Abstract

Iodine absorption cells are extensively employed by high-spectral-resolution Lidars (HSRLs) for aerosol optical properties and atmosphere state parameters profiling. To the best of our knowledge, the optimal design of the parameters of iodine cells has not been talked about systematically. In this paper, a heuristic method based on multi-objective concept is proposed for the design of iodine cells employed in HSRLs for aerosol profiling, and the method can be also applied to different types of HSRLs. The bi-objective model is established based on the retrieval error analysis of HSRL and then the Pareto optimal solutions are obtained through the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The performance of different absorption lines are compared according to the Pareto solution sets, and the stability of transmittance characteristics of different absorption lines are discussed through sensitivity analysis. The results are expected to provide guidance for the design of HSRLs based on iodine absorption filters.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  9. 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(3), 346–358 (2008).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. Z.-S. Liu, D. Wu, J.-T. Liu, K.-L. Zhang, W.-B. Chen, X.-Q. Song, J. W. Hair, and C.-Y. She, “Low-altitude atmospheric wind measurement from the combined Mie and Rayleigh backscattering by Doppler lidar with an iodine filter,” Appl. Opt. 41(33), 7079–7086 (2002).
    [Crossref] [PubMed]
  14. C. Weibiao, “Concept Design of Spaceborne Atmospheric Aerosol and Carbon Lidar,” in The 5th International Symposium on Atmospheric Light Scattering and Remote Sensing, (2015)
  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(32), 7838–7850 (2013).
    [Crossref] [PubMed]
  16. J. Luo, D. Liu, Y. Zhang, Z. Cheng, C. Liu, J. Bai, Y. Shen, Y. Yang, Y. Zhou, P. Tang, Q. Liu, P. Xu, L. Su, X. Zhang, and L. Yang, “Design of the interferometric spectral discrimination filters for a three-wavelength high-spectral-resolution lidar,” Opt. Express 24(24), 27622–27636 (2016).
    [Crossref] [PubMed]
  17. C.-Y. She, “Spectral structure of laser light scattering revisited: bandwidths of nonresonant scattering lidars,” Appl. Opt. 40(27), 4875–4884 (2001).
    [Crossref] [PubMed]
  18. G. Tenti, C. D. Boley, and R. C. Desai, “On the Kinetic Model Description of Rayleigh–Brillouin Scattering from Molecular Gases,” Can. J. Phys. 52, 285–290 (1974).
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    [Crossref]
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    [Crossref] [PubMed]
  21. X. Pan, “Coherent Rayleigh-Brillouin Scattering,” (Princeton University, 2003).
  22. 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(27), 5143–5154 (2009).
    [Crossref] [PubMed]
  23. S. Gerstenkorn and P. Luc, “Atlas du Spectre d’Absorption de la Molecule d’Iode 14800-20000 cm-1,” Paris: Editions du Centre National de la Recherche Scientifique (CNRS), 1978 (1978).
  24. B. Hiller and R. K. Hanson, “Properties of the iodine molecule relevant to laser-induced fluorescence experiments in gas flows,” Exp. Fluids 10(1), 1–11 (1990).
    [Crossref]
  25. J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36(27), 6729–6738 (1997).
    [Crossref] [PubMed]
  26. J. Tellinghuisen, “Intensity factors for the I2 B↔X band system,” J. Quant. Spectrosc. Radiat. Transf. 19(2), 149–161 (1978).
    [Crossref]
  27. J. Tellinghuisen, “Least-squares analysis of overlapped bound-free absorption spectra and predissociation data in diatomics: the C(1Πu) state of I2.,” J. Chem. Phys. 135(5), 054301 (2011).
    [Crossref] [PubMed]
  28. K. Wallmeroth and R. Letterer, “Cesium frequency standard for lasers at λ = 1.06 microm,” Opt. Lett. 15(14), 812–813 (1990).
    [Crossref] [PubMed]
  29. G. Anderson, S. Clough, F. Kneizys, J. Chetwynd, and E. Shettle, “AFGL atmospheric constituent profiles (0-120 km),” AFGL-TR-0208 Environmental Research papers (1986).
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    [Crossref]
  31. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
    [Crossref]
  32. A. E. Eiben and S. K. Smit, “Evolutionary Algorithm Parameters and Methods to Tune Them,” in Autonomous Search, Y. Hamadi, E. Monfroy, and F. Saubion, eds. (Springer Berlin Heidelberg, Berlin, Heidelberg, 2012), pp. 15–36.
  33. T. J. Quinn and J. M. Chartier, “A new type of iodine cell for stabilized lasers,” IEEE Trans. Instrum. Meas. 42(2), 405–406 (1993).
    [Crossref]

