ΔWc)].
Ti(ΔυL)=11R1+R{1+2k=1Rkexp[k2π2γi2FSR2]cos(k2πΔυLFSR)}
Ti(ΔυL)=12[1exp(π2γi2FSR2)cos(2πΔυLFSR)].

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