Abstract

Enhanced control of diffraction through transparent substrates is achieved via disordered gratings in a silica sol–gel film. Tailoring the degree of disorder allows tuning of the diffractive behavior from discrete orders into broad distributions over large angular range. Gratings of optical quality are formed by silica sol–gel nanoimprint lithography and an optical setup for the measurement of continuous diffraction patterns is presented. Sound agreement is found between measurements and simulation, validating both the approach for redirection of light and the fabrication process. The disordered gratings are presented in the context of improved interior daylighting and may furthermore be suited to a wide variety of applications where controlled angular redirection of light is desired.

© 2013 Optical Society of America

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  1. D. Meyerhofer, “Spatial resolution of relief holograms in dichromated gelatin,” Appl. Opt. 10, 416–421 (1971).
    [CrossRef]
  2. S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
    [CrossRef]
  3. X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
    [CrossRef]
  4. S. Singh, “Diffraction gratings: aberrations and applications,” Opt. Laser Technol. 31, 195–218 (1999).
    [CrossRef]
  5. S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
    [CrossRef]
  6. R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41, 1236–1240 (2002).
    [CrossRef]
  7. P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
    [CrossRef]
  8. P. Licinio, M. Lerotic, and M. S. S. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
    [CrossRef]
  9. J. M. Rico-García and L. M. Sanchez-Brea, “Binary gratings with random heights,” Appl. Opt. 48, 3062–3069 (2009).
    [CrossRef]
  10. A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
    [CrossRef]
  11. B. Bläsi, A. Gombert, and M. Niggemann, “Microstructured polymer surfaces with complex optical functions for solar applications,” in Polymers—Opportunities and Risks II SE—14, P. Eyerer, M. Weller, and C. Hübner, eds. (Springer, 2009), Vol. 12, pp. 263–279.
  12. S. Klammt, A. Neyer, and H. F. O. Müller, “Microoptics for efficient redirection of sunlight,” Appl. Opt. 51, 2051–2056 (2012).
    [CrossRef]
  13. O. Masuda and S. M. C. Nascimento, “Lighting spectrum to maximize colorfulness,” Opt. Lett. 37, 407–409 (2012).
    [CrossRef]
  14. R. H. Katyl, “Moiré screens coded with pseudo-random sequences,” Appl. Opt. 11, 2278–2285 (1972).
    [CrossRef]
  15. C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
    [CrossRef]
  16. C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
    [CrossRef]
  17. H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
    [CrossRef]
  18. C. L. Robbins, Daylighting: Design and Analysis (Van Nostrand Reinhold, 1986).
  19. M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
    [CrossRef]
  20. R. G. Hopkinson, “Glare from daylighting in buildings,” Appl. Ergon. 3, 206–215 (1972).
    [CrossRef]
  21. S. W. Lockley, G. C. Brainard, and C. A. Czeisler, “High sensitivity of the human circadian melatonin rhythm to resetting by short wavelength light,” J. Clin. Endocrinol. Metab. 88, 4502–4505 (2003).
    [CrossRef]
  22. M. F. Lewis and C. L. West, “Some focusing properties of chirped gratings,” Opt. Quantum Electron. 21, 17–33 (1989).
    [CrossRef]
  23. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  24. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  25. C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
    [CrossRef]
  26. A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
    [CrossRef]
  27. H. Schmid and B. Michel, “Siloxane polymers for high-resolution, high-accuracy soft lithography,” Macromolecules 33, 3042–3049 (2000).
    [CrossRef]
  28. M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
    [CrossRef]
  29. R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
    [CrossRef]
  30. M. G. Figueiro and M. S. Rea, “Lack of short-wavelength light during the school day delays dim light melatonin onset (DLMO) in middle school students,” Neuroendocrinol. Lett. 31, 92–96 (2010).
  31. L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
    [CrossRef]
  32. K. Papamichael, C. Ehrlich, and G. Ward, “Design and evaluation of daylighting applications of holographic glazings,” Final Report prepared for Physical Optics Corporation under Contract Agreement Number BG-95037 (1996).