2016 (1)

2015 (2)

2014 (3)

Z. Cheng, D. Liu, J. Luo, Y. Yang, L. Su, L. Yang, H. Huang, and Y. Shen, “Effects of spectral discrimination in high-spectral-resolution lidar on the retrieval errors for atmospheric aerosol optical properties,” Appl. Opt. 53(20), 4386–4397 (2014).
[Crossref] [PubMed]

D. Rosenfeld, S. Sherwood, R. Wood, and L. Donner, “Atmospheric science. Climate Effects of Aerosol-Cloud Interactions,” Science 343(6169), 379–380 (2014).
[Crossref] [PubMed]

Z. Gu and W. Ubachs, “A systematic study of Rayleigh-Brillouin scattering in air, N2, and O2 gases,” J. Chem. Phys. 141(10), 104320 (2014).
[Crossref] [PubMed]

2013 (2)

2011 (1)

J. Tellinghuisen, “Least-squares analysis of overlapped bound-free absorption spectra and predissociation data in diatomics: the C(1Πu) state of I2.,” J. Chem. Phys. 135(5), 054301 (2011).
[Crossref] [PubMed]

2009 (1)

2008 (2)

2004 (1)

2002 (2)

2001 (2)

1997 (1)

1994 (2)

P. Piironen and E. W. Eloranta, “Demonstration of a high-spectral-resolution lidar based on an iodine absorption filter,” Opt. Lett. 19(3), 234–236 (1994).
[Crossref] [PubMed]

N. Srinivas and K. Deb, “Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,” Evol. Comput. 2(3), 221–248 (1994).
[Crossref]

1993 (2)

T. J. Quinn and J. M. Chartier, “A new type of iodine cell for stabilized lasers,” IEEE Trans. Instrum. Meas. 42(2), 405–406 (1993).
[Crossref]

J. A. Harrison, M. Zahedi, and J. W. Nibler, “Use of seeded Nd:YAG lasers for high-resolution spectroscopy,” Opt. Lett. 18(2), 149–151 (1993).
[Crossref] [PubMed]

1990 (2)

K. Wallmeroth and R. Letterer, “Cesium frequency standard for lasers at λ = 1.06 microm,” Opt. Lett. 15(14), 812–813 (1990).
[Crossref] [PubMed]

B. Hiller and R. K. Hanson, “Properties of the iodine molecule relevant to laser-induced fluorescence experiments in gas flows,” Exp. Fluids 10(1), 1–11 (1990).
[Crossref]

1983 (1)

1978 (1)

J. Tellinghuisen, “Intensity factors for the I2 B↔X band system,” J. Quant. Spectrosc. Radiat. Transf. 19(2), 149–161 (1978).
[Crossref]

1974 (1)

G. Tenti, C. D. Boley, and R. C. Desai, “On the Kinetic Model Description of Rayleigh–Brillouin Scattering from Molecular Gases,” Can. J. Phys. 52, 285–290 (1974).

1972 (1)

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic Models and Brillouin Scattering in a Molecular Gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[Crossref]

Abchiche, A.

Agarwal, S.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Amarouche, N.

Aouji, O.

Bai, J.

Bi, D.-C.

Blouzon, F.

Boley, C. D.

G. Tenti, C. D. Boley, and R. C. Desai, “On the Kinetic Model Description of Rayleigh–Brillouin Scattering from Molecular Gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic Models and Brillouin Scattering in a Molecular Gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[Crossref]

Bruneau, D.

Buchholtz, G.

Caldwell, L. M.

Chartier, J. M.

T. J. Quinn and J. M. Chartier, “A new type of iodine cell for stabilized lasers,” IEEE Trans. Instrum. Meas. 42(2), 405–406 (1993).
[Crossref]

Chen, W.-B.

Cheng, Z.

Cook, A. L.

Deb, K.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

N. Srinivas and K. Deb, “Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,” Evol. Comput. 2(3), 221–248 (1994).
[Crossref]

Desai, R. C.

G. Tenti, C. D. Boley, and R. C. Desai, “On the Kinetic Model Description of Rayleigh–Brillouin Scattering from Molecular Gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic Models and Brillouin Scattering in a Molecular Gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[Crossref]

Donner, L.

