Abstract

A smart radiation device (SRD) that is a variable emittance radiator has been studied as a method of thermal control for spacecraft. The SRD consists of manganese oxide with a perovskite-type structure, and the total hemispherical emittance of the SRD changes considerably depending on temperature. Here we propose an optimal method of designing multilayer films for the SRD by using a genetic algorithm. The multilayer films reflect solar radiation and transmit far-infrared radiation to maintain variation of the infrared optical properties of the SRD.

© 2003 Optical Society of America

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References

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  1. S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).
  2. K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
    [CrossRef]
  3. L. Li, J. A. Dobrowolski, “Computation speeds of different optical thin-film synthesis methods,” Appl. Opt. 31, 3790–3799 (1992).
    [CrossRef] [PubMed]
  4. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]
  5. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  6. Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
    [CrossRef]
  7. A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
    [CrossRef]
  8. C. Zener, “Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure,” Phys. Rev. 82, 403–405 (1951).
    [CrossRef]
  9. P.-G. de Gennes, “Effects of double exchange in magnetic crystals,” Phys. Rev. 118, 141–154 (1960).
    [CrossRef]
  10. G. H. Jonker, J. H. van Santen, “Ferromagnetic compounds of manganese with perovskite structure,” Physica (The Hague) 16, 337–349 (1950).
    [CrossRef]
  11. A. Ohnishi, T. Hayashi, “Measurement of incidence angle dependence of solar absorptance,” in Proceedings of the International Symposium on Environmental and Thermal Systems for Space Vehicles, ESA SP-200, T. D. Guyenne, J. J. Hunt, eds. (ESA Scientific Technical Publications Branch, Noordwijk, The Netherlands, 1983, pp. 467–470.
  12. T. Arima, Y. Tokura, “Optical study of electric structure in perovskite-type RMO3 (R = La, Y; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu),” J. Phys. Soc. Jpn. 64, 2488–2501 (1995).
    [CrossRef]
  13. R. Horikoshi, Y. Nagasaka, A. Ohnishi, “A method for calculating thermal radiation properties of multilayer films from optical constants,” Int. J. Thermophys. 19, 547–555 (1998).
    [CrossRef]
  14. O. S. Heavens, “Thin film optics,” in Optical Properties of Thin Solid Films (Dover, New York, 1991), pp. 46–95.
  15. M. P. Thekaekara, “The solar constant and the solar spectrum measured from a research aircraft, (NASA Tech.Rep. R-351 (NASA, Greenbelt, Md., 1970), pp. 71–80.
  16. D. M. Roessler, “Kramers-Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).
    [CrossRef]
  17. K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
    [CrossRef]
  18. E. D. Palik, ed., Handbook of Optical Constants of Solids I–III (Academic, New York, 1998).

2001 (2)

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
[CrossRef]

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
[CrossRef]

1998 (1)

R. Horikoshi, Y. Nagasaka, A. Ohnishi, “A method for calculating thermal radiation properties of multilayer films from optical constants,” Int. J. Thermophys. 19, 547–555 (1998).
[CrossRef]

1995 (3)

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

T. Arima, Y. Tokura, “Optical study of electric structure in perovskite-type RMO3 (R = La, Y; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu),” J. Phys. Soc. Jpn. 64, 2488–2501 (1995).
[CrossRef]

1992 (1)

1990 (1)

1965 (1)

D. M. Roessler, “Kramers-Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).
[CrossRef]

1960 (1)

P.-G. de Gennes, “Effects of double exchange in magnetic crystals,” Phys. Rev. 118, 141–154 (1960).
[CrossRef]

1951 (1)

C. Zener, “Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure,” Phys. Rev. 82, 403–405 (1951).
[CrossRef]

1950 (1)

G. H. Jonker, J. H. van Santen, “Ferromagnetic compounds of manganese with perovskite structure,” Physica (The Hague) 16, 337–349 (1950).
[CrossRef]

Arima, T.

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

T. Arima, Y. Tokura, “Optical study of electric structure in perovskite-type RMO3 (R = La, Y; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu),” J. Phys. Soc. Jpn. 64, 2488–2501 (1995).
[CrossRef]

Asamitsu, A.

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

de Gennes, P.-G.

