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 Light & Engineering 26 (3)

Light & Engineering 26 (3)

Volume 26
Date of publication 09/28/2018
Pages 99-108

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Optimization Methods for Spectral Synthesizing of a Tuneable Colour Light Source. L&E 26 (3) 2018
Articles authors:
Nina Carli, Armin Sperling, Grega Bizjak

Nina Carli, M. Sc., studied at the Faculty of Electrical Engineering, University of Ljubljana in Slovenia. She graduated in Electrical Engineering with her diploma thesis about Spectrum Optimization of the Tuneable Colour Light Sources. She gathered the academic experience during an internship at PTB in Germany, and in Laboratory of lighting and photometry at the Faculty of Electrical Engineering in Ljubljana, Slovenia

Armin Sperling, Ph.D. He received his doctoral degree from the TU Braunschweig in 1994. In 2001, after six years being in research and development in industry, he joined the PTB and currently heads the Photometry and Spectroradiometry Department. He is associate Director of the CIE Division 2, Chairman of the German National Committee of the CIE and member of the DIN advisory board of the standardization committee for Light

Grega Bizjak, Ph.D., Professor. At present, he is a Head of Laboratory of Lighting and Photometry at Faculty of Electrical Engineering, University of Ljubljana. He is active in the field of lighting and photometry as well as in the field of electrical power engineering. His main research interests in lighting are photometry, energy efficient indoor and outdoor lighting, use of daylight and use of LEDs in lighting applications. Prof. Bizjak is the President of Slovenian National Committee of CIE and representative of Slovenia in CIE Division 2

Abstract
A method for a tuneable colour light source (TCLS) output spectrum synthesizing is described. A TCLS is a multichannel LED light source, which is able to mimic and produce different spectral distributions and can be used for the realization of different spectra, e.g. the spectra of different CIE standard illuminants. The synthesizing of output spectrum is actually an optimization problem of tuning the output spectrum of a TCLS to the target spectrum. It is also a so called constrained problem as output spectrum is produced by adding the weighted spectra of used light sources (e.g. singlecolour LEDs) and due to the fact that there is no “negative light”. Because of that usual optimization methods like least square method cannot be used. A novel synthesizing method based on a constrained optimization process was developed and tested on the laboratory TCLS to be used for calibration purposes. The developed synthesizing method, described in this paper, gives good results but comparison with more simple methods shows that also these can be successfully used.
References
1. Bizjak G, Lindemann M, Sperling A, et al. “Tunable LED colour source,” CIE Symp, 2010.
2. Fryc I, Brown SW, Eppeldauer GP, et al. “LEDbased spectrally tunable source for radiometric, photometric and colorimetric applications,” Opt. Eng., Vol. 44 (11), pp. 111309–111309–8, 2005.
3. Wu CC, Hu NC, Fong YC, et al. “Optimal pruning for selecting LEDs to synthesize tunable illumination spectra,” Light. Res. Technol., Vol. 44 (4), pp. 484–497, dec. 2012.
4. Luo MR, Xu L and Wang H. “An LED based spectrum design for surgical lighting,” Proc. 28th CIE Sess., 2015.
5. Lawson CL and Hanson RJ. “23. Linear least squares with linear inequality constrains,” Solving least squares problems, Society for industrail and applied mathematics, 1995, pp. 158–173.
6. Tosic I and Frossard P. “Dictionary learning”, IEEE Signal Process. Mag., Vol. 28 (2), pp. 27–38, mar. 2011.
7. Chun S, Kim JC and Lee CS. “Optimization for spectrally tunable lighting control, Proc. 28th CIE Sess., 2015, pp. 2046–2055.
8. Bro R and Jong SD. “A fast nonnegativityconstrained least squares algorithm,” J. Chemom, Vol. 11 (5), pp. 393–401, sep. 1997.
9. Cantarella J and Piatek M. “Tsnnls: A solver for large sparse least squares problems with non­negative vaiables,” Comput. Res Repos: CoRR, 2004.
10. “Solve nonnegative least­squares constrains problem – lsqnonneg,” MATLAB – Maths Works Deutschland, [Online]. Accessible: http://www.mathworks.com/help/matlab/ref/lsqnonneg.html?requestedDomain=www.mathworks.com. [Accessed: 2nov2015].
11. Moore, E. H. (1920). “On the reciprocal of the general algebraic matrix”. Bulletin of the American Mathematical Society. 26 (9): 394–395.
12. Bjerhammar, Arne (1951). “Application of calculus of matrices to method of least squares; with special references to geodetic calculations”. Trans. Roy. Inst. Tech. Stockholm. 49.
13. Penrose, Roger (1955). “A generalized inverse for matrices”. Proceedings of the Cambridge Philosophical Society. 51: 406–413.
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