D. Rosenfeld, S. Sherwood, R. Wood, and L. Donner, “Atmospheric science. Climate Effects of Aerosol-Cloud Interactions,” Science 343(6169), 379–380 (2014).
[Crossref] [PubMed]

Duan, L.

Ehret, G.

Eloranta, E. W.

Esselborn, M.

Ferrare, R. A.

Fix, A.

Forkey, J. N.

Genau, P.

Gu, Z.

Z. Gu and W. Ubachs, “A systematic study of Rayleigh-Brillouin scattering in air, N2, and O2 gases,” J. Chem. Phys. 141(10), 104320 (2014).
[Crossref] [PubMed]

Hair, J. W.

Hanson, R. K.

B. Hiller and R. K. Hanson, “Properties of the iodine molecule relevant to laser-induced fluorescence experiments in gas flows,” Exp. Fluids 10(1), 1–11 (1990).
[Crossref]

Harper, D. B.

Harrison, J. A.

Hiller, B.

B. Hiller and R. K. Hanson, “Properties of the iodine molecule relevant to laser-induced fluorescence experiments in gas flows,” Exp. Fluids 10(1), 1–11 (1990).
[Crossref]

Hostetler, C. A.

Hovis, F. E.

Hua, D.

Huang, H.

Izquierdo, L. R.

Kobayashi, T.

Krueger, D. A.

Lempert, W. R.

Letterer, R.

Ling, T.

Liu, B.-Y.

Liu, C.

Liu, D.

Liu, J.-T.

Liu, Q.

Liu, Z.-S.

Luo, J.

Mack, T. L.

Meyarivan, T.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Miles, R. B.

Nibler, J. W.

Pelon, J.

Piironen, P.

Pratap, A.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

Quinn, T. J.

T. J. Quinn and J. M. Chartier, “A new type of iodine cell for stabilized lasers,” IEEE Trans. Instrum. Meas. 42(2), 405–406 (1993).
[Crossref]

Roesler, F. L.

Rosenfeld, D.

D. Rosenfeld, S. Sherwood, R. Wood, and L. Donner, “Atmospheric science. Climate Effects of Aerosol-Cloud Interactions,” Science 343(6169), 379–380 (2014).
[Crossref] [PubMed]

She, C.-Y.

Shen, Y.

Sherwood, S.

D. Rosenfeld, S. Sherwood, R. Wood, and L. Donner, “Atmospheric science. Climate Effects of Aerosol-Cloud Interactions,” Science 343(6169), 379–380 (2014).
[Crossref] [PubMed]

Shipley, S. T.

Song, X.-Q.

Spatazza, J.

Srinivas, N.

N. Srinivas and K. Deb, “Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,” Evol. Comput. 2(3), 221–248 (1994).
[Crossref]

Sroga, J. T.

Su, L.

Tang, P.

Tellinghuisen, J.

J. Tellinghuisen, “Least-squares analysis of overlapped bound-free absorption spectra and predissociation data in diatomics: the C(1Πu) state of I2.,” J. Chem. Phys. 135(5), 054301 (2011).
[Crossref] [PubMed]

J. Tellinghuisen, “Intensity factors for the I2 B↔X band system,” J. Quant. Spectrosc. Radiat. Transf. 19(2), 149–161 (1978).
[Crossref]

Tenti, G.

G. Tenti, C. D. Boley, and R. C. Desai, “On the Kinetic Model Description of Rayleigh–Brillouin Scattering from Molecular Gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic Models and Brillouin Scattering in a Molecular Gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[Crossref]

Tesche, M.

Tracy, D. H.

Trauger, J. T.

Ubachs, W.

Z. Gu and W. Ubachs, “A systematic study of Rayleigh-Brillouin scattering in air, N2, and O2 gases,” J. Chem. Phys. 141(10), 104320 (2014).
[Crossref] [PubMed]

Uchida, M.

Wallmeroth, K.

Wang, K.

Weibiao, C.

C. Weibiao, “Concept Design of Spaceborne Atmospheric Aerosol and Carbon Lidar,” in The 5th International Symposium on Atmospheric Light Scattering and Remote Sensing, (2015)

Weinman, J. A.

Welch, W.

Wirth, M.

Wood, R.

