Abstract

The analytical model [Moreno and Sun, Opt. Express 16, 1808–1819 (2008)] is applied to LED with attached secondary optics. It is shown that a slightly modified model using only three cosine power functions can be used for the cases with symmetric radiation pattern and that good fitting on realistic examples can be achieved with several standard optimization algorithms including local search heuristics and genetic algorithm.

© 2014 Optical Society of America

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References

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  1. I. Moreno and C.-C. Sun, “Modeling the radiation pattern of leds,” Opt. Express 16(3), 1808–1819 (2008).
    [Crossref] [PubMed]
  2. Ledil Oy., “Technical resources,” http://www.carclo-optics.com/brochures .
  3. Carclo Optics, “Product brochure,” http://www.carclo-optics.com/brochures .
  4. LedLink, “Product catalog,” http://www.ledlink-optics.com/ResourceCatalogs.aspx .
  5. IESNA, Standard File Format for the Electronic Transfare of Photometric Data and Related Information LM-63-02 (ANSI, 2002).
  6. SIST, Light and lighting - Measurement and presentation of photometric data of lamps and luminaries - Part 1: Measurement and file format EN 13032-1:2004+A1:2012 (SIST, 2012).
  7. E. Aarts and J. K. Lenstra, Local Search in Combinatorial Optimization (Princeton University, 2003).
  8. D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
    [Crossref]
  9. N. Mladenović and P. Hansen, “Variable neighborhood search,” Computers & OR 24(11), 1097–1100 (1997).
    [Crossref]
  10. N. Mladenović, P. Hansen, and J. Brimberg, “Sequential clustering with radius and split criteria,” Cent. Europ. J. Oper. Re. 21(1), 95–115 (2013).
    [Crossref]
  11. D. Kaljun and J. Žerovnik, “Local search based optimization of an analytical model of symmetric spatial light distribution,” in Bioinspired optimization methods and their applications : proceedings of the Student Workshop on Bioinspired Optimization Methods and their Applications - BIOMA 2014, J. Šilc and A. Zamuda, eds. (Jožef Stefan Institute, 2014), pp. 81–92.

2013 (1)

N. Mladenović, P. Hansen, and J. Brimberg, “Sequential clustering with radius and split criteria,” Cent. Europ. J. Oper. Re. 21(1), 95–115 (2013).
[Crossref]

2011 (1)

D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
[Crossref]

2008 (1)

1997 (1)

N. Mladenović and P. Hansen, “Variable neighborhood search,” Computers & OR 24(11), 1097–1100 (1997).
[Crossref]

Aarts, E.

E. Aarts and J. K. Lenstra, Local Search in Combinatorial Optimization (Princeton University, 2003).

Brimberg, J.

N. Mladenović, P. Hansen, and J. Brimberg, “Sequential clustering with radius and split criteria,” Cent. Europ. J. Oper. Re. 21(1), 95–115 (2013).
[Crossref]

Hansen, P.

N. Mladenović, P. Hansen, and J. Brimberg, “Sequential clustering with radius and split criteria,” Cent. Europ. J. Oper. Re. 21(1), 95–115 (2013).
[Crossref]

N. Mladenović and P. Hansen, “Variable neighborhood search,” Computers & OR 24(11), 1097–1100 (1997).
[Crossref]

Herrera, F.

D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
[Crossref]

Kaljun, D.

D. Kaljun and J. Žerovnik, “Local search based optimization of an analytical model of symmetric spatial light distribution,” in Bioinspired optimization methods and their applications : proceedings of the Student Workshop on Bioinspired Optimization Methods and their Applications - BIOMA 2014, J. Šilc and A. Zamuda, eds. (Jožef Stefan Institute, 2014), pp. 81–92.

Lenstra, J. K.

E. Aarts and J. K. Lenstra, Local Search in Combinatorial Optimization (Princeton University, 2003).

Lozano, M.

D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
[Crossref]

Mladenovic, N.

