Abstract

We apply transmission gratings under Littrow incidence to produce polychromatic colors by additive color mixing. Parametric optimization of gratings is employed to produce high efficiency. In addition, we show that the system can yield the same color from a wide variety of spectra; i.e., the system can produce metameric colors.

© 2006 Optical Society of America

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References

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  1. P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996).
  2. R. S. Berns, R. J. Motta, and M. E. Gorzynski, "CRT colorimetry. Part 1: Theory and practice," Color Res. Appl. 18, 299-314 (1993).
    [CrossRef]
  3. R. S. Berns, M. E. Gorzynski, and R. Motta, "CRT colorimetry. Part 2: Metrology," Color Res. Appl. 18, 315-325 (1993).
    [CrossRef]
  4. R. L. van Renesse, Optical Document Security (Artech House, 1993).
  5. R. McDonald, Colour Physics for Industry, 2nd ed. (Society of Dyers and Colourists, England, 1997).
  6. G. D. Finlayson and P. Morovic, "Metamer sets," J. Opt. Soc. Am. A 22, 810-819 (2005).
    [CrossRef]
  7. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley-Interscience, 1982).
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    [CrossRef]
  10. M. W. Farn, M. B. Stern, W. B. Veldkamp, and S. S. Medeiros, "Color separation by use of binary optics," Opt. Lett. 18, 1214-1216 (1993).
    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  12. J. Turunen, "Diffraction theory of microrelief gratings," in Micro-optics: Elements, Systems, and Applications, H.P.Herzig, ed. (Taylor & Francis, 1997), Chap. 2.
  13. P. Green and L. MacDonald, Colour Engineering: Achieving Device Independent Colour (Wiley, England, 2002).
  14. R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley-Interscience, 2000).
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  16. W. D. Wright, "The graphical representation of small color differences," J. Opt. Soc. Am. 33, 632-636 (1943).
    [CrossRef]

2005 (1)

2002 (1)

P. Green and L. MacDonald, Colour Engineering: Achieving Device Independent Colour (Wiley, England, 2002).

2000 (1)

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley-Interscience, 2000).

1999 (2)

1997 (2)

R. McDonald, Colour Physics for Industry, 2nd ed. (Society of Dyers and Colourists, England, 1997).

J. Turunen, "Diffraction theory of microrelief gratings," in Micro-optics: Elements, Systems, and Applications, H.P.Herzig, ed. (Taylor & Francis, 1997), Chap. 2.

1996 (1)

P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996).

1993 (4)

R. S. Berns, R. J. Motta, and M. E. Gorzynski, "CRT colorimetry. Part 1: Theory and practice," Color Res. Appl. 18, 299-314 (1993).
[CrossRef]

R. S. Berns, M. E. Gorzynski, and R. Motta, "CRT colorimetry. Part 2: Metrology," Color Res. Appl. 18, 315-325 (1993).
[CrossRef]

R. L. van Renesse, Optical Document Security (Artech House, 1993).

M. W. Farn, M. B. Stern, W. B. Veldkamp, and S. S. Medeiros, "Color separation by use of binary optics," Opt. Lett. 18, 1214-1216 (1993).
[CrossRef] [PubMed]

1982 (1)

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

1978 (1)

1943 (1)

1942 (1)

Berns, R. S.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley-Interscience, 2000).

R. S. Berns, R. J. Motta, and M. E. Gorzynski, "CRT colorimetry. Part 1: Theory and practice," Color Res. Appl. 18, 299-314 (1993).
[CrossRef]

R. S. Berns, M. E. Gorzynski, and R. Motta, "CRT colorimetry. Part 2: Metrology," Color Res. Appl. 18, 315-325 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Boynton, R. M.

P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996).

Cormack, I. G.

Dammann, H.

Farn, M. W.

Finlayson, G. D.

Gorzynski, M. E.

R. S. Berns, R. J. Motta, and M. E. Gorzynski, "CRT colorimetry. Part 1: Theory and practice," Color Res. Appl. 18, 299-314 (1993).
[CrossRef]

R. S. Berns, M. E. Gorzynski, and R. Motta, "CRT colorimetry. Part 2: Metrology," Color Res. Appl. 18, 315-325 (1993).
[CrossRef]

Green, P.

P. Green and L. MacDonald, Colour Engineering: Achieving Device Independent Colour (Wiley, England, 2002).

Kaiser, P. K.

P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996).

Layet, B.

MacAdam, D. L.

MacDonald, L.

P. Green and L. MacDonald, Colour Engineering: Achieving Device Independent Colour (Wiley, England, 2002).

McDonald, R.

