Abstract

A new method of designing nonimaging concentrators is presented and two new types of concentrators are developed. The first is an aspheric lens, and the second is a lens-mirror combination. A ray tracing of three-dimensional concentrators (with rotational symmetry) is also done, showing that the lens-mirror combination has a total transmission as high as that of the full compound parabolic concentrators, while their depth is much smaller than the classical parabolic mirror–nonimaging concentrator combinations. Another important feature of this concentrator is that the optically active surfaces are not in contact with the receiver, as occurs in other nonimaging concentrators in which the rim of the mirror coincides with the rim of the receiver.

© 1992 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. 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. XXVII, pp. 161–226.
    [CrossRef]
  3. J. C. Minano, “Synthesis of concentrators in two-dimensional geometry,” in Solar Cells and Optics for Photovoltaic Concentration, A. Luque, ed. (Hilger, Bristol, UK, 1989), pp. 353–396.
  4. R. Winston, “Ideal light concentrators with reflector gaps,” Appl. Opt. 17, p. 1668 (1978).
    [CrossRef] [PubMed]
  5. R. Winston, “Cavity enhancement by controlled directional scattering,” Appl. Opt. 19, 195–197 (1980).
    [CrossRef] [PubMed]
  6. D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
    [CrossRef]
  7. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics, (Academic, New York, 1972).
  8. G. Schulz, “Achromatic and sharp real imaging of a point by a single aspheric lens,” Appl. Opt. 22, 3242–3248 (1983).
    [CrossRef] [PubMed]
  9. G. Schulz, “Aspheric surfaces,” in Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1988), Vol. XXV, pp. 351–416.
  10. J. C. Minano, “Design of three-dimensional concentrators,” in Solar Cells and Optics for Photovoltaic Concentration, A. Luque, ed. (Hilger, Bristol, UK, 1989), pp. 397–429.
  11. P. Gleckman, J. O’Gallagher, R. Winston, “Approaching the irradiance of the sun through nonimaging optics,” Opt. News 15(5), pp. 33–36 (1989).
    [CrossRef]
  12. R. Winston, W. T. Welford, “Geometrical vector flux and some new nonimaging concentrators,” J. Opt. Soc. Am. 69, 532–536 (1979).
    [CrossRef]
  13. R. Winston, W. T. Welford, “Ideal flux concentrators as shapes that do not disturb the geometrical vector flux field: a new derivation of the compound parabolic concentrator,” J. Opt. Soc. Am. 69, 536–539 (1979).
    [CrossRef]
  14. W. T. Welford, J. O’Gallagher, R. Winston, “Axially symmetric nonimaging flux concentrators with the maximum theoretical concentration ratio,” J. Opt. Soc. Am. A 4, 66–68 (1987).
    [CrossRef]
  15. R. Winston, “Nonimaging Optics,” Sci. Am. 264(3), 76–81, (1991).
    [CrossRef]
  16. G. W. Forbes, I. M. Basset, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
    [CrossRef]

1991 (1)

R. Winston, “Nonimaging Optics,” Sci. Am. 264(3), 76–81, (1991).
[CrossRef]

1990 (1)

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

1989 (1)

P. Gleckman, J. O’Gallagher, R. Winston, “Approaching the irradiance of the sun through nonimaging optics,” Opt. News 15(5), pp. 33–36 (1989).
[CrossRef]

1987 (1)

1983 (1)

1982 (1)

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

1980 (1)

1979 (2)

1978 (1)

Basset, I. M.

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

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. XXVII, pp. 161–226.
[CrossRef]

Cooke, D.

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

Forbes, G. W.

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

Gleckman, P.

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

P. Gleckman, J. O’Gallagher, R. Winston, “Approaching the irradiance of the sun through nonimaging optics,” Opt. News 15(5), pp. 33–36 (1989).
[CrossRef]

Krebs, H.

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

Minano, J. C.

J. C. Minano, “Synthesis of concentrators in two-dimensional geometry,” in Solar Cells and Optics for Photovoltaic Concentration, A. Luque, ed. (Hilger, Bristol, UK, 1989), pp. 353–396.

J. C. Minano, “Design of three-dimensional concentrators,” in Solar Cells and Optics for Photovoltaic Concentration, A. Luque, ed. (Hilger, Bristol, UK, 1989), pp. 397–429.

O’Gallagher, J.

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

P. Gleckman, J. O’Gallagher, R. Winston, “Approaching the irradiance of the sun through nonimaging optics,” Opt. News 15(5), pp. 33–36 (1989).
[CrossRef]

W. T. Welford, J. O’Gallagher, R. Winston, “Axially symmetric nonimaging flux concentrators with the maximum theoretical concentration ratio,” J. Opt. Soc. Am. A 4, 66–68 (1987).
[CrossRef]

Sagie, D.

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

Schulz, G.

G. Schulz, “Achromatic and sharp real imaging of a point by a single aspheric lens,” Appl. Opt. 22, 3242–3248 (1983).
[CrossRef] [PubMed]

G. Schulz, “Aspheric surfaces,” in Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1988), Vol. XXV, pp. 351–416.

Stavroudis, O. N.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics, (Academic, New York, 1972).

Welford, W. T.

Winston, R.