N. Mladenović, P. Hansen, and J. Brimberg, “Sequential clustering with radius and split criteria,” Cent. Europ. J. Oper. Re. 21(1), 95–115 (2013).
[Crossref]

N. Mladenović and P. Hansen, “Variable neighborhood search,” Computers & OR 24(11), 1097–1100 (1997).
[Crossref]

Molina, D.

D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
[Crossref]

Moreno, I.

Sánchez, A. M.

D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
[Crossref]

Sun, C.-C.

Žerovnik, J.

D. Kaljun and J. Žerovnik, “Local search based optimization of an analytical model of symmetric spatial light distribution,” in Bioinspired optimization methods and their applications : proceedings of the Student Workshop on Bioinspired Optimization Methods and their Applications - BIOMA 2014, J. Šilc and A. Zamuda, eds. (Jožef Stefan Institute, 2014), pp. 81–92.

Cent. Europ. J. Oper. Re. (1)

N. Mladenović, P. Hansen, and J. Brimberg, “Sequential clustering with radius and split criteria,” Cent. Europ. J. Oper. Re. 21(1), 95–115 (2013).
[Crossref]

Computers & OR (1)

N. Mladenović and P. Hansen, “Variable neighborhood search,” Computers & OR 24(11), 1097–1100 (1997).
[Crossref]

Opt. Express (1)

Soft Computing (1)

D. Molina, M. Lozano, A. M. Sánchez, and F. Herrera, “Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains,” Soft Computing 15(11), 2201–2220 (2011).
[Crossref]

Other (7)

D. Kaljun and J. Žerovnik, “Local search based optimization of an analytical model of symmetric spatial light distribution,” in Bioinspired optimization methods and their applications : proceedings of the Student Workshop on Bioinspired Optimization Methods and their Applications - BIOMA 2014, J. Šilc and A. Zamuda, eds. (Jožef Stefan Institute, 2014), pp. 81–92.

Ledil Oy., “Technical resources,” http://www.carclo-optics.com/brochures .

Carclo Optics, “Product brochure,” http://www.carclo-optics.com/brochures .

LedLink, “Product catalog,” http://www.ledlink-optics.com/ResourceCatalogs.aspx .

IESNA, Standard File Format for the Electronic Transfare of Photometric Data and Related Information LM-63-02 (ANSI, 2002).

SIST, Light and lighting - Measurement and presentation of photometric data of lamps and luminaries - Part 1: Measurement and file format EN 13032-1:2004+A1:2012 (SIST, 2012).

E. Aarts and J. K. Lenstra, Local Search in Combinatorial Optimization (Princeton University, 2003).

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Figures (3)

Fig. 1
Fig. 1 Schematic representation of a LED with mounted secondary optical element.
Fig. 2
Fig. 2 Above are presented the radiation patterns for three lenses. Viewed form the top to the bottom are C13353(a), CA11268(b), CA12392(c). On the left side is the comparison of the best modeled curve of each lens in blue, worst modeled curve in green and the measured data points from the photometry in red (relative intensity values). On the right side is the 3D representation of the best modeled solution and the function coefficients for that curve.
Fig. 3
Fig. 3 Above are presented the radiation patterns for two lenses. Viewed form the top to the bottom are CA11934(a), FP13030(b). On the left side is the comparison of the best modeled curve of each lens in blue, worst modeled curve in green and the measured data points from the photometry in red (relative intensity values). On the right side is the 3D representation of the best modeled solution and the function coefficients for that curve.

Tables (1)

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Table 1 Calculated RMS error for eleven lenses presented in % according to (3) with four million iterations which took approximately 30 minutes CPU time for each lens on a Core I3 4130 @ 3,4 Ghz (a standard home PC). Best two results in each row are emphasized.

Equations (3)

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I ( Θ ) = i a i * cos ( Θ b i ) c i
I ( Θ ) = I max i a i * cos ( Θ b i ) c i
RMS = 1 M i = 1 N [ I m ( Θ i ) I ( Θ i ) ] 2 ,

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