Abstract

Cylindrical concentrators are viewed as a limit case of toroidal concentrators with the purpose of applying to them some results obtained for axisymmetrical optical systems. This enables us to obtain easily the directional intercept factor of a cylindrical nonimaging concentrator called the Ideal Tubular Concentrator. A useful tool for designing new cylindrical concentrators is also derived.

© 1984 Optical Society of America

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References

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  1. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1964).
  2. J. C. Minano, J. M. Ruiz, A. Luque, “Design of Optimal and Ideal 2-D Concentrators with the Collector Immersed in a Dielectric Tube,” Appl. Opt. 22, 3960 (1983).
    [CrossRef] [PubMed]
  3. W. T. Welford, R. Winston, Optics of Nonimaging Concentrators (Academic, New York, 1978).
  4. L. A. Whitehead, “Simplified Ray Tracing in Cylindrical Systems,” Appl. Opt. 21, 3536 (1982).
    [CrossRef] [PubMed]
  5. A. Luque, “Theoretical Bases of Photovoltaic Concentrators for Extended Light Sources,” Sol. Cells 3, 355 (1981).
    [CrossRef]
  6. To calculate the etendue of a 2-D bundle of rays it is not necessary that these rays be coplanar, as the rays of p = 0 are (a 2-D bundle of rays is the one formed by rays that can be distinguished between them by giving two parameters, see Ref. 7).
  7. J. C. Minano, “Application of the Conservation of Etendue Theorem for 2-D Subdomains of the Phase Space in Nonimaging Concentrators,” Appl. Opt. 23, 2021 (1984).
    [CrossRef] [PubMed]

1984 (1)

1983 (1)

1982 (1)

1981 (1)

A. Luque, “Theoretical Bases of Photovoltaic Concentrators for Extended Light Sources,” Sol. Cells 3, 355 (1981).
[CrossRef]

Appl. Opt. (3)

Sol. Cells (1)

A. Luque, “Theoretical Bases of Photovoltaic Concentrators for Extended Light Sources,” Sol. Cells 3, 355 (1981).
[CrossRef]

Other (3)

To calculate the etendue of a 2-D bundle of rays it is not necessary that these rays be coplanar, as the rays of p = 0 are (a 2-D bundle of rays is the one formed by rays that can be distinguished between them by giving two parameters, see Ref. 7).

W. T. Welford, R. Winston, Optics of Nonimaging Concentrators (Academic, New York, 1978).

R. K. Luneburg, Mathematical Theory of Optics (U. California Press, Berkeley, 1964).

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Figures (5)

Fig. 1
Fig. 1

Cylindrical coordinates used for describing the rays in an axisymmetrical optical system.

Fig. 2
Fig. 2

Ideal tubular concentrator of semiacceptance angle ϕ = 30° for a bifacial collector. The index of refraction of the medium inside the tube is 1.5.

Fig. 3
Fig. 3

Detail of the entry aperture of an ITC of arbitrary collector shape (and consequently the mirror profile is not defined). The hatched region shows where the trajectory of a normal ray must lie if this ray enters the entry aperture at P and arrives at the collector.

Fig. 4
Fig. 4

Directional intercept factor of an ITC of ϕa = 30°, ϕm = 79°, and n = 1.5. This concentrator is ideal with respect to normal rays (p = 0).

Fig. 5
Fig. 5

Directional intercept factor of an ITC of ϕa = 31.07°, ϕm = 79°, and n = 1.5. This concentrator is ideal with respect to rays of p = 0.33.

Equations (10)

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h = ρ p .
lim R h = lim R ρ R p = p .
m ( ρ , z ) = [ n 2 ( ρ , z ) - h 2 ρ 2 ] 1 / 2 .
m ( Y , Z ) = [ n 2 ( Y , Z ) - p 2 ] 1 / 2 .
n r = ( n 2 - p 2 1 - p 2 ) 1 / 2 .
α ( 0 , q ) = 1 if q sin ϕ a ,
α ( 0 , q ) = 0 if q > sin ϕ a .
2 R [ ϕ m + ϕ a - π 2 + cos ( ϕ m - ϕ a ) ] ( 1 - p 2 ) 1 / 2 = 2 ( n 2 - p 2 ) 1 / 2 A c ,
2 R [ ϕ m + ϕ a - π 2 + cos ( ϕ m - ϕ a ) ] = 2 n r A c ,
C g ϕ m [ ϕ m + ϕ a - π 2 + cos ( ϕ m - ϕ a ) ] = 2 n r .

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