Abstract

This paper presents a methodology for including the photometric raw data sets into the diffuse illumination design process. The method is based on computing the luminance distribution on the outgoing side of diffusing elements from measured bidirectional scattering distribution functions (BSDFs). The model is limited to specimens that create rotationally symmetric scattering distribution. The calculation procedure includes the linear superposition and the correcting feedback. As an application example, the method is verified by a commercially available diffusing sheet illuminated by a 32-inch backlighting module. Close agreement (correlation coefficient = 98.6%) with the experimental measurement confirmed the validity of the proposed procedure.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Stover, Optical Scattering: Measurement and Analysis (Mc Graw-Hill, New York, 1990).
  2. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  3. L. Tsang, J. A. Kong, and K. -H. Ding, Scattering of Electromagnetic Waves, Theories and Applications (Wiley, New York, 2000).
    [CrossRef]
  4. L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves, Advanced Topiics s (Wiley, New York, 2001).
  5. A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, Boston, 1994).
  6. A. Voronovich, "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Waves Random Media 4, 337-367 (1994).
    [CrossRef]
  7. A. Voronovich, Wave Scattering from Rough Surfaces, 2nd Edition (Springer-Verlag, Berlin Heidelberg, 1994).
  8. K. E. Torrance and E. M. Sparrow, "Theory for off-specular reflection from roughened surface," J. Opt. Soc. Am. 57, 1105-1114 (1967).
    [CrossRef]
  9. B. van Ginneken, M. Staveridi and J. J. Koendrik, "Diffuse and specular reflectance from rough surface," Appl. Opt. 37, 130-139 (1998).
    [CrossRef]
  10. K. Tang and R. O. Buckius, "A statistical model of wave scattering from random rough surfaces," Int. J. Heat Mass Transfer 44, 4059-4073 (2001).
    [CrossRef]
  11. L. Tsang, J. A. Kong, K, -H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, New York, 2000).
    [CrossRef]
  12. F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).
  13. N. Garcia and E. Stoll, "Monte Carlo calculation for electromagnetic-wave scattering from random rough Surfaces," Phys. Rev. Lett. 52, 1798-1801 (1984).
    [CrossRef]
  14. K. Tang, R. Dimenna, and R. Buckius, "Regions of validity of the geometric optics approximation for angular scattering from very rough surface," Int. Heat J. Mass Transfer 40, 49-59 (1997).
    [CrossRef]
  15. M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Volume II (McGraw-Hill, New York, 1991).
  16. E. Kreyszig, Introductory Mathematical Statistics (Wiley, New York, 1970)
  17. J. de Boer, "Modelling indoor illumination by complex fenestration systems based on bidirectional : Basics, Measurement, and Rating," J. Soc. Info. Dis. 14/11, 1003-1017 (2006).
  18. M. E. Becker, "Evaluation and characterization of display reflectance," Displays 19, 35-54 (1998).
    [CrossRef]
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 2004)
  20. K. Iizuka, Elements of Photonics I (Willey, New York, 2002)
  21. A. M. Nuijs and J. J. L. Horikx, "Diffraction and scattering at antiglare structures for display devices," Appl. Opt. 33, 4058-4068 (1994).
    [CrossRef] [PubMed]
  22. J. E. Harvey and C. L. Vernold, "Transfer function characterization of scattering surface," Proc. SPIE 3141, 113-127 (1997).
    [CrossRef]
  23. M. W. Hodapp, Applications for High-Brightness Light-Emitting Diodes, in Semiconductors and Semimetals Vol. 48, G. B. Stringfellow and M. G. Craford ed., (Academic Press, San Diego, 1997) Semiconductors and Semimetals Vol. 48, Chap. 6, p. 227.

2006 (1)

J. de Boer, "Modelling indoor illumination by complex fenestration systems based on bidirectional : Basics, Measurement, and Rating," J. Soc. Info. Dis. 14/11, 1003-1017 (2006).

2001 (1)

K. Tang and R. O. Buckius, "A statistical model of wave scattering from random rough surfaces," Int. J. Heat Mass Transfer 44, 4059-4073 (2001).
[CrossRef]

1998 (2)

1997 (2)

J. E. Harvey and C. L. Vernold, "Transfer function characterization of scattering surface," Proc. SPIE 3141, 113-127 (1997).
[CrossRef]

K. Tang, R. Dimenna, and R. Buckius, "Regions of validity of the geometric optics approximation for angular scattering from very rough surface," Int. Heat J. Mass Transfer 40, 49-59 (1997).
[CrossRef]

1995 (1)

F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

1994 (2)

A. Voronovich, "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Waves Random Media 4, 337-367 (1994).
[CrossRef]

A. M. Nuijs and J. J. L. Horikx, "Diffraction and scattering at antiglare structures for display devices," Appl. Opt. 33, 4058-4068 (1994).
[CrossRef] [PubMed]

1984 (1)

N. Garcia and E. Stoll, "Monte Carlo calculation for electromagnetic-wave scattering from random rough Surfaces," Phys. Rev. Lett. 52, 1798-1801 (1984).
[CrossRef]

1967 (1)

Becker, M. E.

