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Applied Optics

Applied Optics


  • Vol. 15, Iss. 11 — Nov. 1, 1976
  • pp: 2880–2883

Ideal concentrators for finite sources and restricted exit angles

Ari Rabl and Roland Winston  »View Author Affiliations

Applied Optics, Vol. 15, Issue 11, pp. 2880-2883 (1976)

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Design procedures for ideal radiation concentrators are described which are applicable to finite sources and/or restricted exit angles. Finite sources are relevant for second stage concentrators which collect and further concentrate radiation from a primary focusing element (mirror or lens) in a manner similar to the field optic element in a telescope. Restricting the exit angle is useful for improving the optical efficiency of solar collectors by eliminating grazing angles of incidence of the absorber. It also serves to extend the useful range of angular acceptance values available from solid dielectric concentrators that function by total internal reflection. Concentrators of this type can be used to construct highly efficient radiation traps (spectrally selective filters).

© 1976 Optical Society of America

Original Manuscript: March 4, 1976
Published: November 1, 1976

Ari Rabl and Roland Winston, "Ideal concentrators for finite sources and restricted exit angles," Appl. Opt. 15, 2880-2883 (1976)

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  1. A. Rabl, R. Winston, Design Principles for Ideal Concentrators, in preparation.
  2. R. Winston, J. Opt. Soc. Am. 60, 245 (1970).
  3. H. Hinterberger, R. Winston, Rev. Sci. Instrum. 37, 1094 (1966); Rev. Sci. Instrum. 39, 1217 (1968).
  4. The compound parabolic concentrator was developed independently in the Soviet Union, see V. K. Baranov, G. K. Melnikov, Sov. J. Opt. Technol. 33, 408 (1966).
  5. D. A. Harper, R. H. Hildebrand, R. Stiening, R. Winston, Appl. Opt. 15, 53 (1976).
  6. R. Winston, J. M. Enoch, J. Opt. Soc. Am. 61, 1120 (1971); R. Levi-Setti, D. A. Park, R. Winston, Nature 253, 116 (1975).
  7. R. Winston, Sol. Energy 16, 89 (1974).
  8. A. Rabl, Sol. Energy 18, 93 (1976).
  9. A. Rabl, Optical and Thermal Properties of Compound Parabolic Concentrators, Argonne National Laboratory Report SOL 75-01 (1975). The techniques developed for calculating the absorption losses at the reflector walls can also be employed for the concentrators described in the present paper. For most applications the average number of reflections will be in the 0.5–1.5 range.
  10. R. Winston, Appl. Opt. 15, 291 (1976).
  11. This design procedure can obviously be extended to the case where the index n and/or the maximum exit angle θ2 are allowed to vary across the absorber. Then the term n sinθ2 in Eq. (3) is to be replaced by its average value n sinθ2 = 1/s ∫dsn(s) sinθ2(s). Further generalizations are easily incorporated if desired. For example, asymmetric absorber illumination can be achieved by choosing two different angles θ2′ and −θ2″ instead of +θ2 and −θ2.
  12. See, for example, H. C. Hottel, “Radiant Heat Transmission” in Heat Transmission, W. H. McAdams, Ed. (McGraw-Hill, New York, 1954, Chap. 4.
  13. The mirror turns out to be perpendicular to the absorber at this point, except in the limiting case of a flat absorber (where the corresponding angle is not well defined).
  14. See, for example, E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Brooks Cole, Belmont, Calif., 1970).
  15. The examples described here are symmetric, but the generalization to asymmetric concentrators is straightforward, see Rabl, Ref. 8. Asymmetric ideal concentrators may be useful for solar energy collection, because their output can vary with time of year to match a variable load.
  16. V. K. Baranov, Geliotekhnika 11, 45 (1975).
  17. R. Winston, Light Collectors in Cylindrical Geometry, U.S. Patent3,957,031, 18May1976.
  18. Spectrolab, Inc., Investigation of Terrestrial Photovoltaic Power Systems with Sunlight Concentration, Annual Report (1975).
  19. R. Winston, H. Hinterberger, Sol. Energy 17, 255 (1975).
  20. A. Rabl, Argonne National Laboratory Report SOL 75-05; Appl. Opt.15, 1871 (1976).
  21. The design principle for both θ1 – θ2 transformer and general convex absorber can be stated in a unified way. The solution maximizes the slope of the mirror consistent with reflecting extreme rays onto absorber at angle of incidence not exceeding θ2.

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