One-time ray-tracing optimization method and its application to the design of an illuminator for a tube photo-bioreactor

Shu-Chun Chu; Hai-Li Yang; Yi-Hong Liao; Hong-Yu Wu; Chi Wang

doi:10.1364/OE.22.005357

One-time ray-tracing optimization method and its application to the design of an illuminator for a tube photo-bioreactor

Shu-Chun Chu, Hai-Li Yang, Yi-Hong Liao, Hong-Yu Wu, and Chi Wang

Optics Express
Vol. 22,
Issue 5,
pp. 5357-5374
(2014)
•https://doi.org/10.1364/OE.22.005357

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Shu-Chun Chu, Hai-Li Yang, Yi-Hong Liao, Hong-Yu Wu, and Chi Wang, "One-time ray-tracing optimization method and its application to the design of an illuminator for a tube photo-bioreactor," Opt. Express 22, 5357-5374 (2014)

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Related Topics
Table of Contents Category
- Geometrical Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Illumination design (220.2945)
- Nonimaging optics (220.4298)

About this Article
History
- Original Manuscript: December 2, 2013
- Revised Manuscript: February 8, 2014
- Manuscript Accepted: February 19, 2014
- Published: February 28, 2014

Accessible

Open Access

Abstract

This study details a one-time ray-tracing optimization method for the optimization of LED illumination systems [S.-C. Chu and H.-L. Yang, “One-time ray-tracing method for the optimization of illumination system,” in Proceedings of International Conference on Optics in Precision Engineering and Nanotechnology (icOPEN, 2013), 87692M]. This method optimizes the performance of illumination systems by modifying the light source’s radiant intensity distribution with a freeform lens, instead of modifying the illumination system structure. Because illumination system structures are unchanged in the design process, a designer can avoid the common problems faced when designing illumination systems, i.e., the repeated and time-consuming ray-tracing process when optimizing the illumination system parameters. The easy approaches of the proposed optimization method to sample the target illumination areas and to divide the light source radiant intensity distribution make the proposed method can be applied to both direct-lit and non-direct-lit illumination systems. To demonstrate the proposed method, this study designs an illuminator for a tube photo-bioreactor using the proposed one-time ray-tracing method. A comparison shows that in the designing of the photo-bioreactor, tracing all rays one time requires about 13 hours, while optimizing the light source’s radiant intensity distribution requires only about twenty minutes. The considerable reduction in the ray-tracing time shows that the proposed method is a fast and effective way to design illumination systems.

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References

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Year
|
Author
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Publication

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K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]
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Z. Su, D. Xue, and Z. Ji, “Designing LED array for uniform illumination distribution by simulated annealing algorithm,” Opt. Express 20(S6), A843–A855 (2012).
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Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
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F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]
K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]
J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]
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[Crossref]
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[Crossref]
C.-Y. Chen, K.-L. Yeh, R. Aisyah, D.-J. Lee, and J.-S. Chang, “Cultivation, photobioreactor design and harvesting of microalgae for biodiesel production: A critical review,” Bioresour. Technol. 102(1), 71–81 (2011).
[Crossref] [PubMed]
Z. Csőgör, M. Herrenbauer, K. Schmidt, and C. Posten, “Light distribution in a novel photobioreactor – modelling for optimization,” J. Appl. Phycol. 13(4), 325–333 (2001).
[Crossref]
Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]
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X. Wang, “Method of steepest descent and its applications,” IEEE Microwave Wirel. Compon. Lett. 12, 24–26 (2008).
S. Zhao, K. Wang, F. Chen, D. Wu, and S. Liu, “Lens design of LED searchlight of high brightness and distant spot,” J. Opt. Soc. Am. A 28(5), 815–820 (2011).
[Crossref]
The Language of Technical Computing, see http://www.mathworks.com/ .