D. Rosenfeld, S. Sherwood, R. Wood, and L. Donner, “Atmospheric science. Climate Effects of Aerosol-Cloud Interactions,” Science 343(6169), 379–380 (2014).
[Crossref] [PubMed]

Wu, D.

Xu, P.

Yang, L.

Yang, Y.

Zahedi, M.

Zhang, B.

Zhang, K.-L.

Zhang, X.

Zhang, Y.

Zhou, Y.

Appl. Opt. (11)

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(23), 3716–3724 (1983).
[Crossref] [PubMed]

Z. Cheng, D. Liu, J. Luo, Y. Yang, L. Su, L. Yang, H. Huang, and Y. Shen, “Effects of spectral discrimination in high-spectral-resolution lidar on the retrieval errors for atmospheric aerosol optical properties,” Appl. Opt. 53(20), 4386–4397 (2014).
[Crossref] [PubMed]

D. Bruneau, J. Pelon, F. Blouzon, J. Spatazza, P. Genau, G. Buchholtz, N. Amarouche, A. Abchiche, and O. Aouji, “355-nm high spectral resolution airborne lidar LNG: system description and first results,” Appl. Opt. 54(29), 8776–8785 (2015).
[Crossref] [PubMed]

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(36), 6734–6752 (2008).
[Crossref] [PubMed]

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(3), 346–358 (2008).
[Crossref] [PubMed]

J. W. Hair, L. M. Caldwell, D. A. Krueger, and C.-Y. She, “High-spectral-resolution lidar with iodine-vapor filters: measurement of atmospheric-state and aerosol profiles,” Appl. Opt. 40(30), 5280–5294 (2001).
[Crossref] [PubMed]

Z.-S. Liu, D. Wu, J.-T. Liu, K.-L. Zhang, W.-B. Chen, X.-Q. Song, J. W. Hair, and C.-Y. She, “Low-altitude atmospheric wind measurement from the combined Mie and Rayleigh backscattering by Doppler lidar with an iodine filter,” Appl. Opt. 41(33), 7079–7086 (2002).
[Crossref] [PubMed]

C.-Y. She, “Spectral structure of laser light scattering revisited: bandwidths of nonresonant scattering lidars,” Appl. Opt. 40(27), 4875–4884 (2001).
[Crossref] [PubMed]

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(32), 7838–7850 (2013).
[Crossref] [PubMed]

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(27), 5143–5154 (2009).
[Crossref] [PubMed]

J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36(27), 6729–6738 (1997).
[Crossref] [PubMed]

Can. J. Phys. (2)

G. Tenti, C. D. Boley, and R. C. Desai, “On the Kinetic Model Description of Rayleigh–Brillouin Scattering from Molecular Gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic Models and Brillouin Scattering in a Molecular Gas,” Can. J. Phys. 50(18), 2158–2173 (1972).
[Crossref]

Evol. Comput. (1)

N. Srinivas and K. Deb, “Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,” Evol. Comput. 2(3), 221–248 (1994).
[Crossref]

Exp. Fluids (1)

B. Hiller and R. K. Hanson, “Properties of the iodine molecule relevant to laser-induced fluorescence experiments in gas flows,” Exp. Fluids 10(1), 1–11 (1990).
[Crossref]

IEEE Trans. Evol. Comput. (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6(2), 182–197 (2002).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

T. J. Quinn and J. M. Chartier, “A new type of iodine cell for stabilized lasers,” IEEE Trans. Instrum. Meas. 42(2), 405–406 (1993).
[Crossref]

J. Chem. Phys. (2)

J. Tellinghuisen, “Least-squares analysis of overlapped bound-free absorption spectra and predissociation data in diatomics: the C(1Πu) state of I2.,” J. Chem. Phys. 135(5), 054301 (2011).
[Crossref] [PubMed]

Z. Gu and W. Ubachs, “A systematic study of Rayleigh-Brillouin scattering in air, N2, and O2 gases,” J. Chem. Phys. 141(10), 104320 (2014).
[Crossref] [PubMed]

J. Quant. Spectrosc. Radiat. Transf. (1)

J. Tellinghuisen, “Intensity factors for the I2 B↔X band system,” J. Quant. Spectrosc. Radiat. Transf. 19(2), 149–161 (1978).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Science (1)

D. Rosenfeld, S. Sherwood, R. Wood, and L. Donner, “Atmospheric science. Climate Effects of Aerosol-Cloud Interactions,” Science 343(6169), 379–380 (2014).
[Crossref] [PubMed]

Other (5)

C. Weibiao, “Concept Design of Spaceborne Atmospheric Aerosol and Carbon Lidar,” in The 5th International Symposium on Atmospheric Light Scattering and Remote Sensing, (2015)

X. Pan, “Coherent Rayleigh-Brillouin Scattering,” (Princeton University, 2003).

G. Anderson, S. Clough, F. Kneizys, J. Chetwynd, and E. Shettle, “AFGL atmospheric constituent profiles (0-120 km),” AFGL-TR-0208 Environmental Research papers (1986).