M. E. Becker, "Evaluation and characterization of display reflectance," Displays 19, 35-54 (1998).
[CrossRef]

Broschat, S. L.

F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Buckius, R.

K. Tang, R. Dimenna, and R. Buckius, "Regions of validity of the geometric optics approximation for angular scattering from very rough surface," Int. Heat J. Mass Transfer 40, 49-59 (1997).
[CrossRef]

Buckius, R. O.

K. Tang and R. O. Buckius, "A statistical model of wave scattering from random rough surfaces," Int. J. Heat Mass Transfer 44, 4059-4073 (2001).
[CrossRef]

de Boer, J.

J. de Boer, "Modelling indoor illumination by complex fenestration systems based on bidirectional : Basics, Measurement, and Rating," J. Soc. Info. Dis. 14/11, 1003-1017 (2006).

Dimenna, R.

K. Tang, R. Dimenna, and R. Buckius, "Regions of validity of the geometric optics approximation for angular scattering from very rough surface," Int. Heat J. Mass Transfer 40, 49-59 (1997).
[CrossRef]

Garcia, N.

N. Garcia and E. Stoll, "Monte Carlo calculation for electromagnetic-wave scattering from random rough Surfaces," Phys. Rev. Lett. 52, 1798-1801 (1984).
[CrossRef]

Harvey, J. E.

J. E. Harvey and C. L. Vernold, "Transfer function characterization of scattering surface," Proc. SPIE 3141, 113-127 (1997).
[CrossRef]

Hastings, F. D.

F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Horikx, J. J. L.

Koendrik, J. J.

Nuijs, A. M.

Schneider, J. B.

F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Sparrow, E. M.

Staveridi, M.

Stoll, E.

N. Garcia and E. Stoll, "Monte Carlo calculation for electromagnetic-wave scattering from random rough Surfaces," Phys. Rev. Lett. 52, 1798-1801 (1984).
[CrossRef]

Tang, K.

K. Tang and R. O. Buckius, "A statistical model of wave scattering from random rough surfaces," Int. J. Heat Mass Transfer 44, 4059-4073 (2001).
[CrossRef]

K. Tang, R. Dimenna, and R. Buckius, "Regions of validity of the geometric optics approximation for angular scattering from very rough surface," Int. Heat J. Mass Transfer 40, 49-59 (1997).
[CrossRef]

Torrance, K. E.

van Ginneken, B.

Vernold, C. L.

J. E. Harvey and C. L. Vernold, "Transfer function characterization of scattering surface," Proc. SPIE 3141, 113-127 (1997).
[CrossRef]

Voronovich, A.

A. Voronovich, "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Waves Random Media 4, 337-367 (1994).
[CrossRef]

Appl. Opt. (2)

Displays (1)

M. E. Becker, "Evaluation and characterization of display reflectance," Displays 19, 35-54 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).

Int. Heat J. Mass Transfer (1)

K. Tang, R. Dimenna, and R. Buckius, "Regions of validity of the geometric optics approximation for angular scattering from very rough surface," Int. Heat J. Mass Transfer 40, 49-59 (1997).
[CrossRef]

Int. J. Heat Mass Transfer (1)

K. Tang and R. O. Buckius, "A statistical model of wave scattering from random rough surfaces," Int. J. Heat Mass Transfer 44, 4059-4073 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Soc. Info. Dis. (1)

J. de Boer, "Modelling indoor illumination by complex fenestration systems based on bidirectional : Basics, Measurement, and Rating," J. Soc. Info. Dis. 14/11, 1003-1017 (2006).

