Abstract

Photographs of the Lycurgus Cup with a source light inside and outside exhibit purple and green colors, respectively (dichroism). A model relying on the scattering of light to colors in the photographs is proposed and used within an inverse problem algorithm, to deduce radius and composition of metallic particles, and the refractive index of the surrounding glass medium. The inverse problem algorithm is based on a hybridization of particle swarm optimization and of the simulated annealing methods. The results are compared to experimental measurements on a small sample of glass. The linear laws that are deduced from sets of possible parameters producing the same color in the photographs help simplify the understanding of phenomena. The proportion of silver to gold in nanoparticles is found to be in agreement, but a large proportion of copper is also found. The retrieved refractive index of the surrounding glass is close to 2.

© 2015 Optical Society of America

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  1. British Museum, “The Lycurgus Cup,” http://www.britishmuseum.org/explore/highlights/highlight_objects/pe_mla/t/the_lycurgus_cup.aspx (2015).
  2. D. J. Barber and I. C. Freestone, “An investigation of the origin of the colour of the Lycurgus Cup by analytical transmission electron microscopy,” Archaeometry 32, 33–45 (1990).
    [Crossref]
  3. A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
    [Crossref]
  4. M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
    [Crossref]
  5. J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
    [Crossref]
  6. S. Mestre, C. Chiva, M. D. Palacios, and J. L. Amorós, “Development of a yellow ceramic pigment based on silver nanoparticles,” J. Eur. Ceram. Soc. 32, 2825–2830 (2012).
    [Crossref]
  7. L. M. Liz-Marzán, “Nanometals: formation and color,” Mater. Today 7(2), 26–31 (2004).
    [Crossref]
  8. E. Stratakis and E. Kymakis, “Nanoparticle-based plasmonic organic photovoltaic devices,” Mater. Today 16(4), 133–146 (2013).
    [Crossref]
  9. D. Barchiesi and T. Grosges, “Resonance in metallic nanoparticles: a rigorous formulation of the dipolar approximation,” Eur. J. Phys. 35, 035012 (2014).
    [Crossref]
  10. K. M. Bryan, Z. Jia, N. K. Pervez, M. P. Cox, M. J. Gazes, and I. Kymissis, “Inexpensive photonic crystal spectrometer for colorimetric sensing applications,” Opt. Express 21, 4411–4423 (2013).
    [Crossref]
  11. I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
    [Crossref]
  12. H. E. Ives, “A proposed standard method of colorimetry,” J. Opt. Soc. Am. 5, 469–478 (1921).
    [Crossref]
  13. W. E. R. Davies and G. Wyszecki, “Physical approximation of color-mixture functions,” J. Opt. Soc. Am. 52, 679–685 (1962).
    [Crossref]
  14. M. Born and E. Wolf, Principles of Optics (Pergamon, 1993).
  15. G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen (Contributions to the optics of turbid media, especially colloidal metal solutions),” Ann. Phys. 330, 377–445 (1908).
    [Crossref]
  16. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [Crossref]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  18. T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
    [Crossref]
  19. T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2, 1584–1596 (2011).
    [Crossref]
  20. E. D. Palik, Handbook of Optical Constants (Academic, 1985).
  21. S. Kreft and M. Kreft, “Quantification of dichromatism: a characteristic of color in transparent materials,” J. Opt. Soc. Am. A 26, 1576–1581 (2009).
    [Crossref]
  22. R. S. Berns, “Colorimetry Part I: The basics and materials applications,” Opt. Photon. News 6(9), 23 (1995).
    [Crossref]
  23. G. Hoffmann, “CIE color space,” http://docs-hoffmann.de/ciexyz29082000.pdf (2013).
  24. W. W. Abney, “On the change in hue of spectrum colours by dilution with white light,” Proc. R. Soc. London 83, 120–127 (1909).
    [Crossref]
  25. W. Kurtenbach, C. E. Sternheim, and L. Spillmann, “Change in hue of spectral colors by dilution with white light (Abney effect),” J. Opt. Soc. Am. A 1, 365–372 (1984).
    [Crossref]
  26. J. Qiu, X. Jiang, C. Zhu, H. Inouye, J. Si, and K. Hirao, “Optical properties of structurally modified glasses doped with gold ions,” Opt. Lett. 29, 370–372 (2004).
    [Crossref]
  27. M. L. Simpson and J. F. Jansen, “Imaging colorimetry: a new approach,” Appl. Opt. 30, 4666–4671 (1991).
    [Crossref]
  28. D. Macias and D. Barchiesi, “Identification of unknown experimental parameters from noisy apertureless scanning near-field optical microscope data with an evolutionary procedure,” Opt. Lett. 30, 2557–2559 (2005).
    [Crossref]
  29. D. Barchiesi, “Numerical retrieval of thin aluminum layer properties from SPR experimental data,” Opt. Express 20, 9064–9078 (2012).
    [Crossref]
  30. T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
    [Crossref]
  31. J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
    [Crossref]
  32. S. Kessentini and D. Barchiesi, “Quantitative comparison of optimized nanorods, nanoshells and hollow nanospheres for photothermal therapy,” Biomed. Opt. Express 3, 590–604 (2012).
    [Crossref]
  33. R. Cao, H. J. Trussell, and R. Shamey, “Comparison of the performance of inverse transformation methods from OSA-UCS to CIEXYZ,” J. Opt. Soc. Am. A 30, 1508–1515 (2013).
    [Crossref]
  34. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE International Conference on Neural Networks, Perth, Australia (IEEE, 1995), Vol. IV, pp. 1942–1948.
  35. M. Clerc, “A method to improve standard PSO,” (France Telecom R&D, 2009).
  36. S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
    [Crossref]
  37. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [Crossref]
  38. S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
    [Crossref]
  39. H. Verweij, J. H. J. M. Buster, and G. F. Remmers, “Refractive index and density of Li-, Na- and K-germanosilicate glasses,” J. Mater. Sci. 14, 931–940 (1979).
    [Crossref]
  40. T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
    [Crossref]
  41. Malvern Instruments Ltd., “Sample dispersion & refractive index guide,” http://www.malvern.com/en/support/resource-center/user-manuals/MAN0396EN.aspx (1997).
  42. P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
    [Crossref]
  43. T. Turbadar, “Complete absorption of plane polarized light by thin metallic films,” Opt. Acta 11, 207–210 (1964).
    [Crossref]
  44. D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
    [Crossref]