2012

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

S. Klammt, A. Neyer, and H. F. O. Müller, “Microoptics for efficient redirection of sunlight,” Appl. Opt. 51, 2051–2056 (2012).
[CrossRef]

O. Masuda and S. M. C. Nascimento, “Lighting spectrum to maximize colorfulness,” Opt. Lett. 37, 407–409 (2012).
[CrossRef]

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

2011

X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
[CrossRef]

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
[CrossRef]

2010

M. G. Figueiro and M. S. Rea, “Lack of short-wavelength light during the school day delays dim light melatonin onset (DLMO) in middle school students,” Neuroendocrinol. Lett. 31, 92–96 (2010).

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

2009

C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
[CrossRef]

J. M. Rico-García and L. M. Sanchez-Brea, “Binary gratings with random heights,” Appl. Opt. 48, 3062–3069 (2009).
[CrossRef]

2007

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

2003

S. W. Lockley, G. C. Brainard, and C. A. Czeisler, “High sensitivity of the human circadian melatonin rhythm to resetting by short wavelength light,” J. Clin. Endocrinol. Metab. 88, 4502–4505 (2003).
[CrossRef]

2002

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41, 1236–1240 (2002).
[CrossRef]

M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
[CrossRef]

2000

H. Schmid and B. Michel, “Siloxane polymers for high-resolution, high-accuracy soft lithography,” Macromolecules 33, 3042–3049 (2000).
[CrossRef]

1999

P. Licinio, M. Lerotic, and M. S. S. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[CrossRef]

S. Singh, “Diffraction gratings: aberrations and applications,” Opt. Laser Technol. 31, 195–218 (1999).
[CrossRef]

1998

P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
[CrossRef]

1996

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

1995

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

1993

H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
[CrossRef]

1992

S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef]

1990

S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
[CrossRef]

1989

M. F. Lewis and C. L. West, “Some focusing properties of chirped gratings,” Opt. Quantum Electron. 21, 17–33 (1989).
[CrossRef]

1972

R. G. Hopkinson, “Glare from daylighting in buildings,” Appl. Ergon. 3, 206–215 (1972).
[CrossRef]

R. H. Katyl, “Moiré screens coded with pseudo-random sequences,” Appl. Opt. 11, 2278–2285 (1972).
[CrossRef]

1971

D. Meyerhofer, “Spatial resolution of relief holograms in dichromated gelatin,” Appl. Opt. 10, 416–421 (1971).
[CrossRef]

Amitai, Y.

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41, 1236–1240 (2002).
[CrossRef]

Barthel, E.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
[CrossRef]

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

Becker, M. F.

S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef]

Bläsi, B.

B. Bläsi, A. Gombert, and M. Niggemann, “Microstructured polymer surfaces with complex optical functions for solar applications,” in Polymers—Opportunities and Risks II SE—14, P. Eyerer, M. Weller, and C. Hübner, eds. (Springer, 2009), Vol. 12, pp. 263–279.

Brainard, G. C.

S. W. Lockley, G. C. Brainard, and C. A. Czeisler, “High sensitivity of the human circadian melatonin rhythm to resetting by short wavelength light,” J. Clin. Endocrinol. Metab. 88, 4502–4505 (2003).
[CrossRef]

Chauveau, V.

C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
[CrossRef]

Chemin, N.

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

Czeisler, C. A.

S. W. Lockley, G. C. Brainard, and C. A. Czeisler, “High sensitivity of the human circadian melatonin rhythm to resetting by short wavelength light,” J. Clin. Endocrinol. Metab. 88, 4502–4505 (2003).
[CrossRef]

Dantas, M. S. S.

P. Licinio, M. Lerotic, and M. S. S. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[CrossRef]

Ehrlich, C.

K. Papamichael, C. Ehrlich, and G. Ward, “Design and evaluation of daylighting applications of holographic glazings,” Final Report prepared for Physical Optics Corporation under Contract Agreement Number BG-95037 (1996).

Favuzzi, P. A.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Ferchichi, A. K.

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

Figueiro, M. G.

M. G. Figueiro and M. S. Rea, “Lack of short-wavelength light during the school day delays dim light melatonin onset (DLMO) in middle school students,” Neuroendocrinol. Lett. 31, 92–96 (2010).

