Abstract

A model based on geometrical optics has been developed to describe the photometric observations associated with a novel method to control the reflectance of a surface. In this new reflectance modulation approach, electrophoresis of pigment particles is used to absorb light reflected by total internal reflection (TIR). The pigment particles are sufficiently small that they substantially do not scatter light, but rather they modify the effective refractive index at the reflection interface. An incident light ray interacting with this modified effective index is attenuated in a spectrally selective manner. Although frustrated TIR has been understood and used in various applications for some time, in this case it is used to substantially modify the color of the reflected light, which to our knowledge has not been previously reported. A numerical model of the pigment particle distribution has been developed to describe the observations.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. A. Whitehead, M. A. Mossman, A. Kotlicki, “Visual applications of total internal reflection in prismatic microstructures,” Phys. Can. 57, 329–335 (2001).
  2. M. A. Mossman, V. H. Kwong, J. Pond, L. A. Whitehead, “A high reflectance, wide viewing angle reflective display using total internal reflection in micro-hemispheres,” in Proceedings of the 23rd International Display Research Conference (Society for Information Display, San Jose, Calif., 2003), pp. 233–236.
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, Calif., 1966), pp. 178–182.
  4. J. T. Remillard, J. M. Ginder, H. W. Weber, “Evanescent-wave scattering by electrophoretic microparticles: a mechanism for optical switching,” Appl. Opt. 34, 3777–3785 (1995).
    [CrossRef] [PubMed]
  5. N. Harrick, Internal Reflection Spectroscopy (Harrick Scientific, Ossining, N.Y., 1979), pp. 35–40.
  6. M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.
  7. L. A. Whitehead, “Method and apparatus for controllable frustration of total internal reflection,” U.S. patent5,999, 307 (7December1999).
  8. R. J. N. Coope, L. A. Whitehead, A. Kotlicki, “Modulation of retroreflection by controlled frustration of total internal reflection,” Appl. Opt. 41, 5357–5361 (2002).
    [CrossRef] [PubMed]
  9. L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).
  10. T. C. Patton, ed., Pigment Handbook (Wiley, New York, 1973), Vol. 3, p. 72.
  11. TSL 251 light-to-voltage optical sensor, manufactured by Texas Advanced Optoelectronic Solutions, Inc., 800 Jupiter Road, Suite 205, Plano, Tex. 75974.
  12. S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), p. 46.
  13. Coulter Model N4 Plus particle size analyzer, manufactured by Coulter Electronics, Inc., 590 West 20th St., Hialeah, Fla., 33012-0145.
  14. S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), pp. 252–254.
  15. M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.
  16. L. A. Whitehead, M. A. Mossman, “Subtractive filtering frustrated TIR display,” U.S. patent6,384,979 (7May2002).
  17. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

2002 (1)

2001 (1)

L. A. Whitehead, M. A. Mossman, A. Kotlicki, “Visual applications of total internal reflection in prismatic microstructures,” Phys. Can. 57, 329–335 (2001).

1995 (1)

Arney, D. S.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

Biernath, R. W.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.

Bohren, C.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Coope, R. J.

L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).

Coope, R. J. N.

R. J. N. Coope, L. A. Whitehead, A. Kotlicki, “Modulation of retroreflection by controlled frustration of total internal reflection,” Appl. Opt. 41, 5357–5361 (2002).
[CrossRef] [PubMed]

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

Ginder, J. M.

Grandmaison, D. N.

L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).

Harrick, N.

N. Harrick, Internal Reflection Spectroscopy (Harrick Scientific, Ossining, N.Y., 1979), pp. 35–40.

Huffman, D.

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kotlicki, A.

R. J. N. Coope, L. A. Whitehead, A. Kotlicki, “Modulation of retroreflection by controlled frustration of total internal reflection,” Appl. Opt. 41, 5357–5361 (2002).
[CrossRef] [PubMed]

L. A. Whitehead, M. A. Mossman, A. Kotlicki, “Visual applications of total internal reflection in prismatic microstructures,” Phys. Can. 57, 329–335 (2001).

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.

L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

Kwong, V. H.

M. A. Mossman, V. H. Kwong, J. Pond, L. A. Whitehead, “A high reflectance, wide viewing angle reflective display using total internal reflection in micro-hemispheres,” in Proceedings of the 23rd International Display Research Conference (Society for Information Display, San Jose, Calif., 2003), pp. 233–236.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, Calif., 1966), pp. 178–182.

Morrison, I.

S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), pp. 252–254.

S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), p. 46.

Mossman, M. A.

L. A. Whitehead, M. A. Mossman, A. Kotlicki, “Visual applications of total internal reflection in prismatic microstructures,” Phys. Can. 57, 329–335 (2001).

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.

L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).

L. A. Whitehead, M. A. Mossman, “Subtractive filtering frustrated TIR display,” U.S. patent6,384,979 (7May2002).

M. A. Mossman, V. H. Kwong, J. Pond, L. A. Whitehead, “A high reflectance, wide viewing angle reflective display using total internal reflection in micro-hemispheres,” in Proceedings of the 23rd International Display Research Conference (Society for Information Display, San Jose, Calif., 2003), pp. 233–236.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

Pellerite, M. J.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

Pond, J.

M. A. Mossman, V. H. Kwong, J. Pond, L. A. Whitehead, “A high reflectance, wide viewing angle reflective display using total internal reflection in micro-hemispheres,” in Proceedings of the 23rd International Display Research Conference (Society for Information Display, San Jose, Calif., 2003), pp. 233–236.

Potts, J. E.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

Rao, S. P.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.

Remillard, J. T.

Ross, S.

