Abstract

The technique used by Leonardo da Vinci to paint flesh tints—the sfumato—has never been scientifically depicted until now. From 100,000,000 reflectance spectra recorded on Mona Lisa, a virtual removal of the varnish is first obtained. A unique umber pigment is then identified in the upper layer and an exceptional maximum of the color saturation is underlined, both characteristics of a glaze technique. The modeling calling upon the radiative transfer equation confirms this maximum of saturation, the identification of an umber in the upper layer, and moreover underlines a mixture of 1% vermilion and 99% lead white in the base layer. Finally, the modeling, using the auxiliary function method, explains the spectacular maximum of saturation by the multiple scattering.

© 2008 Optical Society of America

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References

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  1. L. Simonot and M. Elias, “Special visual effect of art glazes explained by the radiative transfer equation,” Appl. Opt. 43, 2580-2587 (2004).
    [CrossRef] [PubMed]
  2. M. Elias and L. Simonot, “Separation between the different fluxes scattered by art glazes: explanation of the special color saturation,” Appl. Opt. 45, 3163-3172 (2006).
    [CrossRef] [PubMed]
  3. E. Panofski, Les Primitifs Flamands (Hazan, 1992).
  4. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  5. M. Elias and G. Elias, “Radiative transfer in inhomogeneous stratified media using the auxiliary function method,” J. Opt. Soc. Am. A 21, 580-589 (2004).
    [CrossRef]
  6. C. N. Cochin, Voyage Pittoresque d'Italie (Ch.-Ant. Jombert, 1773).
  7. V. Pomarède, La Joconde (Prat / Europa, 1988).
  8. G. Vasari, The Lives of the Artists (Penguin, 1987), English translation.
  9. J. Franck, “The Unrestorable Sfumato,” in Academia Leonardi Vinci (UCLA , 1993), Vol. VI, p. 238.
  10. M. Kemp, Leonardo da Vinci (Oxford, 2006).
  11. D. Arasse, Léonard de Vinci (Hazan, 2003).
  12. E. H. Gombrich, The Story of Art (Phaidon, 1999), p. 300.
  13. K. Clark, “Mona Lisa,” The Burlington Magazine 115, 144-150 (1973).
  14. M. Gelb, The How to Think Like Leonardo Da Vinci Workbook (Dell, 1998).
  15. M. S. Livingstone, “Is it warm? Is it real? Or just low spatial frequency,” Science 290, 1299 (2000), doi: 10.1126/science.290.5495.1299b.
    [CrossRef]
  16. D. Queiros-Conde, “The turbulent structure of sfumato within Mona Lisa,” Leonardo 37, 223-228 (2004).
    [CrossRef]
  17. J. F. Asmus, “Mona Lisa symbolism uncovered by computer processing,” Mater. Charact. 29, 119-128 (1992).
    [CrossRef]
  18. L. L. Kontsevich and C. W. Tyler, “Making Mona frown,” Science 304, 1900 (2004), doi: 10.1126/science.304.5679.1900b.
    [CrossRef]
  19. F. Blais, J. Taylor, L. Cournoyer, M. Picard, L. Borgeat, G. Godin, J. A. Beraldin, and M. Rioux, “More than a poplar plank: the shape and subtle colours of the masterpiece 'Mona Lisa' by Leonardo,” Proc. SPIE 6491, 649106 (2007).
    [CrossRef]
  20. J. P. Mohen, M. Menu, and B. Mottin, Mona Lisa: Inside the Painting (Abrams, 2006), p. 92.
  21. P. Cotte and M. Dupouy, “CRISATEL: a high resolution multispectral system,” Proceedings of PICS'03 Conference, Rochester, USA (2003), pp. 161-165.
  22. P. Cotte and D. Dupraz, “Spectral imaging of Leonardo da Vinci's Mona Lisa: an authentic smile at 1523 dpi,” Proceedings of IS&T Archiving'06, Ottawa, USA (2006), p. 228.
  23. M. Elias, L. Simonot, L. M. Thoury, and J. M. Frigerio, “Bi-directional reflectance of a varnished painting part 2: influence of the refractive indices, surface state and absorption--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
    [CrossRef]
  24. M. Elias, M. R. De La Rie, J. Delanay, and E. Charron, “Leveling of varnishes over rough substrates,” Opt. Commun. 266, 586-591 (2006).
    [CrossRef]
  25. P. Cotte and D. Dupraz, “Spectral imaging of Leonardo da Vinci's Mona Lisa: a true colour smile without the influence of aged varnish,” Proceeding IS&T CGVI '06, 311, Leeds, UK (2006).
  26. G. Dupuis, M. Elias, and L. Simonot, “Pigment identification by fiber-optics diffuse reflectance spectroscopy,” Appl. Spectrosc. 56, 1329-1336 (2002).
    [CrossRef]
  27. G. Wyszecki and W. S. Stiles,Color Science: Concepts and Methods, Quantitative Data and Formulae 2nd ed. (Wiley, 1982).
  28. G. Latour, M. Elias, and J. M. Frigerio, “Color modeling of stratified pictorial layers using the radiative transfer equation solved by the auxiliary function method,” J. Opt. Soc. Am. A 24, 3045-3053 (2007).
    [CrossRef]