R. Winston, “Nonimaging Optics,” Sci. Am. 264(3), 76–81, (1991).
[CrossRef]

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

P. Gleckman, J. O’Gallagher, R. Winston, “Approaching the irradiance of the sun through nonimaging optics,” Opt. News 15(5), pp. 33–36 (1989).
[CrossRef]

W. T. Welford, J. O’Gallagher, R. Winston, “Axially symmetric nonimaging flux concentrators with the maximum theoretical concentration ratio,” J. Opt. Soc. Am. A 4, 66–68 (1987).
[CrossRef]

R. Winston, “Cavity enhancement by controlled directional scattering,” Appl. Opt. 19, 195–197 (1980).
[CrossRef] [PubMed]

R. Winston, W. T. Welford, “Ideal flux concentrators as shapes that do not disturb the geometrical vector flux field: a new derivation of the compound parabolic concentrator,” J. Opt. Soc. Am. 69, 536–539 (1979).
[CrossRef]

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

R. Winston, “Ideal light concentrators with reflector gaps,” Appl. Opt. 17, p. 1668 (1978).
[CrossRef] [PubMed]

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. XXVII, pp. 161–226.
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Nature (London) (1)

D. Cooke, P. Gleckman, H. Krebs, J. O’Gallagher, D. Sagie, R. Winston, “Sunlight brighter than the Sun,” Nature (London) 346, 802 (1990).
[CrossRef]

Opt. Acta (1)

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

Opt. News (1)

P. Gleckman, J. O’Gallagher, R. Winston, “Approaching the irradiance of the sun through nonimaging optics,” Opt. News 15(5), pp. 33–36 (1989).
[CrossRef]

Sci. Am. (1)

R. Winston, “Nonimaging Optics,” Sci. Am. 264(3), 76–81, (1991).
[CrossRef]

Other (6)

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics, (Academic, New York, 1972).

G. Schulz, “Aspheric surfaces,” in Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1988), Vol. XXV, pp. 351–416.

J. C. Minano, “Design of three-dimensional concentrators,” in Solar Cells and Optics for Photovoltaic Concentration, A. Luque, ed. (Hilger, Bristol, UK, 1989), pp. 397–429.

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. XXVII, pp. 161–226.
[CrossRef]

J. C. Minano, “Synthesis of concentrators in two-dimensional geometry,” in Solar Cells and Optics for Photovoltaic Concentration, A. Luque, ed. (Hilger, Bristol, UK, 1989), pp. 353–396.

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Figures (13)

Fig. 1
Fig. 1

General scheme of a concentrator showing the source of radiation SS′, receiver RR′, and entry (∑i) and exit (∑o) apertures of the concentrator. Several rays linking the source and the concentrator’s entry aperture and linking the concentrator’s exit aperture and the receiver are also shown (rays that are denoted r and r′ are not necessarily the same ray even if the subscript is coincident).

Fig. 2
Fig. 2

Representation in phase space xp of the set of rays i linking the source and the entry aperture (left) and the set of rays o linking the exit aperture and the receiver (right). The rays that are represented by the borders of the shaded regions are called edge rays. Some of these edge rays are drawn in Fig. 1.

Fig. 3
Fig. 3

Construction of an aspheric nonimaging lens begins at the extreme points of lenses X and N. Rays with the same subscript are the same ray.

Fig. 4
Fig. 4

Representation in the phase space of i and o. Some special edge rays are marked with a solid circle and their trajectories can be seen in Fig. 3.

Fig. 5
Fig. 5

Remaining points of the lens are obtained with the point-by-point method departing from Cartesian ovals NM and XY.

Fig. 6
Fig. 6

Construction of the lens at the center, where the method requires an additional degree of freedom for obtaining an ideal nonimaging concentrator rigorously. In practice this additional degree of freedom is not needed and ray tracing shows that the resulting lenses cannot be distinguished from ideal concentrators.

Fig. 7
Fig. 7

Method ensures that the part of ∂i represented with a solid line in this figure is transformed by the lens in rays of ∂o. Ray tracing shows that, in the studied cases, the remaining rays of ∂i are also transformed in rays of ∂o. xL is the x coordinate of point L.

Fig. 8
Fig. 8

Transmission-angle curves for several 3D aspheric nonimaging lenses with rotational symmetry. The lenses are designed for sources at infinity that subtend an angle called the acceptance angle of the concentrator. The number by each curve is the design acceptance angle of each lens. Other characteristics of the lenses can be seen in Table I.

Fig. 9
Fig. 9

Aspheric nonimaging lens with an acceptance angle of 10° and a geometric concentration of 12.25. Cartesian ovals MN and XY and points L and Z are specified.

Fig. 10
Fig. 10

Aspheric nonimaging lens with an acceptance angle of 10° and a geometric concentration of 6.25.

Fig. 11
Fig. 11

Nonimaging lens-mirror combination for a source at infinity subtending an angle of 1° with respect to the z axis. This concentrator has maximal concentration. Cartesian oval XY and points Z and L are also shown.

Fig. 12
Fig. 12

Construction of the nonimaging lens-mirror combination begins at the extreme points of lens X and of mirror N.

Fig. 13
Fig. 13

Transmission-angle curves for several 3D nonimaging lens-mirror combinations with rotational symmetry. The concentrators are designed for sources at infinity that subtend an angle called the acceptance angle of the concentrator. The number attached to each curve is the design acceptance angle of each concentrator. Other characteristics of these concentrators can be seen in Table II.

Tables (2)

Tables Icon

Table I Geometric Characteristics and 3D Ray-Tracing Results of Some Selected Nonimaging Lensesa

Tables Icon

Table II Geometric Characteristics and 3D Ray-Tracing Results of Some selected Lens–Mirror Combinationsa

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E = 4 C g sin ( θ a ) ,
E 3 D = π A e sin 2 θ a = π 2 / 4 ( X R - X R ) 2 ,
T ( θ a ) = [ A e 0 θ a T ( θ , θ a ) sin 2 θ d θ ] / E 3 D .
Err = 100 [ 1 - A e E 3 D 0 π / 2 T ( θ , θ 0 ) sin 2 θ d θ ] .

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