S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), pp. 252–254.

S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), p. 46.

Weber, H. W.

Whitehead, L. A.

R. J. N. Coope, L. A. Whitehead, A. Kotlicki, “Modulation of retroreflection by controlled frustration of total internal reflection,” Appl. Opt. 41, 5357–5361 (2002).
[CrossRef] [PubMed]

L. A. Whitehead, M. A. Mossman, A. Kotlicki, “Visual applications of total internal reflection in prismatic microstructures,” Phys. Can. 57, 329–335 (2001).

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.

L. A. Whitehead, “Method and apparatus for controllable frustration of total internal reflection,” U.S. patent5,999, 307 (7December1999).

L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).

L. A. Whitehead, M. A. Mossman, “Subtractive filtering frustrated TIR display,” U.S. patent6,384,979 (7May2002).

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

M. A. Mossman, V. H. Kwong, J. Pond, L. A. Whitehead, “A high reflectance, wide viewing angle reflective display using total internal reflection in micro-hemispheres,” in Proceedings of the 23rd International Display Research Conference (Society for Information Display, San Jose, Calif., 2003), pp. 233–236.

Appl. Opt. (2)

Phys. Can. (1)

L. A. Whitehead, M. A. Mossman, A. Kotlicki, “Visual applications of total internal reflection in prismatic microstructures,” Phys. Can. 57, 329–335 (2001).

Other (14)

M. A. Mossman, V. H. Kwong, J. Pond, L. A. Whitehead, “A high reflectance, wide viewing angle reflective display using total internal reflection in micro-hemispheres,” in Proceedings of the 23rd International Display Research Conference (Society for Information Display, San Jose, Calif., 2003), pp. 233–236.

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, Calif., 1966), pp. 178–182.

N. Harrick, Internal Reflection Spectroscopy (Harrick Scientific, Ossining, N.Y., 1979), pp. 35–40.

M. A. Mossman, D. S. Arney, R. W. Biernath, R. J. N. Coope, A. Kotlicki, M. J. Pellerite, J. E. Potts, S. P. Rao, L. A. Whitehead, “New reflective display technique based on total internal reflection in prismatic microstructures,” in Proceedings of the 20th International Display Research Conference (Society for Information Display, San Jose, Calif., 2000), pp. 311–314.

L. A. Whitehead, “Method and apparatus for controllable frustration of total internal reflection,” U.S. patent5,999, 307 (7December1999).

L. A. Whitehead, D. N. Grandmaison, R. J. Coope, M. A. Mossman, A. Kotlicki, “Electrophoretic, high index and phase transition control of total internal reflection in high efficiency variable reflective image display devices,” U.S. patent6,215,920 (10April2001).

T. C. Patton, ed., Pigment Handbook (Wiley, New York, 1973), Vol. 3, p. 72.

TSL 251 light-to-voltage optical sensor, manufactured by Texas Advanced Optoelectronic Solutions, Inc., 800 Jupiter Road, Suite 205, Plano, Tex. 75974.

S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), p. 46.

Coulter Model N4 Plus particle size analyzer, manufactured by Coulter Electronics, Inc., 590 West 20th St., Hialeah, Fla., 33012-0145.

S. Ross, I. Morrison, Colloidal Systems and Interfaces (Wiley, New York, 1988), pp. 252–254.

M. A. Mossman, A. Kotlicki, L. A. Whitehead, R. W. Biernath, S. P. Rao, “New reflective colour display technique based on total internal reflection and subtractive colour filtering,” in Proceedings of the Society for Information Display Symposium (Society for Information Display, San Jose, Calif., 2001), pp. 1054–1057.

L. A. Whitehead, M. A. Mossman, “Subtractive filtering frustrated TIR display,” U.S. patent6,384,979 (7May2002).

C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Path of light rays in a refractive-index gradient.

Fig. 2
Fig. 2

Schematic image of a reflectance modulation device with TIR.

Fig. 3
Fig. 3

Measuring attenuation in (a) TIR and (b) frustrated TIR states.

Fig. 4
Fig. 4

Reflectance modulated by electrophoresis of black pigment particles.

Fig. 5
Fig. 5

Modulation by different concentrations of particles.

Fig. 6
Fig. 6

Reflectance at different angles of incidence.

Fig. 7
Fig. 7

Uniform density layer of particles.

Fig. 8
Fig. 8

Predicted reflectance values obtained from the uniform density model.

Fig. 9
Fig. 9

Best model fit distribution of particles obtained from the uniform density model.

Fig. 10
Fig. 10

Density gradient of particles.

Fig. 11
Fig. 11

Linear density gradient of particles.

Fig. 12
Fig. 12

Best fit for reflectance predicted by the linear density gradient model.

Fig. 13
Fig. 13

Best fit distributions obtained with the linear density gradient model.

Fig. 14
Fig. 14

Exponentially tapered density gradient of particles.

Fig. 15
Fig. 15

Reflectance predicted by the exponentially tapered gradient model.

Fig. 16
Fig. 16

Distribution predicted by the exponentially tapered gradient model.

Tables (1)

Tables Icon

Table 1 Dielectric Constants and Refractive-Index Values for Materials

Equations (7)

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

θ 2 = arcsin [ ( n 1 / n 2 ) sin θ 1 ] .
θ c = arcsin ( n 2 / n 1 ) .
d d l ( n r ^ ) = n ,
D Δ n λ .
n eff = ( 1 - f ) n 1 + f n p .
f = [ f max if d d 0 f max - m ( d - t ) if d > d 0 ] .
f = f max [ exp ( d - V / f max σ ) + 1 ] - 1 ,

Metrics