Friesem, A. A.

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41, 1236–1240 (2002).
[CrossRef]

Furukawa, Y.

S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
[CrossRef]

Gaylord, T. K.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

Goletto, V.

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

Gombert, A.

B. Bläsi, A. Gombert, and M. Niggemann, “Microstructured polymer surfaces with complex optical functions for solar applications,” in Polymers—Opportunities and Risks II SE—14, P. Eyerer, M. Weller, and C. Hübner, eds. (Springer, 2009), Vol. 12, pp. 263–279.

Gourgon, C.

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

Grann, E. B.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

Haatainen, T.

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

Han, S. T.

S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef]

Heitz, C.

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

Hopkinson, R. G.

R. G. Hopkinson, “Glare from daylighting in buildings,” Appl. Ergon. 3, 206–215 (1972).
[CrossRef]

Jagla, W.

L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
[CrossRef]

Jägle, H.

L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
[CrossRef]

Johnson, S. G.

X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
[CrossRef]

Katyl, R. H.

R. H. Katyl, “Moiré screens coded with pseudo-random sequences,” Appl. Opt. 11, 2278–2285 (1972).
[CrossRef]

Kawakami, Y.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Kimerling, L. C.

X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
[CrossRef]

Kischkoweit-Lopin, M.

M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
[CrossRef]

Klammt, S.

S. Klammt, A. Neyer, and H. F. O. Müller, “Microoptics for efficient redirection of sunlight,” Appl. Opt. 51, 2051–2056 (2012).
[CrossRef]

Kristensen, A.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

Kubiza, R.

H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
[CrossRef]

Lalanne, P.

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

Lerotic, M.

P. Licinio, M. Lerotic, and M. S. S. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[CrossRef]

Letailleur, A.

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

Letailleur, A. A.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

Lewis, M. F.

M. F. Lewis and C. L. West, “Some focusing properties of chirped gratings,” Opt. Quantum Electron. 21, 17–33 (1989).
[CrossRef]

Licinio, P.

P. Licinio, M. Lerotic, and M. S. S. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[CrossRef]

Lockley, S. W.

S. W. Lockley, G. C. Brainard, and C. A. Czeisler, “High sensitivity of the human circadian melatonin rhythm to resetting by short wavelength light,” J. Clin. Endocrinol. Metab. 88, 4502–4505 (2003).
[CrossRef]

Maker, P. D.

P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
[CrossRef]

Marie, R.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

Masuda, O.

O. Masuda and S. M. C. Nascimento, “Lighting spectrum to maximize colorfulness,” Opt. Lett. 37, 407–409 (2012).
[CrossRef]

Maurer, R.

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

Meyerhofer, D.

D. Meyerhofer, “Spatial resolution of relief holograms in dichromated gelatin,” Appl. Opt. 10, 416–421 (1971).
[CrossRef]

Michel, B.

H. Schmid and B. Michel, “Siloxane polymers for high-resolution, high-accuracy soft lithography,” Macromolecules 33, 3042–3049 (2000).
[CrossRef]

Michel, J.

X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
[CrossRef]

Mikkelsen, M. B.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

Moharam, M. G.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

Morris, G. M.

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

Mouroulis, P.

P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
[CrossRef]

Muller, R. E.

P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
[CrossRef]

Müller, H. F. O.

S. Klammt, A. Neyer, and H. F. O. Müller, “Microoptics for efficient redirection of sunlight,” Appl. Opt. 51, 2051–2056 (2012).
[CrossRef]

Nascimento, S. M. C.

O. Masuda and S. M. C. Nascimento, “Lighting spectrum to maximize colorfulness,” Opt. Lett. 37, 407–409 (2012).
[CrossRef]

Neyer, A.

S. Klammt, A. Neyer, and H. F. O. Müller, “Microoptics for efficient redirection of sunlight,” Appl. Opt. 51, 2051–2056 (2012).
[CrossRef]

Niggemann, M.

B. Bläsi, A. Gombert, and M. Niggemann, “Microstructured polymer surfaces with complex optical functions for solar applications,” in Polymers—Opportunities and Risks II SE—14, P. Eyerer, M. Weller, and C. Hübner, eds. (Springer, 2009), Vol. 12, pp. 263–279.