2007 (2)

F. Blais, J. Taylor, L. Cournoyer, M. Picard, L. Borgeat, G. Godin, J. A. Beraldin, and M. Rioux, “More than a poplar plank: the shape and subtle colours of the masterpiece 'Mona Lisa' by Leonardo,” Proc. SPIE 6491, 649106 (2007).
[CrossRef]

G. Latour, M. Elias, and J. M. Frigerio, “Color modeling of stratified pictorial layers using the radiative transfer equation solved by the auxiliary function method,” J. Opt. Soc. Am. A 24, 3045-3053 (2007).
[CrossRef]

2006 (2)

M. Elias and L. Simonot, “Separation between the different fluxes scattered by art glazes: explanation of the special color saturation,” Appl. Opt. 45, 3163-3172 (2006).
[CrossRef] [PubMed]

M. Elias, M. R. De La Rie, J. Delanay, and E. Charron, “Leveling of varnishes over rough substrates,” Opt. Commun. 266, 586-591 (2006).
[CrossRef]

2004 (5)

M. Elias and G. Elias, “Radiative transfer in inhomogeneous stratified media using the auxiliary function method,” J. Opt. Soc. Am. A 21, 580-589 (2004).
[CrossRef]

L. Simonot and M. Elias, “Special visual effect of art glazes explained by the radiative transfer equation,” Appl. Opt. 43, 2580-2587 (2004).
[CrossRef] [PubMed]

M. Elias, L. Simonot, L. M. Thoury, and J. M. Frigerio, “Bi-directional reflectance of a varnished painting part 2: influence of the refractive indices, surface state and absorption--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

D. Queiros-Conde, “The turbulent structure of sfumato within Mona Lisa,” Leonardo 37, 223-228 (2004).
[CrossRef]

L. L. Kontsevich and C. W. Tyler, “Making Mona frown,” Science 304, 1900 (2004), doi: 10.1126/science.304.5679.1900b.
[CrossRef]

2002 (1)

2000 (1)

M. S. Livingstone, “Is it warm? Is it real? Or just low spatial frequency,” Science 290, 1299 (2000), doi: 10.1126/science.290.5495.1299b.
[CrossRef]

1992 (1)

J. F. Asmus, “Mona Lisa symbolism uncovered by computer processing,” Mater. Charact. 29, 119-128 (1992).
[CrossRef]

1973 (1)

K. Clark, “Mona Lisa,” The Burlington Magazine 115, 144-150 (1973).

Appl. Opt. (2)

Appl. Spectrosc. (1)

J. Opt. Soc. Am. A (2)

Leonardo (1)

D. Queiros-Conde, “The turbulent structure of sfumato within Mona Lisa,” Leonardo 37, 223-228 (2004).
[CrossRef]

Mater. Charact. (1)

J. F. Asmus, “Mona Lisa symbolism uncovered by computer processing,” Mater. Charact. 29, 119-128 (1992).
[CrossRef]

Opt. Commun. (2)

M. Elias, L. Simonot, L. M. Thoury, and J. M. Frigerio, “Bi-directional reflectance of a varnished painting part 2: influence of the refractive indices, surface state and absorption--experiments and simulations,” Opt. Commun. 231, 25-33 (2004).
[CrossRef]

M. Elias, M. R. De La Rie, J. Delanay, and E. Charron, “Leveling of varnishes over rough substrates,” Opt. Commun. 266, 586-591 (2006).
[CrossRef]

Proc. SPIE (1)

F. Blais, J. Taylor, L. Cournoyer, M. Picard, L. Borgeat, G. Godin, J. A. Beraldin, and M. Rioux, “More than a poplar plank: the shape and subtle colours of the masterpiece 'Mona Lisa' by Leonardo,” Proc. SPIE 6491, 649106 (2007).
[CrossRef]

Science (2)

L. L. Kontsevich and C. W. Tyler, “Making Mona frown,” Science 304, 1900 (2004), doi: 10.1126/science.304.5679.1900b.
[CrossRef]

