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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 3 — Jan. 20, 2008
  • pp: 431–441

Illuminance formation and color difference of mixed-color light emitting diodes in a rectangular light pipe: an analytical approach

Chu-Ming Cheng and Jyh-Long Chern  »View Author Affiliations

Applied Optics, Vol. 47, Issue 3, pp. 431-441 (2008)

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We developed an analytical method of illuminance formation for mixed-color LEDs in a rectangular light pipe in order to derive American National Standards Institute (ANSI) light uniformity, ANSI color uniformity, and color difference of light output using photometry, nonimaging, and colorimetry. The analytical results indicate that the distributions of illuminance and color difference vary with different geometric structures of light pipes and the location of the light sources. It was found that both the ANSI light and the ANSI color uniformity on the exit plane of the light pipe are reduced exponentially with the increase in length of the light pipe. It is evident that a length scale LA greater than unity assures that the mixed-color LED sources on the entrance plane are uniformly illuminated with acceptable uniform brightness and color on the exit plane of the rectangular light pipe, where L is the length of the light pipe, and A is a constant, which is a geometric parameter for the scale unit of the light pipe's input face. Furthermore, the ANSI light uniformity can be minimized, and the ANSI color uniformity can be maximized under the condition of multilight-source locations P = Q = ± A / 4 , where P and Q are the coordinates along the long axis and the short axis, respectively, with one being the entrance plane of the light pipe. We can conclude that the optimum form factor of the light pipe is a square shaped cross section, with the length scale LA being equal to unity and with multilight sources located individually on positions of A∕4 in order to achieve very uniform illuminations with the highest light efficiency and compact package for the optical system with mixed-color LEDs, where L is the length of the light pipe.

© 2008 Optical Society of America

OCIS Codes
(120.5240) Instrumentation, measurement, and metrology : Photometry
(220.2740) Optical design and fabrication : Geometric optical design
(230.3670) Optical devices : Light-emitting diodes
(230.7370) Optical devices : Waveguides
(330.1730) Vision, color, and visual optics : Colorimetry

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: April 18, 2007
Revised Manuscript: September 13, 2007
Manuscript Accepted: November 29, 2007
Published: January 18, 2008

Virtual Issues
Vol. 3, Iss. 2 Virtual Journal for Biomedical Optics

Chu-Ming Cheng and Jyh-Long Chern, "Illuminance formation and color difference of mixed-color light emitting diodes in a rectangular light pipe: an analytical approach," Appl. Opt. 47, 431-441 (2008)

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