2014 (2)

D. Barchiesi and T. Grosges, “Resonance in metallic nanoparticles: a rigorous formulation of the dipolar approximation,” Eur. J. Phys. 35, 035012 (2014).
[Crossref]

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

2013 (3)

2012 (3)

2011 (2)

S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
[Crossref]

T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2, 1584–1596 (2011).
[Crossref]

2010 (1)

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

2009 (3)

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

S. Kreft and M. Kreft, “Quantification of dichromatism: a characteristic of color in transparent materials,” J. Opt. Soc. Am. A 26, 1576–1581 (2009).
[Crossref]

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

2008 (3)

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[Crossref]

2007 (1)

I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
[Crossref]

2005 (1)

2004 (2)

1995 (1)

R. S. Berns, “Colorimetry Part I: The basics and materials applications,” Opt. Photon. News 6(9), 23 (1995).
[Crossref]

1991 (1)

1990 (1)

D. J. Barber and I. C. Freestone, “An investigation of the origin of the colour of the Lycurgus Cup by analytical transmission electron microscopy,” Archaeometry 32, 33–45 (1990).
[Crossref]

1984 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

1980 (1)

1979 (1)

H. Verweij, J. H. J. M. Buster, and G. F. Remmers, “Refractive index and density of Li-, Na- and K-germanosilicate glasses,” J. Mater. Sci. 14, 931–940 (1979).
[Crossref]

1977 (1)

T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
[Crossref]

1973 (1)

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

1964 (1)

T. Turbadar, “Complete absorption of plane polarized light by thin metallic films,” Opt. Acta 11, 207–210 (1964).
[Crossref]

1962 (1)

1959 (1)

T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
[Crossref]

1921 (1)

1909 (1)

W. W. Abney, “On the change in hue of spectrum colours by dilution with white light,” Proc. R. Soc. London 83, 120–127 (1909).
[Crossref]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen (Contributions to the optics of turbid media, especially colloidal metal solutions),” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Abney, W. W.

W. W. Abney, “On the change in hue of spectrum colours by dilution with white light,” Proc. R. Soc. London 83, 120–127 (1909).
[Crossref]

Amorós, J. L.