P.-G. de Gennes, “Effects of double exchange in magnetic crystals,” Phys. Rev. 118, 141–154 (1960).
[CrossRef]

Dobrowolski, J. A.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Hayashi, T.

A. Ohnishi, T. Hayashi, “Measurement of incidence angle dependence of solar absorptance,” in Proceedings of the International Symposium on Environmental and Thermal Systems for Space Vehicles, ESA SP-200, T. D. Guyenne, J. J. Hunt, eds. (ESA Scientific Technical Publications Branch, Noordwijk, The Netherlands, 1983, pp. 467–470.

Heavens, O. S.

O. S. Heavens, “Thin film optics,” in Optical Properties of Thin Solid Films (Dover, New York, 1991), pp. 46–95.

Horikoshi, R.

R. Horikoshi, Y. Nagasaka, A. Ohnishi, “A method for calculating thermal radiation properties of multilayer films from optical constants,” Int. J. Thermophys. 19, 547–555 (1998).
[CrossRef]

Ishikawa, T.

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

Jonker, G. H.

G. H. Jonker, J. H. van Santen, “Ferromagnetic compounds of manganese with perovskite structure,” Physica (The Hague) 16, 337–349 (1950).
[CrossRef]

Katsufiji, T.

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

Kemp, R. A.

Kido, G.

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

Kosaka, M.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Li, L.

Mori, T.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Moritomo, Y.

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

Nagasaka, Y.

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
[CrossRef]

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
[CrossRef]

R. Horikoshi, Y. Nagasaka, A. Ohnishi, “A method for calculating thermal radiation properties of multilayer films from optical constants,” Int. J. Thermophys. 19, 547–555 (1998).
[CrossRef]

Nakamura, Y.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Ochi, A.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Ohnishi, A.

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
[CrossRef]

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
[CrossRef]

R. Horikoshi, Y. Nagasaka, A. Ohnishi, “A method for calculating thermal radiation properties of multilayer films from optical constants,” Int. J. Thermophys. 19, 547–555 (1998).
[CrossRef]

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

A. Ohnishi, T. Hayashi, “Measurement of incidence angle dependence of solar absorptance,” in Proceedings of the International Symposium on Environmental and Thermal Systems for Space Vehicles, ESA SP-200, T. D. Guyenne, J. J. Hunt, eds. (ESA Scientific Technical Publications Branch, Noordwijk, The Netherlands, 1983, pp. 467–470.

Okamoto, A.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Okimoto, Y.

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

Roessler, D. M.

D. M. Roessler, “Kramers-Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).
[CrossRef]

Shimakawa, Y.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Shimazaki, K.

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
[CrossRef]

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
[CrossRef]

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Tachikawa, S.

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
[CrossRef]

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
[CrossRef]

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

Thekaekara, M. P.

M. P. Thekaekara, “The solar constant and the solar spectrum measured from a research aircraft, (NASA Tech.Rep. R-351 (NASA, Greenbelt, Md., 1970), pp. 71–80.

Tokura, Y.

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

T. Arima, Y. Tokura, “Optical study of electric structure in perovskite-type RMO3 (R = La, Y; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu),” J. Phys. Soc. Jpn. 64, 2488–2501 (1995).
[CrossRef]

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

Urushibara, A.

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

van Santen, J. H.

G. H. Jonker, J. H. van Santen, “Ferromagnetic compounds of manganese with perovskite structure,” Physica (The Hague) 16, 337–349 (1950).
[CrossRef]

Zener, C.

C. Zener, “Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure,” Phys. Rev. 82, 403–405 (1951).
[CrossRef]

Appl. Opt. (2)

Br. J. Appl. Phys. (1)

D. M. Roessler, “Kramers-Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).
[CrossRef]

High Temp.—High Pressures (1)

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Temperature dependence of total hemispherical emittance in perovskite-type manganese oxide, La1–xSr1–xMnO3,” High Temp.—High Pressures 33, 525–531 (2001).
[CrossRef]

Int. J. Thermophys. (2)

K. Shimazaki, S. Tachikawa, A. Ohnishi, Y. Nagasaka, “Radiative and optical properties of La1–xSrxMnO3 (0≤ x ≤ 0.4) in the vicinity of metal-insulator transition temperatures from 173 to 413 K,” Int. J. Thermophys. 22, 1549–1561 (2001).
[CrossRef]