2013 (4)

X. Hu and K. Qian, “Optimal design of optical system for LED road lighting with high illuminance and luminance uniformity,” Appl. Opt. 52(24), 5888–5893 (2013).
[Crossref] [PubMed]

X.-H. Lee, I. Moreno, and C.-C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express 21(9), 10612–10621 (2013).
[Crossref] [PubMed]

J.-C. Yu, J.-H. Chen, and S.-C. Liu, “Design of LED edge-lit light bar for automotive taillight applications,” Proc. SPIE 8835, 88350G (2013).

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).
[Crossref] [PubMed]

2012 (3)

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]

J.-W. Pan and Y.-W. Hu, “Light-guide plate using periodical and single-sized microstructures to create a uniform backlight system,” Opt. Lett. 37(17), 3726–3728 (2012).
[Crossref] [PubMed]

Z. Su, D. Xue, and Z. Ji, “Designing LED array for uniform illumination distribution by simulated annealing algorithm,” Opt. Express 20(S6), A843–A855 (2012).
[Crossref]

2011 (4)

J.-W. Pan and C.-W. Fan, “High luminance hybrid light guide plate for backlight module application,” Opt. Express 19(21), 20079–20087 (2011).
[Crossref] [PubMed]

C.-Y. Chen, K.-L. Yeh, R. Aisyah, D.-J. Lee, and J.-S. Chang, “Cultivation, photobioreactor design and harvesting of microalgae for biodiesel production: A critical review,” Bioresour. Technol. 102(1), 71–81 (2011).
[Crossref] [PubMed]

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

S. Zhao, K. Wang, F. Chen, D. Wu, and S. Liu, “Lens design of LED searchlight of high brightness and distant spot,” J. Opt. Soc. Am. A 28(5), 815–820 (2011).
[Crossref]

2010 (2)

Z. Qin, K. Wang, F. Chen, X. B. Luo, and S. Liu, “Analysis of condition for uniform lighting generated by array of light emitting diodes with large view angle,” Opt. Express 18(16), 17460–17476 (2010).
[Crossref] [PubMed]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

2009 (2)

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

2008 (2)

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
[Crossref] [PubMed]

X. Wang, “Method of steepest descent and its applications,” IEEE Microwave Wirel. Compon. Lett. 12, 24–26 (2008).

2007 (2)

S. R. Park, O. J. Kwon, D. Shin, S.-H. Song, H. S. Lee, and H. Y. Choi, “Grating micro-dot patterned light guide plates for LED backlights,” Opt. Express 15(6), 2888–2899 (2007).
[Crossref] [PubMed]

J.-G. Chang and Y.-B. Fang, “Dot-pattern design of a light guide in an edge-lit backlight using a regional partition approach,” Opt. Eng. 46(4), 043002 (2007).
[Crossref]

2006 (1)

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
[Crossref] [PubMed]

2001 (1)

Z. Csőgör, M. Herrenbauer, K. Schmidt, and C. Posten, “Light distribution in a novel photobioreactor – modelling for optimization,” J. Appl. Phycol. 13(4), 325–333 (2001).
[Crossref]

1999 (1)

Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]

Aisyah, R.

Avendaño-Alejo, M.

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
[Crossref] [PubMed]

Bezus, E. A.

Chang, J.-G.

J.-G. Chang and Y.-B. Fang, “Dot-pattern design of a light guide in an edge-lit backlight using a regional partition approach,” Opt. Eng. 46(4), 043002 (2007).
[Crossref]

Chang, J.-S.

Chen, C.-Y.

Chen, F.

S. Zhao, K. Wang, F. Chen, D. Wu, and S. Liu, “Lens design of LED searchlight of high brightness and distant spot,” J. Opt. Soc. Am. A 28(5), 815–820 (2011).
[Crossref]

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]

Chen, J.-H.

J.-C. Yu, J.-H. Chen, and S.-C. Liu, “Design of LED edge-lit light bar for automotive taillight applications,” Proc. SPIE 8835, 88350G (2013).

Chen, J.-J.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]

Choi, H. Y.

Csogör, Z.