S. Mestre, C. Chiva, M. D. Palacios, and J. L. Amorós, “Development of a yellow ceramic pigment based on silver nanoparticles,” J. Eur. Ceram. Soc. 32, 2825–2830 (2012).
[Crossref]

Andraud, C.

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

Ayed, N.

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

Barber, D. J.

D. J. Barber and I. C. Freestone, “An investigation of the origin of the colour of the Lycurgus Cup by analytical transmission electron microscopy,” Archaeometry 32, 33–45 (1990).
[Crossref]

Barchiesi, D.

D. Barchiesi and T. Grosges, “Resonance in metallic nanoparticles: a rigorous formulation of the dipolar approximation,” Eur. J. Phys. 35, 035012 (2014).
[Crossref]

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

S. Kessentini and D. Barchiesi, “Quantitative comparison of optimized nanorods, nanoshells and hollow nanospheres for photothermal therapy,” Biomed. Opt. Express 3, 590–604 (2012).
[Crossref]

D. Barchiesi, “Numerical retrieval of thin aluminum layer properties from SPR experimental data,” Opt. Express 20, 9064–9078 (2012).
[Crossref]

T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2, 1584–1596 (2011).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
[Crossref]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[Crossref]

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

D. Macias and D. Barchiesi, “Identification of unknown experimental parameters from noisy apertureless scanning near-field optical microscope data with an evolutionary procedure,” Opt. Lett. 30, 2557–2559 (2005).
[Crossref]

Berns, R. S.

R. S. Berns, “Colorimetry Part I: The basics and materials applications,” Opt. Photon. News 6(9), 23 (1995).
[Crossref]

Berthier, S.

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1993).

Botelho, M. L.

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

Boulenguez, J.

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

Bryan, K. M.

Buster, J. H. J. M.

H. Verweij, J. H. J. M. Buster, and G. F. Remmers, “Refractive index and density of Li-, Na- and K-germanosilicate glasses,” J. Mater. Sci. 14, 931–940 (1979).
[Crossref]

Cao, R.

Chiva, C.

S. Mestre, C. Chiva, M. D. Palacios, and J. L. Amorós, “Development of a yellow ceramic pigment based on silver nanoparticles,” J. Eur. Ceram. Soc. 32, 2825–2830 (2012).
[Crossref]

Clerc, M.

M. Clerc, “A method to improve standard PSO,” (France Telecom R&D, 2009).

Colomban, P.

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

Cox, M. P.

Davies, W. E. R.

de Matos, A. B. A. P.

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

Eberhart, R.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE International Conference on Neural Networks, Perth, Australia (IEEE, 1995), Vol. IV, pp. 1942–1948.

Freestone, I.

I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
[Crossref]

Freestone, I. C.

D. J. Barber and I. C. Freestone, “An investigation of the origin of the colour of the Lycurgus Cup by analytical transmission electron microscopy,” Archaeometry 32, 33–45 (1990).
[Crossref]

Gazes, M. J.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Giraud-Moreau, L.

S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
[Crossref]

Gomes, C.

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

Gréhan, G.

Grosges, T.

D. Barchiesi and T. Grosges, “Resonance in metallic nanoparticles: a rigorous formulation of the dipolar approximation,” Eur. J. Phys. 35, 035012 (2014).
[Crossref]

S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
[Crossref]

T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2, 1584–1596 (2011).
[Crossref]

T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008).
[Crossref]

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

Higgitt, C.

I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
[Crossref]

Hirao, K.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Inouye, H.

Ishida, K.

T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
[Crossref]

Ives, H. E.

Jaeger, R. E.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Jansen, J. F.

Jia, Z.

Jiang, X.

Katsuyama, T.

T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
[Crossref]

Kennedy, J.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE International Conference on Neural Networks, Perth, Australia (IEEE, 1995), Vol. IV, pp. 1942–1948.

Kessentini, S.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Kreft, M.

Kreft, S.

Kremer, E.

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

Kurtenbach, W.

Kymakis, E.

E. Stratakis and E. Kymakis, “Nanoparticle-based plasmonic organic photovoltaic devices,” Mater. Today 16(4), 133–146 (2013).
[Crossref]

Kymissis, I.

Lafait, J.

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

Lamy de la Chapelle, M.

S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
[Crossref]

T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2, 1584–1596 (2011).
[Crossref]

Lima, A.