Nishihara, H.

S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
[CrossRef]

Noda, S.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Oskooi, A.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Papamichael, K.

K. Papamichael, C. Ehrlich, and G. Ward, “Design and evaluation of daylighting applications of holographic glazings,” Final Report prepared for Physical Optics Corporation under Contract Agreement Number BG-95037 (1996).

Peroz, C.

C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
[CrossRef]

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

Pietroy, D.

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

Pommet, D. A.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

Rascher, R.

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

Rea, M. S.

M. G. Figueiro and M. S. Rea, “Lack of short-wavelength light during the school day delays dim light melatonin onset (DLMO) in middle school students,” Neuroendocrinol. Lett. 31, 92–96 (2010).

Rico-García, J. M.

J. M. Rico-García and L. M. Sanchez-Brea, “Binary gratings with random heights,” Appl. Opt. 48, 3062–3069 (2009).
[CrossRef]

Robbins, C. L.

C. L. Robbins, Daylighting: Design and Analysis (Van Nostrand Reinhold, 1986).

Sanchez-Brea, L. M.

J. M. Rico-García and L. M. Sanchez-Brea, “Binary gratings with random heights,” Appl. Opt. 48, 3062–3069 (2009).
[CrossRef]

Schinhaerl, M.

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

Schmid, H.

H. Schmid and B. Michel, “Siloxane polymers for high-resolution, high-accuracy soft lithography,” Macromolecules 33, 3042–3049 (2000).
[CrossRef]

Schneider, F.

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

Sharpe, L. T.

L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
[CrossRef]

Shechter, R.

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41, 1236–1240 (2002).
[CrossRef]

Sheng, X.

X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
[CrossRef]

Shigeta, H.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Singh, S.

S. Singh, “Diffraction gratings: aberrations and applications,” Opt. Laser Technol. 31, 195–218 (1999).
[CrossRef]

Søndergård, E.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
[CrossRef]

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

Sperber, P.

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

Stockman, A.

L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
[CrossRef]

Stojanoff, C. G.

H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
[CrossRef]

Suhara, T.

S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
[CrossRef]

Tanaka, Y.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Teisseire, J.

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

Tesseire, J.

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

Tholl, H. D.

H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
[CrossRef]

Tsao, Y.-L.

S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef]

Ura, S.

S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
[CrossRef]

Vogt, C.

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

Walser, R. M.

S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef]

Ward, G.

K. Papamichael, C. Ehrlich, and G. Ward, “Design and evaluation of daylighting applications of holographic glazings,” Final Report prepared for Physical Optics Corporation under Contract Agreement Number BG-95037 (1996).

West, C. L.

M. F. Lewis and C. L. West, “Some focusing properties of chirped gratings,” Opt. Quantum Electron. 21, 17–33 (1989).
[CrossRef]

Willbold-Lohr, G.

H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
[CrossRef]

Wilson, D. W.

P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
[CrossRef]

Adv. Mater.

C. Peroz, V. Chauveau, E. Barthel, and E. Søndergård, “Nanoimprint lithography on silica sol-gels: a simple route to sequential patterning,” Adv. Mater. 21, 555–558 (2009).
[CrossRef]

Am. J. Phys.

P. Licinio, M. Lerotic, and M. S. S. Dantas, “Diffraction by disordered gratings and the Debye–Waller effect,” Am. J. Phys. 67, 1013–1016 (1999).
[CrossRef]

Appl. Ergon.

R. G. Hopkinson, “Glare from daylighting in buildings,” Appl. Ergon. 3, 206–215 (1972).
[CrossRef]

Appl. Opt.