Z. Csőgör, M. Herrenbauer, K. Schmidt, and C. Posten, “Light distribution in a novel photobioreactor – modelling for optimization,” J. Appl. Phycol. 13(4), 325–333 (2001).
[Crossref]

Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]

Ding, Y.

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
[Crossref] [PubMed]

Dmitriev, A. Y.

Doskolovich, L. L.

Fan, C.-W.

J.-W. Pan and C.-W. Fan, “High luminance hybrid light guide plate for backlight module application,” Opt. Express 19(21), 20079–20087 (2011).
[Crossref] [PubMed]

Fang, Y.-B.

J.-G. Chang and Y.-B. Fang, “Dot-pattern design of a light guide in an edge-lit backlight using a regional partition approach,” Opt. Eng. 46(4), 043002 (2007).
[Crossref]

Gu, P. F.

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
[Crossref] [PubMed]

Herrenbauer, M.

Z. Csőgör, M. Herrenbauer, K. Schmidt, and C. Posten, “Light distribution in a novel photobioreactor – modelling for optimization,” J. Appl. Phycol. 13(4), 325–333 (2001).
[Crossref]

Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]

Kwon, O. J.

Lee, D.-J.

Lee, H. S.

Lee, X.-H.

X.-H. Lee, I. Moreno, and C.-C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express 21(9), 10612–10621 (2013).
[Crossref] [PubMed]

Lin, C.-T.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]

Liu, S.

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

S. Zhao, K. Wang, F. Chen, D. Wu, and S. Liu, “Lens design of LED searchlight of high brightness and distant spot,” J. Opt. Soc. Am. A 28(5), 815–820 (2011).
[Crossref]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

Liu, S.-C.

J.-C. Yu, J.-H. Chen, and S.-C. Liu, “Design of LED edge-lit light bar for automotive taillight applications,” Proc. SPIE 8835, 88350G (2013).

Liu, T.-S.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]

Liu, X.

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
[Crossref] [PubMed]

Liu, Z.

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

Liu, Z. Y.

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]

Luo, X.

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

Luo, X. B.

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]

Moiseev, M. A.

Moreno, I.

X.-H. Lee, I. Moreno, and C.-C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express 21(9), 10612–10621 (2013).
[Crossref] [PubMed]

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
[Crossref] [PubMed]

Pan, J.-W.

J.-W. Pan and Y.-W. Hu, “Light-guide plate using periodical and single-sized microstructures to create a uniform backlight system,” Opt. Lett. 37(17), 3726–3728 (2012).
[Crossref] [PubMed]

J.-W. Pan and C.-W. Fan, “High luminance hybrid light guide plate for backlight module application,” Opt. Express 19(21), 20079–20087 (2011).
[Crossref] [PubMed]

Park, S. R.

Perner, I.

Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]

Posten, C.

Z. Csőgör, M. Herrenbauer, K. Schmidt, and C. Posten, “Light distribution in a novel photobioreactor – modelling for optimization,” J. Appl. Phycol. 13(4), 325–333 (2001).
[Crossref]

Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]

Qian, K.

X. Hu and K. Qian, “Optimal design of optical system for LED road lighting with high illuminance and luminance uniformity,” Appl. Opt. 52(24), 5888–5893 (2013).
[Crossref] [PubMed]

Qin, Z.

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

Schmidt, K.

Z. Csőgör, M. Herrenbauer, K. Schmidt, and C. Posten, “Light distribution in a novel photobioreactor – modelling for optimization,” J. Appl. Phycol. 13(4), 325–333 (2001).
[Crossref]

Z. Csőgör, M. Herrenbauer, I. Perner, K. Schmidt, and C. Posten, “Design of a photo-bioreactor for modelling purposes,” Chem. Eng. Process. 38(4-6), 517–523 (1999).
[Crossref]

Shin, D.

Song, S.-H.

Su, Z.