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

Liz-Marzán, L. M.

L. M. Liz-Marzán, “Nanometals: formation and color,” Mater. Today 7(2), 26–31 (2004).
[Crossref]

Macchiarola, M.

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

Macias, D.

Mai, V. P.

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

Meeks, N.

I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
[Crossref]

Mehta, A.

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

Melo, R.

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

Mestre, S.

S. Mestre, C. Chiva, M. D. Palacios, and J. L. Amorós, “Development of a yellow ceramic pigment based on silver nanoparticles,” J. Eur. Ceram. Soc. 32, 2825–2830 (2012).
[Crossref]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen (Contributions to the optics of turbid media, especially colloidal metal solutions),” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Palacios, M. D.

S. Mestre, C. Chiva, M. D. Palacios, and J. L. Amorós, “Development of a yellow ceramic pigment based on silver nanoparticles,” J. Eur. Ceram. Soc. 32, 2825–2830 (2012).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants (Academic, 1985).

Pervez, N. K.

Pinnow, D. A.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Qiu, J.

Reillon, V.

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

Remmers, G. F.

H. Verweij, J. H. J. M. Buster, and G. F. Remmers, “Refractive index and density of Li-, Na- and K-germanosilicate glasses,” J. Mater. Sci. 14, 931–940 (1979).
[Crossref]

Ricciardi, P.

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

Rich, T. C.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Ruivo, A.

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

Salvi, J.

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

Sax, M.

I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
[Crossref]

Shamey, R.

Si, J.

Simpson, M. L.

Spillmann, L.

Sternheim, C. E.

Stratakis, E.

E. Stratakis and E. Kymakis, “Nanoparticle-based plasmonic organic photovoltaic devices,” Mater. Today 16(4), 133–146 (2013).
[Crossref]

Suganuma, T.

T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
[Crossref]

Svoboda, M.

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

Toda, G.

T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
[Crossref]

Tournié, A.

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

Toury, T.

Trentelman, K.

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

Trussell, H. J.

Turbadar, T.

T. Turbadar, “Complete absorption of plane polarized light by thin metallic films,” Opt. Acta 11, 207–210 (1964).
[Crossref]

T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
[Crossref]

Uitert, L. G. V.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Verweij, H.

H. Verweij, J. H. J. M. Buster, and G. F. Remmers, “Refractive index and density of Li-, Na- and K-germanosilicate glasses,” J. Mater. Sci. 14, 931–940 (1979).
[Crossref]

Walton, M. S.

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

Webb, S.

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

Wemple, S. H.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

Wiscombe, W. J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1993).

Wyszecki, G.

Zhu, C.

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen (Contributions to the optics of turbid media, especially colloidal metal solutions),” Ann. Phys. 330, 377–445 (1908).
[Crossref]

Appl. Opt. (2)

Appl. Phys. A (1)

J. Salvi and D. Barchiesi, “Measurement of thicknesses and optical properties of thin films from surface plasmon resonance (SPR),” Appl. Phys. A 115, 245–255 (2014).
[Crossref]

Archaeometry (1)

D. J. Barber and I. C. Freestone, “An investigation of the origin of the colour of the Lycurgus Cup by analytical transmission electron microscopy,” Archaeometry 32, 33–45 (1990).
[Crossref]

Biomed. Opt. Express (2)

C.R. Phys. (1)

J. Lafait, S. Berthier, C. Andraud, V. Reillon, and J. Boulenguez, “Physical colors in cultural heritage: surface plasmons in glass,” C.R. Phys. 10, 649–659 (2009).
[Crossref]

Eur. J. Phys. (1)

D. Barchiesi and T. Grosges, “Resonance in metallic nanoparticles: a rigorous formulation of the dipolar approximation,” Eur. J. Phys. 35, 035012 (2014).
[Crossref]

Gold Bull. (Geneva) (1)

I. Freestone, N. Meeks, M. Sax, and C. Higgitt, “The Lycurgus Cup–a Roman nanotechnology,” Gold Bull. (Geneva) 40, 270–277 (2007).
[Crossref]

Int. J. Appl. Metaheuristics Comput. (1)

S. Kessentini, D. Barchiesi, T. Grosges, L. Giraud-Moreau, and M. Lamy de la Chapelle, “Adaptive non-uniform particle swarm application to plasmonic design,” Int. J. Appl. Metaheuristics Comput. 2, 18–28 (2011).
[Crossref]