R. Horikoshi, Y. Nagasaka, A. Ohnishi, “A method for calculating thermal radiation properties of multilayer films from optical constants,” Int. J. Thermophys. 19, 547–555 (1998).
[CrossRef]

J. Phys. Soc. Jpn. (1)

T. Arima, Y. Tokura, “Optical study of electric structure in perovskite-type RMO3 (R = La, Y; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu),” J. Phys. Soc. Jpn. 64, 2488–2501 (1995).
[CrossRef]

Phys. Rev. (2)

C. Zener, “Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure,” Phys. Rev. 82, 403–405 (1951).
[CrossRef]

P.-G. de Gennes, “Effects of double exchange in magnetic crystals,” Phys. Rev. 118, 141–154 (1960).
[CrossRef]

Phys. Rev. B (2)

Y. Okimoto, T. Katsufiji, T. Ishikawa, T. Arima, Y. Tokura, “Variation of electronic structure in La1–xSrxMnO3 (0≤×≤0.3) as investigated by optical conductivity spectra,” Phys. Rev. B 55, 4206–4214 (1995).
[CrossRef]

A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, “Insulator-metal transition and giant magnetoresistance in La1–xSrxMnO3,” Phys. Rev. B 51, 14103–14109 (1995).
[CrossRef]

Physica (The Hague) (1)

G. H. Jonker, J. H. van Santen, “Ferromagnetic compounds of manganese with perovskite structure,” Physica (The Hague) 16, 337–349 (1950).
[CrossRef]

Other (6)

A. Ohnishi, T. Hayashi, “Measurement of incidence angle dependence of solar absorptance,” in Proceedings of the International Symposium on Environmental and Thermal Systems for Space Vehicles, ESA SP-200, T. D. Guyenne, J. J. Hunt, eds. (ESA Scientific Technical Publications Branch, Noordwijk, The Netherlands, 1983, pp. 467–470.

S. Tachikawa, A. Ohnishi, K. Shimazaki, A. Okamoto, Y. Nakamura, Y. Shimakawa, M. Kosaka, T. Mori, A. Ochi, “Design and ground test results of a variable emittance radiator,” SAE Technical Paper 00ICES-314 (Society of Automotive Engineers, Warrendale, Pa., 2000).

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

O. S. Heavens, “Thin film optics,” in Optical Properties of Thin Solid Films (Dover, New York, 1991), pp. 46–95.

M. P. Thekaekara, “The solar constant and the solar spectrum measured from a research aircraft, (NASA Tech.Rep. R-351 (NASA, Greenbelt, Md., 1970), pp. 71–80.

E. D. Palik, ed., Handbook of Optical Constants of Solids I–III (Academic, New York, 1998).

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Figures (9)

Fig. 1
Fig. 1

Temperature dependence of ε H of the SRD.

Fig. 2
Fig. 2

Schematic drawing of the cryostat and the optical unit for Fourier-transform infrared measurements.

Fig. 3
Fig. 3

Temperature dependence of the spectral reflectance of the SRD.

Fig. 4
Fig. 4

Schematic drawing of the coding.

Fig. 5
Fig. 5

Flow chart of the GA.

Fig. 6
Fig. 6

Fitness.

Fig. 7
Fig. 7

Results of the calculation of the spectral reflectance of the SRD at room temperature.

Fig. 8
Fig. 8

Results of the calculation of the spectral reflectance of the SRD with multilayer films at 173 and 313 K.

Fig. 9
Fig. 9

Comparison of the ε H of the SRD: ○, calculated data; ●, measured data. The solid curves provided as a guide for the eye.

Tables (2)

Tables Icon

Table 1 Optimum Sequence of Materials and Thickness Obtained with the GA

Tables Icon

Table 2 Comparison of α S and Δε H (173–313 K) of the SRD

Equations (6)

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

P=Pd1, M1;;dN, MN,
Rmλ, θ=rm+Rm-1λ, θ exp-iηm1+rmRm-1λ, θ exp-iηm,
εHT=0π/20.251001-Rλ, θ ibλ, T cos θ sin θ dλdθ0π/20.25100ibλ, T cos θ sin θ dλdθ,
αs=0.252.51-Rλ, θIsλdλ0.252.5 Isλdλ,
merit function=12i2QiD-QiPδQi2,
fitness=1merit function.

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