Abstract

A detailed description of the design procedure for a new concentrator, RX, and some examples of it’s use are given. The method of design is basically the same as that used in the design of two other concentrators: the RR and the XR [Appl. Opt. 31, 3051 (1992)]. The RX is ideal in two-dimensional geometry. The performance of the rotational RX is good when the average angular spread of the input bundle is small: up to 95% of the power of the input bundle can be transferred to the output bundle (with the assumption of a constant radiance for the rays of the input bundle).

© 1995 Optical Society of America

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References

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  1. D. S. Goodman, “Tower of Babel,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 216.
  2. H. Poincaré, Les méthodes nouvelles de la mécanique céleste (Dover, New York, 1957), Vol. 3.
  3. R. Winston, W. T. Welford, “Geometrical vector flux and some new nonimaging concentrators,” J. Opt. Soc. Am. 69, 532–536 (1979).
    [CrossRef]
  4. W. T. Welford, R. Winston, High-Collection Nonimaging Optics (Academic, New York, 1989).
  5. J. C. Minano, “Design of three-dimensional nonimaging concentrators with inhomogeneous media,” J. Opt. Soc. Am. A 3, 1345–1353 (1986).
    [CrossRef]
  6. R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” J. Opt. Soc. Am. A 10, 1902–1908 (1993).
    [CrossRef]
  7. R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 2–11 (1993).
  8. 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, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 66–77 (1993).
  9. J. M. Gordon, P. Kashin, A. Rabl, “Nonimaging reflectors for efficient uniform illumination,” Appl. Opt. 31, 6027–6035 (1992).
    [CrossRef] [PubMed]
  10. 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, pp. 161–226.
    [CrossRef]
  11. J. C. Minano, “Two-dimensional nonimaging concentrators with inhomogeneous media: a new look,” J. Opt. Soc. Am. A 2, 1826–1831 (1985).
    [CrossRef]
  12. J. C. Minano, J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. 31, 3051–3060 (1992).
    [CrossRef] [PubMed]
  13. 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).
  14. J. M. Gordon, H. Ries, “Tailored edge-ray concentrators as ideal second stages for Fresnel reflectors,” Appl. Opt. 32, 2243–2251 (1993).
    [CrossRef] [PubMed]
  15. H. Hottel, “Radiant-heat transmission,” in Heat Transmission, W. H. McAdams, ed. (McGraw-Hill, New York, 1954).
  16. P. Benítez, “Diseno y análisis de un concentrador anidólico,” in Proyecto Fin de Carrera (Escuela Técnica Superior Ingenieros Telecomunicación, Universidad Politécnica de Madrid, Madrid, 1993).
  17. J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York, 1983).

1993

1992

1986

1985

1979

Bassett, I. M.

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, pp. 161–226.
[CrossRef]

Benítez, P.

P. Benítez, “Diseno y análisis de un concentrador anidólico,” in Proyecto Fin de Carrera (Escuela Técnica Superior Ingenieros Telecomunicación, Universidad Politécnica de Madrid, Madrid, 1993).

Bulirsch, R.

J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York, 1983).

González, J. C.

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).

Goodman, D. S.

D. S. Goodman, “Tower of Babel,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 216.

Gordon, J. M.

Hottel, H.

H. Hottel, “Radiant-heat transmission,” in Heat Transmission, W. H. McAdams, ed. (McGraw-Hill, New York, 1954).

Kashin, P.

Minano, J. C.

Poincaré, H.

H. Poincaré, Les méthodes nouvelles de la mécanique céleste (Dover, New York, 1957), Vol. 3.

Rabl, A.

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, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 66–77 (1993).

Ries, H.

J. M. Gordon, H. Ries, “Tailored edge-ray concentrators as ideal second stages for Fresnel reflectors,” Appl. Opt. 32, 2243–2251 (1993).
[CrossRef] [PubMed]

R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” J. Opt. Soc. Am. A 10, 1902–1908 (1993).
[CrossRef]

R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 2–11 (1993).

Stoer, J.

J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York, 1983).

Welford, W. T.

R. Winston, W. T. Welford, “Geometrical vector flux and some new nonimaging concentrators,” J. Opt. Soc. Am. 69, 532–536 (1979).
[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, pp. 161–226.
[CrossRef]

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

Winston, R.