Phys. Rev. Lett. (1)

N. Garcia and E. Stoll, "Monte Carlo calculation for electromagnetic-wave scattering from random rough Surfaces," Phys. Rev. Lett. 52, 1798-1801 (1984).
[CrossRef]

Proc. SPIE (1)

J. E. Harvey and C. L. Vernold, "Transfer function characterization of scattering surface," Proc. SPIE 3141, 113-127 (1997).
[CrossRef]

Waves Random Media (1)

A. Voronovich, "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Waves Random Media 4, 337-367 (1994).
[CrossRef]

Other (12)

A. Voronovich, Wave Scattering from Rough Surfaces, 2nd Edition (Springer-Verlag, Berlin Heidelberg, 1994).

L. Tsang, J. A. Kong, K, -H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations (Wiley, New York, 2000).
[CrossRef]

J. C. Stover, Optical Scattering: Measurement and Analysis (Mc Graw-Hill, New York, 1990).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

L. Tsang, J. A. Kong, and K. -H. Ding, Scattering of Electromagnetic Waves, Theories and Applications (Wiley, New York, 2000).
[CrossRef]

L. Tsang and J. A. Kong, Scattering of Electromagnetic Waves, Advanced Topiics s (Wiley, New York, 2001).

A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, Boston, 1994).

M. W. Hodapp, Applications for High-Brightness Light-Emitting Diodes, in Semiconductors and Semimetals Vol. 48, G. B. Stringfellow and M. G. Craford ed., (Academic Press, San Diego, 1997) Semiconductors and Semimetals Vol. 48, Chap. 6, p. 227.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 2004)

K. Iizuka, Elements of Photonics I (Willey, New York, 2002)

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Volume II (McGraw-Hill, New York, 1991).

E. Kreyszig, Introductory Mathematical Statistics (Wiley, New York, 1970)

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 (7)

Fig. 1.
Fig. 1.

Photometric and geometric quantities in the polar coordinate system.

Fig. 2.
Fig. 2.

(a) Schematic measurement setup of BTDFs, (b) the measured angular spread functions of an available diffuser.

Fig. 3.
Fig. 3.

The measured BTDFs and their corresponding OM pictures with (a) low spatial frequency and (b) high spatial frequency.

Fig. 4.
Fig. 4.

Modeling procedure for a commercially available diffusing specimen.

Fig. 5.
Fig. 5.

The convolution of 40°-inclination (j=4) BTDF.

Fig. 6.
Fig. 6.

The cross-section of individual 1D-BTDF and summation under Lambertian illumination.

Fig. 7
Fig. 7

Angular luminance distribution transmitted through the diffuser from a 32-inch backlighting source by (a) calculation, and (b) comparison of the cross-sections at ϕ = 0 and 360 degree, where the CC between two curves is 98.6%.

Tables (1)

Tables Icon

Table 1. Nomenclature

Equations (13)

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

q(θi,ϕi,θt,ϕt)=dLt(θt,ϕt)dEi(θi,ϕi)=dLt(θt,ϕt)Li(θt,ϕt)cosθidωi[cdm2lx],
Lt(θt,ϕt)=Ω q (θi,ϕi,θt,ϕt) Li (θi,ϕi) cos θi d ωi ,
Lt(θt,ϕt)=jqj(θi,j,ϕi,j,θt,ϕt)Li,j(θi,j,ϕi,j)cosθi,j·Δωj,
qjR(θt,ϕt)=qj(θt,ϕt)*mj=0Mjδ(θtjΔθ,ϕtmjΔϕj)
=mj=0Mjqj(θtjΔθ,ϕtmjΔϕj),
Wi,j=Li,r(θj,ϕ0)Li,r(θ0,ϕ0)=Li,rθϕ·δ(θjΔθ,ϕϕ0)Li,rθϕ·δ(θθ0,ϕϕ0)θ0=0°,ϕ0=90°.
Lt(θt,ϕt)=A·j=0JWi,jcosθi,j·qjR(θt,ϕt)
=A · j=0Jmj=0MjWi,jcosθi,j·qj(θjΔθ,ϕtmjdj),
A1=j=0Jmj=0MjWi,jcosθi,j·qj(θtjΔθ,ϕtmjdj)θ=0,ϕ=0.
CC=θϕ[LcθϕL̄c][LeθϕL̄e]θϕ[LcθϕL̄c]2θϕ[LeθϕL̄e]2,
Wi,mj=Li(θj,ϕmj)Li(θ0,ϕ0)=Liθϕ·δ(θjΔθ,ϕmjΔϕj)Liθϕ·δ(θθ0,ϕϕ0)θ0=0°,ϕ0=90°.
Lt(θt,ϕt)=jJmjMjWj,mj·cosθi,j·qi(θtjΔθ,ϕtmjΔϕj).
τ(θi)=ΦtΦi(θi)=ΩiLt(ωt)Ei(ωi)cosθtdωt=Ωtq(ωi,ωt)cosθtdωt,

Metrics