J. Appl. Phys. (1)

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, and L. G. V. Uitert, “Binary SiO2-B2O3 glass system: refractive index behavior and energy gap considerations,” J. Appl. Phys. 44, 5432–5437 (1973).
[Crossref]

J. Archaeol. Sci. (2)

P. Ricciardi, P. Colomban, A. Tournié, M. Macchiarola, and N. Ayed, “A non-invasive study of Roman age mosaic glass tesserae by means of Raman spectroscopy,” J. Archaeol. Sci. 36, 2551–2559 (2009).
[Crossref]

M. S. Walton, M. Svoboda, A. Mehta, S. Webb, and K. Trentelman, “Material evidence for the use of attic white-ground lekythoi ceramics in cremation burials,” J. Archaeol. Sci. 37, 936–940 (2010).
[Crossref]

J. Cult. Heritage (1)

A. Ruivo, C. Gomes, A. Lima, M. L. Botelho, R. Melo, and A. B. A. P. de Matos, “Gold nanoparticles in ancient and contemporary ruby glass,” J. Cult. Heritage 9, e134–e137 (2008).
[Crossref]

J. Eur. Ceram. Soc. (1)

S. Mestre, C. Chiva, M. D. Palacios, and J. L. Amorós, “Development of a yellow ceramic pigment based on silver nanoparticles,” J. Eur. Ceram. Soc. 32, 2825–2830 (2012).
[Crossref]

J. Mater. Sci. (1)

H. Verweij, J. H. J. M. Buster, and G. F. Remmers, “Refractive index and density of Li-, Na- and K-germanosilicate glasses,” J. Mater. Sci. 14, 931–940 (1979).
[Crossref]

J. Microsc. (1)

D. Barchiesi, E. Kremer, V. P. Mai, and T. Grosges, “A Poincaré’s approach for plasmonics: the plasmon localization,” J. Microsc. 229, 525–532 (2008).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Mater. Today (2)

L. M. Liz-Marzán, “Nanometals: formation and color,” Mater. Today 7(2), 26–31 (2004).
[Crossref]

E. Stratakis and E. Kymakis, “Nanoparticle-based plasmonic organic photovoltaic devices,” Mater. Today 16(4), 133–146 (2013).
[Crossref]

Opt. Acta (1)

T. Turbadar, “Complete absorption of plane polarized light by thin metallic films,” Opt. Acta 11, 207–210 (1964).
[Crossref]

Opt. Commun. (1)

T. Katsuyama, T. Suganuma, K. Ishida, and G. Toda, “Refractive index behavior of SiO2-P2O5 glass in optical fiber application,” Opt. Commun. 21, 182–184 (1977).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Opt. Photon. News (1)

R. S. Berns, “Colorimetry Part I: The basics and materials applications,” Opt. Photon. News 6(9), 23 (1995).
[Crossref]

Proc. Phys. Soc. London (1)

T. Turbadar, “Complete absorption of light by thin metal films,” Proc. Phys. Soc. London 73, 40–44 (1959).
[Crossref]

Proc. R. Soc. London (1)

W. W. Abney, “On the change in hue of spectrum colours by dilution with white light,” Proc. R. Soc. London 83, 120–127 (1909).
[Crossref]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref]

Other (8)

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in IEEE International Conference on Neural Networks, Perth, Australia (IEEE, 1995), Vol. IV, pp. 1942–1948.

M. Clerc, “A method to improve standard PSO,” (France Telecom R&D, 2009).

Malvern Instruments Ltd., “Sample dispersion & refractive index guide,” http://www.malvern.com/en/support/resource-center/user-manuals/MAN0396EN.aspx (1997).

G. Hoffmann, “CIE color space,” http://docs-hoffmann.de/ciexyz29082000.pdf (2013).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1993).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

E. D. Palik, Handbook of Optical Constants (Academic, 1985).

British Museum, “The Lycurgus Cup,” http://www.britishmuseum.org/explore/highlights/highlight_objects/pe_mla/t/the_lycurgus_cup.aspx (2015).

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Figures (16)

Fig. 1.
Fig. 1. Photograph of the Lycurgus Cup, courtesy of the British Museum. The light source is (a) in the cup or (b) outside the cup. Black circles indicate the positions of extracted colors.