R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” J. Opt. Soc. Am. A 10, 1902–1908 (1993).
[CrossRef]

R. Winston, W. T. Welford, “Geometrical vector flux and some new nonimaging concentrators,” J. Opt. Soc. Am. 69, 532–536 (1979).
[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, pp. 161–226.
[CrossRef]

R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 2–11 (1993).

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

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Other

D. S. Goodman, “Tower of Babel,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 216.

H. Poincaré, Les méthodes nouvelles de la mécanique céleste (Dover, New York, 1957), Vol. 3.

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

R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” in Nonimaging Optics: Maximum Efficiency Light Transfer II, R. Winston, R. L. Holman, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2016, 2–11 (1993).

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, 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, pp. 161–226.
[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).

H. Hottel, “Radiant-heat transmission,” in Heat Transmission, W. H. McAdams, ed. (McGraw-Hill, New York, 1954).

P. Benítez, “Diseno y análisis de un concentrador anidólico,” in Proyecto Fin de Carrera (Escuela Técnica Superior Ingenieros Telecomunicación, Universidad Politécnica de Madrid, Madrid, 1993).

J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York, 1983).

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the cross section of an RX concentrator: Rays emitted by the disk SS′ toward II′ are concentrated on the receiver in such a way that the lower face of the receiver becomes isotropically illuminated by the input bundle.

Fig. 2
Fig. 2

Input and output bundles of the RX concentrator in 2D geometry. The rays of the input bundle are those linking the segments SS′ and II′, and the rays of the output bundle are those linking OO′ and RR′.

Fig. 3
Fig. 3

Representation of (a) the input and (b) the output bundles in the xp plane. The figure also shows some particular points (r a , r b , r c , and r d ) of the input bundle whose trajectories in the xz plane can be seen in Fig. 2.

Fig. 4
Fig. 4

Classification of the points of the xz plane according to the edge rays: (a) drawing of the input bundle, and (b) drawing of the output bundle.

Fig. 5
Fig. 5

Trajectories of the rays of ∂ i with (a) the greatest value of p and (b) the smallest value of p. Some wave fronts are also shown.

Fig. 6
Fig. 6

First points on the refractive and reflective curves.

Fig. 7
Fig. 7

Sequence of points of the refractive and reflective curves.

Fig. 8
Fig. 8

Edge rays used for calculation of the points shown in Figs. 6 and 7.

Fig. 9
Fig. 9

Lines crossed by a single edge ray for the input and output bundles. Also drawn are the sequences {d 2 i } and {m 2 i +1} for convergence (D = M) and the point P, which is the only possible point at which, if D = M, then i may be coupled to o (in general there could be another possibility if virtual receivers were considered).

Fig. 10
Fig. 10

RX concentrator 1: The input bundle comprises the rays emitted by the disk SS′ toward II′. The output bundle comprises the rays impinging on the lower face of the receiver at any angle. Other data for this concentrator are shown in Table 1.

Fig. 11
Fig. 11

RX concentrators 2, 3, and 4: The input and output bundles are the same as those shown in Fig. 10. Other data for these concentrators are shown in Table 1.

Fig. 12
Fig. 12

RX concentrator 5: The points S and S′ of the input bundle of this concentrator are at infinity.

Fig. 13
Fig. 13

Transmission function of RX concentrator 3 (Fig. 11). The function plotted here shows the percentage of power that reaches the receiver relative to the power emitted by the points of the ring [ρ a , ρ a + dρ a ], of the circle SS′, toward the ring [ρ b , ρ b + dρ b ], of the circle II′.

Tables (1)

Tables Icon

Table 1 Geometrical Characteristics and 3D Ray-Tracing Results of Selected RX Concentratorsa

Equations (7)

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T t = E ( M c ) E ( M i ) = E ( M c ) E ( M o ) .
S I - S I = n ( R O - R O ) ,
l = [ S , d 0 ] + n d 0 m 1 + [ m 1 , R ] ,
[ S , d 2 ] + n d 2 m 1 + [ m 1 , R ] = l .
[ S , d 2 ] + n d 2 m 3 + [ m 3 , R ] = l .
    S I - S I = n R R .
d E = cos 2 θ D 2 d S s d S i ,

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