R. McDonald, Colour Physics for Industry, 2nd ed. (Society of Dyers and Colourists, England, 1997).

Medeiros, S. S.

Morovic, P.

Motta, R.

R. S. Berns, M. E. Gorzynski, and R. Motta, "CRT colorimetry. Part 2: Metrology," Color Res. Appl. 18, 315-325 (1993).
[CrossRef]

Motta, R. J.

R. S. Berns, R. J. Motta, and M. E. Gorzynski, "CRT colorimetry. Part 1: Theory and practice," Color Res. Appl. 18, 299-314 (1993).
[CrossRef]

Stern, M. B.

Stiles, W. S.

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

Taghizadeh, M. R.

Turunen, J.

J. Turunen, "Diffraction theory of microrelief gratings," in Micro-optics: Elements, Systems, and Applications, H.P.Herzig, ed. (Taylor & Francis, 1997), Chap. 2.

van Renesse, R. L.

R. L. van Renesse, Optical Document Security (Artech House, 1993).

Veldkamp, W. B.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wright, W. D.

Wyszecki, G.

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

Appl. Opt. (2)

Color Res. Appl. (2)

R. S. Berns, R. J. Motta, and M. E. Gorzynski, "CRT colorimetry. Part 1: Theory and practice," Color Res. Appl. 18, 299-314 (1993).
[CrossRef]

R. S. Berns, M. E. Gorzynski, and R. Motta, "CRT colorimetry. Part 2: Metrology," Color Res. Appl. 18, 315-325 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Other (8)

P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996).

R. L. van Renesse, Optical Document Security (Artech House, 1993).

R. McDonald, Colour Physics for Industry, 2nd ed. (Society of Dyers and Colourists, England, 1997).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

J. Turunen, "Diffraction theory of microrelief gratings," in Micro-optics: Elements, Systems, and Applications, H.P.Herzig, ed. (Taylor & Francis, 1997), Chap. 2.

P. Green and L. MacDonald, Colour Engineering: Achieving Device Independent Colour (Wiley, England, 2002).

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley-Interscience, 2000).

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

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Figures (7)

Fig. 1
Fig. 1

Different wavelengths (primary colors λ 1 , λ 2 , λ 3 , λ 4 , and λ 5 ) propagate to the same direction.

Fig. 2
Fig. 2

Example of a coded grating surface.

Fig. 3
Fig. 3

Radiance spectra of the light sources used: fluorescent lamp (dashed curve) and incandescent lamp (solid curve).

Fig. 4
Fig. 4

Spectral lines produced by the grating for two different illuminations: incandescent lamp (white bars) and fluorescent lamp (black bars).

Fig. 5
Fig. 5

Location of the primary wavelengths in the CIE 1931 coordinates and the color coordinates of the two different spectra [incandescent lamp (asterisk) and fluorescent lamp (open circle)] illustrated in Fig. 4. The colors corresponding to these coordinates are seen as equal by the human eye.

Fig. 6
Fig. 6

Color coordinates corresponding to the wavelengths and the proportions shown in Table 1. Incandescent lamp (asterisks) and fluorescent lamp (open circles).

Fig. 7
Fig. 7

Different metameric colors produced by the same primary wavelengths of 387, 425, 526, 539, and 738 nm . Incandescent lamp (asterisks) and fluorescent lamp (open circles).

Tables (1)

Tables Icon

Table 1 Primary Wavelengths λ i (nm) and Their Proportions w i in the Grating a

Equations (8)

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

[ x ¯ y ¯ z ¯ ] P w = c 1 ( X Y Z ) ,
E = [ x ¯ y ¯ z ¯ ] P ,
d i = λ ( n in sin θ in sin θ v ) ,
1 c 1 [ x ¯ y ¯ z ¯ ] P w = 1 c 2 [ x ¯ y ¯ z ¯ ] P w .
[ x ¯ y ¯ z ¯ ] ( c P P ) w = 0 .
E = [ x ¯ y ¯ z ¯ ] ( c P P ) ,
[ E 11 E 12 E 13 E 14 E 15 E 21 E 22 E 23 E 24 E 25 E 31 E 32 E 33 E 34 E 35 ] ( w 1 w 2 w 3 w 4 w 5 ) = 0 ,
[ E 11 E 12 E 13 E 21 E 22 E 23 E 31 E 32 E 33 ] ( w 1 w 2 w 3 ) = [ E 14 a + E 15 b E 24 a + E 25 b E 34 a + E 35 b ] .

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