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Fig. 2.
Fig. 2. Best scattered and backscattered spectra obtained by varying the refractive index n 1 of the embedding glass and the radius R of nanoparticles, for p Ag = 66.2 % , p Au = 31.2 % , and p Cu = 2.6 % .

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Fig. 3.
Fig. 3. Spectra obtained from the scattering efficiency for the red sRGB target under constraint p Ag > p Au . The reference color and the retrieved color are shown. The whole sRGB spectrum is shown for clarity.

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Fig. 4.
Fig. 4. Histogram of the radii R of particles, leading to agreement between the reference and sRGB colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au .

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Fig. 5.
Fig. 5. Histogram of the proportions p Ag of silver in particles, leading to agreement between the reference and sRGB colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au .

Download Full Size | PPT Slide | PDF

Fig. 6.
Fig. 6. Histogram of the proportions p Au of gold in particles, leading to agreement between the reference and sRGB purple colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au .

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Fig. 7.
Fig. 7. Histogram of the proportions p Cu of copper in particles, leading to agreement between the reference and sRGB purple colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au .

Download Full Size | PPT Slide | PDF

Fig. 8.
Fig. 8. Histogram of the refractive indices n 1 of glass embedding particles, leading to agreement between the reference and sRGB purple colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au .

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Fig. 9.
Fig. 9. Correlation diagram of all the parameters among the solutions given by the inverse problem resolution in the purple case under constraint p Ag > p Au .

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Fig. 10.
Fig. 10. Spectra obtained from the scattering efficiency for the green sRGB target under constraint p Ag > p Au . The reference color and the retrieved color are shown. The whole sRGB spectrum is shown for clarity. (a) Scattering and (b) back scattering.

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Fig. 11.
Fig. 11. Histogram of the radii R of particles, leading to agreement between the reference and green sRGB colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au . (a) Scattering and (b) back scattering.

Download Full Size | PPT Slide | PDF

Fig. 12.
Fig. 12. Histogram of the proportions p Ag of silver in particles, leading to agreement between the reference and green sRGB colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au . (a) Scattering and (b) back scattering.

Download Full Size | PPT Slide | PDF

Fig. 13.
Fig. 13. Histogram of the proportions p Au of gold in particles, leading to agreement between the reference and sRGB green colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au . (a) Scattering and (b) back scattering.

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Fig. 14.
Fig. 14. Histogram of the proportions p Cu of copper in particles, leading to agreement between the reference and sRGB green colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au . (a) Scattering and (b) back scattering.

Download Full Size | PPT Slide | PDF

Fig. 15.
Fig. 15. Histogram of the refractive indices n 1 of glass embedding particles, leading to agreement between the reference and sRGB green colors. The black histogram corresponds to all solutions; the light one corresponds to the selected under constraint p Ag > p Au . (a) Scattering and (b) back scattering.

Download Full Size | PPT Slide | PDF

Fig. 16.
Fig. 16. Correlation diagram of all the parameters among the solutions given by the inverse problem resolution using scattering in the green case under constraint p Ag > p Au . (a) Scattering and (b) back scattering.

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Tables (4)

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Table 1. Mean Value and Standard Deviation (between Brackets) of the 20 sRGB Colors Extracted from Figs. 1(a) and 1(b)

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Table 2. Best Radius and Refractive Index of Glass Calculated with the Proportions of Metals p Ag = 66.2 % , p Au = 31.2 % , and p Cu = 2.6 % a

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Table 3. Mean Value and Standard Deviation of the Solutions of the Inverse Problem Using Intervals for the Proportions of Metals p Ag = 66.2 ± 2.5 % , p Au = 31.2 ± 1.5 % , and p Cu = 2.6 ± 0.3 % [2], and [1.44; 2.5] for the Refractive Index n 1 of Glass

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Table 4. Mean Value and Standard Deviation of the Solutions of the Inverse Problem, Best Parameters over the Realizations, and Mean Value and Standard Deviation of the Solutions of the Inverse Problem under Constraint p Ag > p Au a

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Equations (34)