M. S. Livingstone, “Is it warm? Is it real? Or just low spatial frequency,” Science 290, 1299 (2000), doi: 10.1126/science.290.5495.1299b.
[CrossRef]

The Burlington Magazine (1)

K. Clark, “Mona Lisa,” The Burlington Magazine 115, 144-150 (1973).

Other (15)

M. Gelb, The How to Think Like Leonardo Da Vinci Workbook (Dell, 1998).

C. N. Cochin, Voyage Pittoresque d'Italie (Ch.-Ant. Jombert, 1773).

V. Pomarède, La Joconde (Prat / Europa, 1988).

G. Vasari, The Lives of the Artists (Penguin, 1987), English translation.

J. Franck, “The Unrestorable Sfumato,” in Academia Leonardi Vinci (UCLA , 1993), Vol. VI, p. 238.

M. Kemp, Leonardo da Vinci (Oxford, 2006).

D. Arasse, Léonard de Vinci (Hazan, 2003).

E. H. Gombrich, The Story of Art (Phaidon, 1999), p. 300.

J. P. Mohen, M. Menu, and B. Mottin, Mona Lisa: Inside the Painting (Abrams, 2006), p. 92.

P. Cotte and M. Dupouy, “CRISATEL: a high resolution multispectral system,” Proceedings of PICS'03 Conference, Rochester, USA (2003), pp. 161-165.

P. Cotte and D. Dupraz, “Spectral imaging of Leonardo da Vinci's Mona Lisa: an authentic smile at 1523 dpi,” Proceedings of IS&T Archiving'06, Ottawa, USA (2006), p. 228.

P. Cotte and D. Dupraz, “Spectral imaging of Leonardo da Vinci's Mona Lisa: a true colour smile without the influence of aged varnish,” Proceeding IS&T CGVI '06, 311, Leeds, UK (2006).

E. Panofski, Les Primitifs Flamands (Hazan, 1992).

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

G. Wyszecki and W. S. Stiles,Color Science: Concepts and Methods, Quantitative Data and Formulae 2nd ed. (Wiley, 1982).

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Figures (9)

Fig. 1
Fig. 1

Mona Lisa (a) Today, image obtained with the multispectral camera. (b) After virtual removal of the varnish. (c) Eleven selected areas in the unvarnished face. (d) Diffuse reflectance spectra of the 11 locations.

Fig. 2
Fig. 2

Pigment identification of the upper layer corresponding to the unvarnished spectrum of location (j). The four best matches are presented with the smallest least-squares distance ε between the unknown spectrum (solid line) and those of reference pigments (dotted line) supplied by OKHRA (Provence).

Fig. 3
Fig. 3

Reflectance spectra of the mixture made of vermilion and lead white with various volume concentrations in vermilion (shown above each spectrum) compared to the previous spectrum of location (j) in Mona Lisa’s face.

Fig. 4
Fig. 4

Colorimetric variations in the chroma C * and lightness L * planes of the CIE-Lab space of Mona Lisa’s face deduced from the 11 previous experimental unvarnished spectra presented in Fig. 1d.

Fig. 5
Fig. 5

Spectral variations of absorption k and scattering s coefficients (in m 1 ) of the umber identified in the upper layer of Mona Lisa’s face.

Fig. 6
Fig. 6

Colorimetric variations in the chroma C * and lightness L * planes of the CIE-Lab space, deduced from the modeling of an umber glaze (solid line) from 1–13 layers (number in parentheses) and applied on a mixture of 1% vermilion and 99% lead white. The coordinates of a pure dry lead white (L), a dry umber (U), and a dry mixture (M) of 1% vermilion and 99% lead white pigments have been added.

Fig. 7
Fig. 7

Comparison between the simulated color variations of the previous glaze and those of a pigment mixture made of umber and lead white with varying proportions .

Fig. 8
Fig. 8

Three contributions to the global diffusion coming from the light flux, according to the number of glaze layers for an umber embedded in an oil binder and applied to a 1% vermilion and 99% lead white base layer: (a) single scattering, (b) multiple scattering, (c) scattering by the background.

Fig. 9
Fig. 9

Colorimetric variations in the chroma C * and lightness L * planes of the CIE-Lab space as a function of the glaze layer number for each contribution to the diffuse light: (a) single scattering, (b) multiple scattering, (c) scattering by the background.

Equations (2)

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d w ± ( μ , τ ) d τ = w ± ( μ , τ ) | μ | ± q 2 [ ( f ( τ ) + g ( τ ) ] ,
w ( μ , 0 ) = w s s ( μ , 0 ) + w m s ( μ , 0 ) + w B ( μ , 0 ) .

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