S. Gerstenkorn and P. Luc, “Atlas du Spectre d’Absorption de la Molecule d’Iode 14800-20000 cm-1,” Paris: Editions du Centre National de la Recherche Scientifique (CNRS), 1978 (1978).

A. E. Eiben and S. K. Smit, “Evolutionary Algorithm Parameters and Methods to Tune Them,” in Autonomous Search, Y. Hamadi, E. Monfroy, and F. Saubion, eds. (Springer Berlin Heidelberg, Berlin, Heidelberg, 2012), pp. 15–36.

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram for an HSRL return spectra (the ratio of Mie scattering and Cabannes-Brillouin scattering is ploted in arbitrary value)
Fig. 2
Fig. 2 A example of the transmittance profile of the iodine cell with the temperature of 38 °C, the pressure of 0.7 torr and length of 15cm (lines 1104-1112)
Fig. 3
Fig. 3 The Pareto front of different iodide absorption lines
Fig. 4
Fig. 4 The distributions of Pareto solutions in the independent variable space. (a)the Pareto solutions distribution of cell pressure versus Tm; (b) the Pareto solutions distribution of cell temperature versus Tm; (c) the Pareto solutions distribution of cell length versus Tm; (d) the Pareto solutions distribution of cell pressure versus SDR; (e) the Pareto solutions distribution of cell temperature versus SDR; (f) the Pareto solutions distribution of cell length versus SDR.
Fig. 5
Fig. 5 Sensitivity analysis of “saturated” iodine cell due to controlling uncertainties for Parote solutions show in Fig. 3.(a)uncertainties of Tm versus Tm of line 1104; (b)uncertainties of SDR versus SDR of line 1104; (c)uncertainties of Tm versus Tm of line 1105; (d)uncertainties of SDR versus SDR of line 1105; (e)uncertainties of Tm versus Tm of line 1109; (f)uncertainties of SDR versus SDR of line 1109; (g)uncertainties of Tm versus Tm of line 1110; (h)uncertainties of SDR versus SDR of line 1110; (i)uncertainties of Tm versus Tm of line 1111; (j)uncertainties of SDR versus SDR of line 1111.
Fig. 6
Fig. 6 Same as Fig. 5 but for sensitivity analysis of “starved” iodine cell

Tables (3)

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Table 1 Assignments of the line number and the calculated center wavenumber

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Table 2 Initial parameters for NSGA-II

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Table 3 The statistic characters of the laser center frquency of the Pareto solutions.

Equations (10)

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S ( ν ν 0 ) = 2 ln 2 γ π exp [ ( 4 ln 2 ) ( ν ν 0 ) 2 γ 2 ] ,
f ( ν ) = exp [ l i n Γ i g i ( ν ) ] ,
T m ( x , T a t m , P a t m ) = ( ν , ν 0 , T a t m , p a t m ) f ( ν , T , p , l ) d ν ,
T a ( x ) = S ( ν ν 0 ) f ( ν , T , p , l ) d ν .
S D R ( x , T a t m , p a t m ) = 10 log 10 ( T m ( x , T a t m , P a t m ) T a ( x ) ) .
log 10 P s = 9.75715 2867.028 T c + 254.180 .
{ M a x i m u m T m ( x ) M a x i m u m R S D ( x ) ,
{ T m ( x ) = T m ( x , T a t m , 0 , P a t m , 0 ) R S D ( x ) = R S D ( x , T a t m , 0 , P a t m , 0 ) P P s , log 10 P s = 9.75715 2867.028 ( T 2 ) + 254.180 T min < T < T max l l max ν l o w ν 0 ν h i g h .
i = 1 , 2 , ... , N , f i ( x A ) f i ( x B ) j = 1 , 2 , ... , N , f j ( x A ) > f j ( x B ) ,
P = T T 0 P 0 ( w h e n T > T 0 ) ,

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