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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 5 — Feb. 10, 2010
  • pp: 817–822

Analytic solution for quasi-Lambertian radiation transfer

Avi Braun and Jeffrey M. Gordon  »View Author Affiliations

Applied Optics, Vol. 49, Issue 5, pp. 817-822 (2010)

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An analytic solution is derived for radiation transfer between flat quasi-Lambertian surfaces of arbitrary orientation, i.e., surfaces that radiate in a Lambertian fashion but within a numerical aperture smaller than unity. These formulas obviate the need for ray trace simulations and provide exact, physically transparent results. Illustrative examples that capture the salient features of the flux maps and the efficiency of flux transfer are presented for a few configurations of practical interest. There is also a fundamental reciprocity relation for quasi-Lambertian exchange, akin to the reciprocity theorem for fully Lambertian surfaces. Applications include optical fiber coupling, fiber-optic biomedical procedures, and solar concentrators.

© 2010 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2175) Geometric optics : Etendue
(220.2945) Optical design and fabrication : Illumination design
(220.4298) Optical design and fabrication : Nonimaging optics

Original Manuscript: December 11, 2009
Manuscript Accepted: December 31, 2009
Published: February 2, 2010

Avi Braun and Jeffrey M. Gordon, "Analytic solution for quasi-Lambertian radiation transfer," Appl. Opt. 49, 817-822 (2010)

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  1. M. Young, Optics and Lasers Including Fibers and Optical Waveguides, 5th ed. (Springer, 2000), pp. 265-315.
  2. A. Katzir, Lasers and Optical Fibers in Medicine (Academic, 1993), pp. 107-207.
  3. J. M. Gordon, E. A. Katz, D. Feuermann, and M. Huleihil, “Toward ultrahigh-flux photovoltaic concentration,” Appl. Phys. Lett. 84, 3642-3644 (2004). [CrossRef]
  4. M. F. Modest, Radiative Heat Transfer, 2nd ed. (McGraw-Hill, 2003), pp. 131-158. [CrossRef]
  5. R. Winston, J. C. Miñano, P. Benítez, with contributions by N. Shatz, and J. Bortz, Nonimaging Optics (Elsevier, 2005), pp. 7-43, 415-420.
  6. A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, 1985), pp. 114-145.

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