Z. Su, D. Xue, and Z. Ji, “Designing LED array for uniform illumination distribution by simulated annealing algorithm,” Opt. Express 20(S6), A843–A855 (2012).
[Crossref]

Sun, C.-C.

X.-H. Lee, I. Moreno, and C.-C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express 21(9), 10612–10621 (2013).
[Crossref] [PubMed]

Tsai, M.-D.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]

Tzonchev, R. I.

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
[Crossref] [PubMed]

Wang, K.

S. Zhao, K. Wang, F. Chen, D. Wu, and S. Liu, “Lens design of LED searchlight of high brightness and distant spot,” J. Opt. Soc. Am. A 28(5), 815–820 (2011).
[Crossref]

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Liu, and X. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009).
[Crossref]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illuminance quality light-emitting diode MR16 lamps,” Opt. Eng. 48(12), 123002 (2009).
[Crossref]

Wang, T.-Y.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20(10), 10984–10995 (2012).
[Crossref] [PubMed]

Wang, X.

X. Wang, “Method of steepest descent and its applications,” IEEE Microwave Wirel. Compon. Lett. 12, 24–26 (2008).

Wu, D.

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4), A830–A840 (2011).
[Crossref] [PubMed]

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Fig. 1 A schematic diagram of a common edge-lit LED illuminator designed to provide homogeneous illuminance at the target illumination area. The figure also illustrates an example of dividing the target illumination area into several target zones (T-zones).

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Fig. 2 A schematic diagram showing the dividing of the LED radiant intensity distribution into multiple light source zones. The proposed method divides the LED radiant intensity distribution into M source zones (S-zones) according to its light-emitting angle θ to a reference direction

\hat{n}

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Fig. 3 Illustration of the steepest descent method used to maximize the R value: (a) the change of the flux weighting array G_n is along the R-increasing direction,

\nabla R (G_{n})

; (b) the contour lines of the R value of a illumination system. With the suitable choice of each step size of the steepest descent method, the R value increases with every change of flux weighting array G.

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Fig. 4 Illustration of the method for finding a freeform lens to create a specified LIDC: (a) parameters used in the proposed method; (b) calculation of the freeform lens curve.

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Fig. 5 Flow chart showing the one-time ray-tracing optimization method process used for designing illumination systems. The symbol ε denotes the residual error of the gradient of R.

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Fig. 6 Posten's illuminator for a tube photo-bioreactor [23,24]

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Fig. 7 Schematic diagram of the structure of the tube photo-bioreactor illuminator: (a) composition of tube illuminator, with a tube lightguide, several point-like light sources and two tube reflectors at each end of the tube lightguide. The blue rectangle indicates the location of the cross-section plot, as shown in Fig. 7(b); (b) radial cross-section plot of the tube illuminator showing the circular groove structure on both tube lightguide surfaces; (c) transverse cross-section of the tube illuminator showing locations of the inner and outer cylindrical target surfaces in the following optimization settings. The division of two target surfaces is along the direction of cylinder axis (i.e., z-axis).

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Fig. 8 Unfolded illuminance distributions of the two cylindrical target surfaces of the initial tube illuminator design: (a) illuminance distribution on inner target surface; (b) illuminance distribution on outer target surface. The color bar of each figure shows the ratio of the illuminance distribution composition. The minimum-to-maximum illuminance ratio R of the two target surfaces was 45.9% and 47.2%, respectively.

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Fig. 9 Cross-section average illuminance distributions resulting from each light source zone on the two cylindrical target surfaces: (a) inner target surface and (b) outer target surface.

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Fig. 10 Performance of the tube illuminator after LED LIDC optimization: (a) optimized LED LIDC; (b) unfolded illuminance distribution on inner target surface; (c) unfolded illuminance distribution on outer target surface. The color bars of Figs. 10(b) and 10(c) indicate the relative composition of the illuminance distributions of the two cylindrical target surfaces.

