Abstract

We show that ideal flux collectors in the form of systems of axially symmetric systems which concentrate flux from a given angular extent with no loss in étendue are impossible; on the other hand, systems approaching this limit very closely can be designed.

© 1978 Optical Society of America

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References

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  1. R. Winston, J. Opt. Soc. Am. 60, 245–247 (1970).
    [CrossRef]
  2. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley and Los Angeles, 1964).
  4. V. K. Baranov, Geliotekhnika (Applied Solar Energy) 2, 9–12 (1966) (English translation).
  5. M. Ploke, Optik (Stuttg.) 25, 31–43 (1967).
  6. H. Hinterberger and R. Winston, Rev. Sci. Instrum. 37, 1094–1095 (1966).
    [CrossRef]
  7. R. I. Garwin, Rev. Sci. Instrum. 23, 755–757 (1952).
    [CrossRef]
  8. J. Clerk Maxwell, Q. J. Pure Appl. Math. 2, 233–247 (1858).
  9. See, for example, C. G. Wynne, Proc. Phys. Soc. Lond. B65, 429–437 (1952), M. HerzbergerModern Geometrical Optics (Interscience, New York, 1958); O. N. StavroudisOptics of Rays, Wavefronts and Caustics (Academic, New York, 1972).
    [CrossRef]
  10. See, for example, A. K. Head, Proc. Phys. Soc. Lond. 61, 546–551 (1958); C. R. Burch, Proc. Phys. Soc. Lond. 57, 567–576 (1945).
    [CrossRef]
  11. For a useful survey giving several of these variations see A. Rabl, Solar Energy 18, 93–111 (1976).
    [CrossRef]

1976 (1)

For a useful survey giving several of these variations see A. Rabl, Solar Energy 18, 93–111 (1976).
[CrossRef]

1970 (1)

1967 (1)

M. Ploke, Optik (Stuttg.) 25, 31–43 (1967).

1966 (2)

H. Hinterberger and R. Winston, Rev. Sci. Instrum. 37, 1094–1095 (1966).
[CrossRef]

V. K. Baranov, Geliotekhnika (Applied Solar Energy) 2, 9–12 (1966) (English translation).

1958 (1)

See, for example, A. K. Head, Proc. Phys. Soc. Lond. 61, 546–551 (1958); C. R. Burch, Proc. Phys. Soc. Lond. 57, 567–576 (1945).
[CrossRef]

1952 (1)

R. I. Garwin, Rev. Sci. Instrum. 23, 755–757 (1952).
[CrossRef]

1858 (1)

J. Clerk Maxwell, Q. J. Pure Appl. Math. 2, 233–247 (1858).

Baranov, V. K.

V. K. Baranov, Geliotekhnika (Applied Solar Energy) 2, 9–12 (1966) (English translation).

Clerk Maxwell, J.

J. Clerk Maxwell, Q. J. Pure Appl. Math. 2, 233–247 (1858).

Garwin, R. I.

R. I. Garwin, Rev. Sci. Instrum. 23, 755–757 (1952).
[CrossRef]

Head, A. K.

See, for example, A. K. Head, Proc. Phys. Soc. Lond. 61, 546–551 (1958); C. R. Burch, Proc. Phys. Soc. Lond. 57, 567–576 (1945).
[CrossRef]

Hinterberger, H.

H. Hinterberger and R. Winston, Rev. Sci. Instrum. 37, 1094–1095 (1966).
[CrossRef]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley and Los Angeles, 1964).

Ploke, M.

M. Ploke, Optik (Stuttg.) 25, 31–43 (1967).

Rabl, A.

For a useful survey giving several of these variations see A. Rabl, Solar Energy 18, 93–111 (1976).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

Winston, R.

R. Winston, J. Opt. Soc. Am. 60, 245–247 (1970).
[CrossRef]

H. Hinterberger and R. Winston, Rev. Sci. Instrum. 37, 1094–1095 (1966).
[CrossRef]

Wynne, C. G.

See, for example, C. G. Wynne, Proc. Phys. Soc. Lond. B65, 429–437 (1952), M. HerzbergerModern Geometrical Optics (Interscience, New York, 1958); O. N. StavroudisOptics of Rays, Wavefronts and Caustics (Academic, New York, 1972).
[CrossRef]

Geliotekhnika (Applied Solar Energy) (1)

V. K. Baranov, Geliotekhnika (Applied Solar Energy) 2, 9–12 (1966) (English translation).

J. Opt. Soc. Am. (1)

Optik (Stuttg.) (1)

M. Ploke, Optik (Stuttg.) 25, 31–43 (1967).

Proc. Phys. Soc. Lond. (1)

See, for example, A. K. Head, Proc. Phys. Soc. Lond. 61, 546–551 (1958); C. R. Burch, Proc. Phys. Soc. Lond. 57, 567–576 (1945).
[CrossRef]

Q. J. Pure Appl. Math. (1)

J. Clerk Maxwell, Q. J. Pure Appl. Math. 2, 233–247 (1858).

Rev. Sci. Instrum. (2)

H. Hinterberger and R. Winston, Rev. Sci. Instrum. 37, 1094–1095 (1966).
[CrossRef]

R. I. Garwin, Rev. Sci. Instrum. 23, 755–757 (1952).
[CrossRef]

Solar Energy (1)

For a useful survey giving several of these variations see A. Rabl, Solar Energy 18, 93–111 (1976).
[CrossRef]

Other (3)

See, for example, C. G. Wynne, Proc. Phys. Soc. Lond. B65, 429–437 (1952), M. HerzbergerModern Geometrical Optics (Interscience, New York, 1958); O. N. StavroudisOptics of Rays, Wavefronts and Caustics (Academic, New York, 1972).
[CrossRef]

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley and Los Angeles, 1964).

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Figures (4)

FIG. 1
FIG. 1

Non-image-forming light concentrator.

FIG. 2
FIG. 2

The compound parabolic concentrator.1 PQ is a portion of a parabola with its focus at Q′ and its axis as indicated, similarly for PQ′. All rays which enter at angles less than θ1 are transmitted and all outside θ1 are reflected in the two-dimensional form.

FIG. 3
FIG. 3

Rays of an off-axis pencil.

FIG. 4
FIG. 4

Transmission of a concentrator with the profile of Fig. 2 in two dimensions (full line) and three dimensions (broken line).

Equations (2)

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F ( y 1 , z 1 ( y 1 ) , y 2 , z 2 ( y 2 ) , , y N , z N ( y N ) ) = 0.
F 1 = 0             and             F 2 = 0 ,