J. M. Rico-García and L. M. Sanchez-Brea, “Binary gratings with random heights,” Appl. Opt. 48, 3062–3069 (2009).
[CrossRef]

D. Meyerhofer, “Spatial resolution of relief holograms in dichromated gelatin,” Appl. Opt. 10, 416–421 (1971).
[CrossRef]

S. T. Han, Y.-L. Tsao, R. M. Walser, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
[CrossRef]

R. Shechter, Y. Amitai, and A. A. Friesem, “Compact beam expander with linear gratings,” Appl. Opt. 41, 1236–1240 (2002).
[CrossRef]

P. Mouroulis, D. W. Wilson, P. D. Maker, and R. E. Muller, “Convex grating types for concentric imaging spectrometers,” Appl. Opt. 37, 7200–7208 (1998).
[CrossRef]

S. Klammt, A. Neyer, and H. F. O. Müller, “Microoptics for efficient redirection of sunlight,” Appl. Opt. 51, 2051–2056 (2012).
[CrossRef]

R. H. Katyl, “Moiré screens coded with pseudo-random sequences,” Appl. Opt. 11, 2278–2285 (1972).
[CrossRef]

Appl. Phys. Lett.

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100, 181110–181114 (2012).
[CrossRef]

Chem. Mater.

A. Letailleur, J. Teisseire, N. Chemin, E. Barthel, and E. Søndergård, “Chemorheology of sol–gel silica for the patterning of high aspect ratio structures by nanoimprint,” Chem. Mater. 22, 3143–3151 (2010).
[CrossRef]

Color Res. Appl.

L. T. Sharpe, A. Stockman, W. Jagla, and H. Jägle, “A luminous efficiency function, VD65* (λ), for daylight adaptation: a correction,” Color Res. Appl. 36, 42–46 (2011).
[CrossRef]

J. Clin. Endocrinol. Metab.

S. W. Lockley, G. C. Brainard, and C. A. Czeisler, “High sensitivity of the human circadian melatonin rhythm to resetting by short wavelength light,” J. Clin. Endocrinol. Metab. 88, 4502–4505 (2003).
[CrossRef]

J. Opt. Soc. Am. A

S. Ura, Y. Furukawa, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel pickup,” J. Opt. Soc. Am. A 7, 1759–1763 (1990).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

J. Vac. Sci. Technol. B

C. Peroz, C. Heitz, E. Barthel, E. Søndergård, and V. Goletto, “Glass nanostructures fabricated by soft thermal nanoimprint,” J. Vac. Sci. Technol. B 25, L27–L30 (2007).
[CrossRef]

Lab Chip

M. B. Mikkelsen, A. A. Letailleur, E. Søndergård, E. Barthel, J. Teisseire, R. Marie, and A. Kristensen, “All-silica nanofluidic devices for DNA-analysis fabricated by imprint of sol–gel silica with silicon stamp,” Lab Chip 12, 262–267 (2011).
[CrossRef]

Macromolecules

H. Schmid and B. Michel, “Siloxane polymers for high-resolution, high-accuracy soft lithography,” Macromolecules 33, 3042–3049 (2000).
[CrossRef]

Microelectron. Eng.

C. Gourgon, A. K. Ferchichi, D. Pietroy, T. Haatainen, and J. Tesseire, “Scatterometry analysis of sequentially imprinted patterns: influence of thermal parameters,” Microelectron. Eng. 98, 270–274 (2012).
[CrossRef]

Neuroendocrinol. Lett.

M. G. Figueiro and M. S. Rea, “Lack of short-wavelength light during the school day delays dim light melatonin onset (DLMO) in middle school students,” Neuroendocrinol. Lett. 31, 92–96 (2010).

Opt. Express

X. Sheng, S. G. Johnson, J. Michel, and L. C. Kimerling, “Optimization-based design of surface textures for thin-film Si solar cells,” Opt. Express 19, A841–A850 (2011).
[CrossRef]

Opt. Laser Technol.

S. Singh, “Diffraction gratings: aberrations and applications,” Opt. Laser Technol. 31, 195–218 (1999).
[CrossRef]

Opt. Lett.

O. Masuda and S. M. C. Nascimento, “Lighting spectrum to maximize colorfulness,” Opt. Lett. 37, 407–409 (2012).
[CrossRef]

Opt. Quantum Electron.