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

T = ( 1 − n 1 1 + n 1 ) 2 ( n 1 − 1 1 + n 1 ) 2 .
Q sca ( λ 0 ) = 2 x 0 2 ∑ n ( 2 n + 1 ) [ | a n | 2 + | b n | 2 ] ,
Q back ( λ 0 ) = 1 x 0 2 | ∑ n ( 2 n + 1 ) ( − 1 ) n [ a n − b n ] | 2 .
max ( n ) = x 0 + 4 x 0 1 / 3 + 2 .
a n = m 2 j n ( m x 0 ) [ x 0 j n ( x 0 ) ] ′ − j n ( x 0 ) [ m x 0 j n ( m x 0 ) ] ′ m 2 j n ( m x 0 ) [ x 0 h n ( 1 ) ( x 0 ) ] ′ − h n ( 1 ) ( x 0 ) [ m x 0 j n ( m x 0 ) ] ′ ,
b n = j n ( m x 0 ) [ x 0 j n ( x 0 ) ] ′ − j n ( x 0 ) [ m x 0 j n ( m x 0 ) ] ′ j n ( m x 0 ) [ x 0 h n ( 1 ) ( x 0 ) ] ′ − h n ( 1 ) ( x 0 ) [ m x 0 j n ( m x 0 ) ] ′ .
n ^ eff = ( p Ag n ^ Ag 2 + p Au n ^ Au 2 + ( 1 − p Ag − p Au ) n ^ Cu 2 ) 1 / 2 ,
X = ∫ T Q ( λ 0 ) x ¯ d λ 0 , Y = ∫ T Q ( λ 0 ) y ¯ d λ 0 , Z = ∫ T Q ( λ 0 ) z ¯ d λ 0 .
( R sRGB G sRGB B sRGB ) = ( 3.2406 − 1.5372 − 0.4986 − 0.9689 1.8758 0.0415 0.0557 − 0.2040 1.0570 ) . ( X Y Z ) .
R = 12.92 R sRGB , G = 12.92 G sRGB , B = 12.92 B sRGB ,
R = 1.055 ( R sRGB ) 1 / 2.4 − 0.055 , G = 1.055 ( G sRGB ) 1 / 2.4 − 0.055 , B = 1.055 ( B sRGB ) 1 / 2.4 − 0.055 .
F ( p Ag , p Au , R , n 1 ) = r g ( R ) 2 + r g ( G ) 2 + r g ( B ) 2 ,
r g ( R ) = 1 − R R ref .
x ( t a + 1 ) = x ( t a ) + ( ( t a + 1 ) − t a ) V ( t a + 1 ) = x ( t a ) + V ( t a + 1 ) .
V ( t a + 1 ) = ω PSO V ( t a ) + U 1 c 1 ( p ( t a ) − x ( t a ) ) + U 2 c 2 ( g ( t a ) − x ( t a ) ) ,
n ^ eff = p Ag ′ n ^ Ag + p Au ′ n ^ Au + ( 1 − p Ag ′ − p Au ′ ) n ^ Cu .
Q ^ sca ( λ 0 ) ≈ 8 3 x 0 4 | m 2 − 1 m 2 + 2 | 2 ,
Q ^ back ( λ 0 ) ≈ 4 x 0 4 | m 2 − 1 m 2 + 2 | 2 .
n 1 = − 0.1109 S + 3.755 ( 3.10 − 4 ) ,
p Ag = − 0.1589 S + 2.541 ( 1.10 − 3 ) ,
p Au = 0.1345 S − 1.983 ( 3.10 − 4 ) .
S = 15.995 − 6.295 p Ag = 14.748 + 7.437 p Au ,
n 1 = 1.982 + 0.698 p Ag = 2.120 − 0.824 p Au .
p Ag p Au = − 1.181 + 0.198 p Au ,
= 18.896 – 1.1814 S − 14.748 + S ,
= 2.341 − 1.18138 n 1 − 2.120 + n 1 .
n 1 = − 0.1059 S + 3.436 ( 3.10 − 4 ) ,
p Ag = − 0.1216 S + 2.065 ( 9.10 − 3 ) ,
p Au = 0.1260 S − 1.619 ( 5.10 − 3 ) .
S = 16.982 − 8.224 p Ag = 12.849 + 7.937 p Au ,
n 1 = 1.872 + 0.912 p Ag = 2.120 − 0.824 p Au .
p Ag p Au = − 0.965 + 0.502 p Au ,
= 16.389 – 0.965 S − 12.849 + S ,
= 1.580 − 0.965 n 1 − 2.075 + n 1 .

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