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Fig. 11 Performance of the tube illuminator using freeform lens-constructed light sources: (a) side view of the built freeform lens; (b) LIDC of freeform lens-constructed light source using Lambertian LED chips of different widths (colored lines). The black dotted line denotes the ideal situation, i.e., the optimized LIDC. The symbol r denotes the ratio of the LED chip diameter to the diameter of the spherical side of the lens; (c) unfolded illuminance distribution on inner target surface (while LED chip r = 0.05 mm); (d) unfolded illuminance distribution on outer target surface (while LED chip r = 0.05 mm); (e) cross-section illuminance distributions in the photo-bioreactor in water from the axis of the tube illuminator in six different distances: 10mm, 20mm, 30mm, 60mm, 70mm and 80mm. The color bars of Figs. 11(c) and 11(d) indicate the relative composition of the illuminance distributions of the two target surfaces.

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Fig. 12 Performance of the tube illuminator using a 10-time-contraction freeform lens-constructed light source rather than the light source used in Fig. 11: (a) unfolded illuminance distribution on inner target surface; (b) unfolded illuminance distribution on outer target surface. The color bars of Figs. 12(a) and 12(b) indicate the relative composition of the illuminance distributions.

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Equations (11)

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F = [\begin{matrix} F_{1}^{1} & F_{2}^{1} & F_{3}^{1} & \dots & \dots & F_{N}^{1} \\ F_{1}^{2} & F_{2}^{2} & F_{3}^{2} & \dots & \dots & F_{N}^{2} \\ ⋮ & ⋮ & ⋮ & \dots & \dots & ⋮ \\ ⋮ & ⋮ & ⋮ & \dots & \dots & ⋮ \\ F_{1}^{M} & F_{2}^{M} & F_{3}^{M} & \dots & \dots & F_{N}^{M} \end{matrix}],

G = [\begin{matrix} g^{1}, & g^{2}, & ... & g^{M} \end{matrix}],

P = G F = [\begin{matrix} p_{1} & p_{2} & ... & p_{N} \end{matrix}],

R = \frac{P_{\min}}{\bar{P_{\max}}},

G_{n + 1} = G_{n} + γ \cdot \nabla R (G_{n}),

Φ (θ) = {\begin{matrix} g^{1} Φ^{1} \\ g^{2} Φ^{2} \\ g^{3} Φ^{3} \\ ⋮ \\ g^{M} Φ^{M} \end{matrix} \begin{matrix} ; \\ ; \\ ; \\ ; \end{matrix} \begin{matrix} θ_{0} \leq θ < θ_{1} \\ θ_{1} \leq θ < θ_{2} \\ θ_{2} \leq θ < θ_{3} \\ ⋮ \\ θ_{M - 1} \leq θ < θ_{M} \end{matrix},

I (θ) = {\begin{matrix} I^{1} \\ I^{2} \\ I^{3} \\ ⋮ \\ I^{M} \end{matrix} \begin{matrix} ; \\ ; \\ ; \\ ; \\ ; \end{matrix} \begin{matrix}  \end{matrix} \begin{matrix} θ_{0} \leq θ < θ_{1} \\ θ_{1} \leq θ < θ_{2} \\ θ_{2} \leq θ < θ_{3} \\ ⋮ \\ θ_{M - 1} \leq θ < θ_{M} \end{matrix},

g^{i} Φ^{i} = 2 π \int_{θ_{i}}^{θ_{i + 1}} I^{i} \sin θ d θ .

\vec{N} = \vec{O} - n \vec{I},

2 π \int_{0}^{ϕ_{i}} (I_{0} \cos φ) \sin φ d φ = 2 π \int_{0}^{θ_{i}} I (θ) \sin θ d θ,

R = R_{i n} + R_{o u t},

Abstract

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Bioresour. Technol. (1)

Chem. Eng. Process. (1)

IEEE Microwave Wirel. Compon. Lett. (1)

J. Appl. Phycol. (1)

J. Opt. A, Pure Appl. Opt. (1)

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Opt. Eng. (2)

Opt. Express (9)