M. F. Lewis and C. L. West, “Some focusing properties of chirped gratings,” Opt. Quantum Electron. 21, 17–33 (1989).
[CrossRef]

Proc. SPIE

R. Maurer, F. Schneider, C. Vogt, M. Schinhaerl, P. Sperber, and R. Rascher, “Physical marker based stitching process of circular and non-circular interferograms,” Proc. SPIE 8083, 80830Q (2011).
[CrossRef]

H. D. Tholl, C. G. Stojanoff, R. Kubiza, and G. Willbold-Lohr, “Design optimization and manufacturing of holographic windows for daylighting applications in buildings,” Proc. SPIE 2017, 35–45 (1993).
[CrossRef]

Sol. Energy

M. Kischkoweit-Lopin, “An overview of daylighting systems,” Sol. Energy 73, 77–82 (2002).
[CrossRef]

Other

K. Papamichael, C. Ehrlich, and G. Ward, “Design and evaluation of daylighting applications of holographic glazings,” Final Report prepared for Physical Optics Corporation under Contract Agreement Number BG-95037 (1996).

C. L. Robbins, Daylighting: Design and Analysis (Van Nostrand Reinhold, 1986).

B. Bläsi, A. Gombert, and M. Niggemann, “Microstructured polymer surfaces with complex optical functions for solar applications,” in Polymers—Opportunities and Risks II SE—14, P. Eyerer, M. Weller, and C. Hübner, eds. (Springer, 2009), Vol. 12, pp. 263–279.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Illustration of light distribution inside a room with regular, unstructured windows. (b) Daylighting windows comprising, e.g., disordered gratings cause the light to spread more homogenously throughout the room and toward the ceiling. This results in an improved interior lighting during daylight hours. The angles of incident and transmitted light are denoted φ and θ, respectively, both measured from the horizontal. Figure adapted from [32].

Fig. 2.
Fig. 2.

(a) Disordered gratings are used in order to achieve broadening of the nonzero order diffraction peaks. For every M periods, a random shift of {λ/2;0;+λ/2} is inserted. (b) Diffraction of a 500 nm periodic grating for light incident at 30° from the surface normal. The 0th and 1st diffraction order for light of wavelengths 410, 532, and 661 nm are shown with peak positions at approximately 19°, 33°, and 55°, respectively. (c) The same grating with disordered period (ξ=25%) leads to broadening of the peaks around the locations for the uniform grating. (d) Cross-sectional drawings (to scale) of the different grating designs which are investigated. For illustration, adjacent blocks of M periods are shown in black/gray color. The height of the grating lines is 350 nm.

Fig. 3.
Fig. 3.

Fabrication process, consisting of sol–gel preparation, spin-coating of the thin-film, imprinting, and demolding.

Fig. 4.
Fig. 4.

(a) AFM-generated profile of a disordered grating (M=2). (b) Top view SEM image of a disordered grating (M=2).

Fig. 5.
Fig. 5.

(a) Schematic of the measurement setup. Light from three lasers is combined into a single beam and directed at the sample under a fixed angle of incidence. A CCD camera rotates around the sample to measure the transmitted diffraction pattern. Each measurement is comprised of multiple images, taken with a small overlap. (b) Detail of the angle definitions. 0° is defined as normal to the grating, positive angles correspond to light which is diffracted toward the ceiling, i.e., contributes to the daylighting.

Fig. 6.
Fig. 6.

Transmitted diffraction pattern of a grating with Λ=500 and M=2, measured separately for 410, 532, and 661 nm TE polarized light at 30° angle of incidence (artificial color). The 0th order, located at 30°, has been attenuated by a factor of 1000 for better visibility of the diffracted light.

Fig. 7.
Fig. 7.

Curves showing the measured and simulated diffraction results for the four investigated samples at 410, 532, and 661 nm. For each of the four samples, a drawing of the grating and a photograph of the diffraction pattern when illuminated with white xenon light is shown on top of the plots.

Tables (2)

Tables Icon

Table 1. Calculated Daylighting Efficiency of a 400 nm Grating with M=2 for Different Heights of the Grating Lines

Tables Icon

Table 2. Measured and Simulated Daylighting Efficiencies of the Samplesa

Equations (2)

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

ξ=1/(2M).
ηdaylighting=0°90°I(θ)dθ/90°90°I(θ)dθ,

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