Abstract

The design procedure of a new nonimaging concentrator (called an RXI) is explained. Rays that impinge on the concentrator aperture, within the acceptance angle, are directed to the receiver by means of one refraction, one reflection, and one total internal reflection. The concentrator can be made as a single dielectric piece (in which the receiver is immersed) whose aspect ratio (thickness/aperture diameter) is close to 1/3. Ray-tracing analysis of a rotational symmetric RXI shows total transmissions of greater than 94.5% (no absorption or reflection losses are considered) when the acceptance angle of the incoming rays is small (<3°) and when the receiver area is the smallest possible (maximal concentration.)

© 1995 Optical Society of America

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References

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  1. W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, New York, 1989).
  2. R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” J. Opt. Soc. Am. A 10, 1902–1908 (1993).
    [CrossRef]
  3. A. Rabl, “Reflector design for illumination with extended sources: the basic solution,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L.Holman Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 66–77 (1993).
  4. J. M. Gordon, P. Kashin, A. Rabl, “Nonimaging reflectors for efficient uniform illumination,” Appl. Opt. 31, 6027–6035 (1992).
    [CrossRef] [PubMed]
  5. H. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
    [CrossRef]
  6. I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27.
    [CrossRef]
  7. J. C. Minano, “Two-dimensional nonimaging concentrators with inhomogeneous media: a new look,” J. Opt. Soc. Am. A 2, 1826–1831 (1985).
    [CrossRef]
  8. J. C. Minano, “Design of three-dimensional nonimaging concentrators with inhomogeneous media,” J. Opt. Soc. Am. A 3, 1345–1353 (1986).
    [CrossRef]
  9. J. C. Minano, J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. 31, 3051–3060 (1992).
    [CrossRef] [PubMed]
  10. J. C. Minano, J. C. González, “Design of nonimaging lenses and lens-mirror combinations,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1528, 104–116 (1991).
  11. H. Ries, A. Rabl, “Edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A 11, 2627–2632 (1994).
    [CrossRef]
  12. J. C. Minano, P. Benítez, J. C. González, “RX, a nonimaging concentrator,” Appl. Opt. 34, 2226–2235 (1995).
    [CrossRef] [PubMed]
  13. G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
    [CrossRef]
  14. I. M. Bassett, G. W. Forbes, “A new class of ideal non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
    [CrossRef]
  15. J. C. Minano, “Application of the conservation of etendue theorem for 2D subdomains of the phase space in nonimaging concentrators,” Appl. Opt. 23, 2021–2025 (1984).
    [CrossRef] [PubMed]
  16. T. Jannson, R. Winston, “Liouville’s theorem and concentration optics,” J. Opt. Soc. Am. A 3, 7–8 (1986).
    [CrossRef]
  17. See, for instance, O. N. Stavroudis, Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972), p. 97.

1995 (1)

1994 (2)

1993 (1)

1992 (2)

1986 (2)

1985 (1)

1984 (1)

1982 (2)

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

I. M. Bassett, G. W. Forbes, “A new class of ideal non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

Bassett, I. M.

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

I. M. Bassett, G. W. Forbes, “A new class of ideal non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27.
[CrossRef]

Benítez, P.

Forbes, G. W.

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

I. M. Bassett, G. W. Forbes, “A new class of ideal non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

González, J. C.

J. C. Minano, P. Benítez, J. C. González, “RX, a nonimaging concentrator,” Appl. Opt. 34, 2226–2235 (1995).
[CrossRef] [PubMed]

J. C. Minano, J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. 31, 3051–3060 (1992).
[CrossRef] [PubMed]

J. C. Minano, J. C. González, “Design of nonimaging lenses and lens-mirror combinations,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1528, 104–116 (1991).

Gordon, J. M.

Jannson, T.

Kashin, P.

Minano, J. C.

Rabl, A.

H. Ries, A. Rabl, “Edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A 11, 2627–2632 (1994).
[CrossRef]

J. M. Gordon, P. Kashin, A. Rabl, “Nonimaging reflectors for efficient uniform illumination,” Appl. Opt. 31, 6027–6035 (1992).
[CrossRef] [PubMed]

A. Rabl, “Reflector design for illumination with extended sources: the basic solution,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L.Holman Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 66–77 (1993).

Ries, H.

Stavroudis, O. N.

See, for instance, O. N. Stavroudis, Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972), p. 97.

Welford, W. T.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, New York, 1989).

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27.
[CrossRef]

Winston, R.

Appl. Opt. (4)

J. Opt. Soc. Am. A (6)

Opt. Acta (2)

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

I. M. Bassett, G. W. Forbes, “A new class of ideal non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

Other (5)

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, New York, 1989).

See, for instance, O. N. Stavroudis, Optics of Rays, Wavefronts and Caustics (Academic, New York, 1972), p. 97.

A. Rabl, “Reflector design for illumination with extended sources: the basic solution,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L.Holman Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 66–77 (1993).

I. M. Bassett, W. T. Welford, R. Winston, “Nonimaging optics for flux concentration,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27.
[CrossRef]

J. C. Minano, J. C. González, “Design of nonimaging lenses and lens-mirror combinations,” in Nonimaging Optics: Maximum Efficiency Light Transfer, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1528, 104–116 (1991).

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Figures (9)

Fig. 1
Fig. 1

Input and output bundles of a 2D concentrator.

Fig. 2
Fig. 2

Representation of the input and the output bundles in the xp plane. The figure also shows some particular points (r a , r b , r c , r d ) of the input bundle whose trajectories in the xz plane can be seen in Fig. 1.

Fig. 3
Fig. 3

Curve 2 obtained in the first iteration of an RXI design. Curve 1X (coincident with curve 1R at this design step) is the one proposed at the begining of the design procedure. The RXI is designed for a source at infinity (subtending an angle of ±5°) as the input bundle and for maximal concentration.

Fig. 4
Fig. 4

Curve 1X obtained at step (6) of the first iteration of the RXI design.

Fig. 5
Fig. 5

RXI designed for a source at infinity subtending an angle ±1° (θ i = 1°) and for maximal concentration. The refractive index is 1.5; other data can be found in Table 1. The active side of the receiver faces upward.

Fig. 6
Fig. 6

Same as in Fig. 5, but with an angle θ i = 3°.

Fig. 7
Fig. 7

Same as in Fig. 5, but with an angle θ i = 5°.

Fig. 8
Fig. 8

RXI concentrators for the input bundle i formed by the rays issuing from any point of AA′ toward any point of BB′. o is formed by all the rays that reach the receiver.

Fig. 9
Fig. 9

Angle-transmission curves of four rotational RXI designed for sources at infinity subtending angles 0.5°, 1°, 3°, and 5° and for maximal concentration on the receiver.

Tables (2)

Tables Icon

Table 1 Geometric Characteristics and 3D Ray-Tracing Results of Selected RXI Concentratorsa

Tables Icon

Table 2 Geometric Characteristics and 3D Ray-Tracing Results of Selected RXI Concentratorsa

Equations (3)

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T t = E ( M c ) E ( M i ) .
4 A i n i sin θ i = 4 A o n o sin θ o .
T ( θ ) = E ( M c M θ ) E ( M θ ) ,

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