Abstract

The use of properly designed light pipes to redistribute the energy of a solar furnace or an arc imaging furnace is discussed. Compared to alternate schemes of obtaining uniform irradiation over a large area, the light pipe has the advantage of good uniformity without a serious loss of efficiency. Theoretical analyses concerning the principle of operation, as well as formulas for estimating the flux uniformity and reflection losses, are discussed. The results also indicate that the only suitable cross sections are the square, triangular, hexagonal, and rectangular. Other cross sections, including the circular, are not satisfactory unless used with diffusely reflecting surfaces.

© 1963 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. E. Glaser, J. Solar, Energy Sci. Eng. 1, 63 (1957).
  2. P. E. Glaser, J. Electrochem. Soc. 107, 226 (1960).
    [Crossref]
  3. R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
    [Crossref]
  4. E. Loh, P. Duwez, N. K. Hiester, T. E. Tietz, “Theoretical Considerations on Performance Characteristics of Solar Furnaces.” Stanford Research Institute, Report No. 3, Technical Report No. 1, S.R.I. Project No. CV-1410 under Air Force Contract No. AF 18(600)-1499.
  5. R. J. Potter, J. Opt. Soc. Am. 51, 1079 (1961).
    [Crossref]
  6. N. S. Kapany, J. A. Eyer, R. E. Keim, J. Opt. Soc. Am. 46, 872 (1956); ibid. 47, 423 (1957).
    [Crossref]
  7. D. E. Williamson, J. Opt. Soc. Am. 42, 712 (1952).
    [Crossref]

1961 (1)

1960 (1)

P. E. Glaser, J. Electrochem. Soc. 107, 226 (1960).
[Crossref]

1957 (2)

R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
[Crossref]

P. E. Glaser, J. Solar, Energy Sci. Eng. 1, 63 (1957).

1956 (1)

N. S. Kapany, J. A. Eyer, R. E. Keim, J. Opt. Soc. Am. 46, 872 (1956); ibid. 47, 423 (1957).
[Crossref]

1952 (1)

Brenner, J. L.

R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
[Crossref]

de la Rue, R. E.

R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
[Crossref]

Duwez, P.

E. Loh, P. Duwez, N. K. Hiester, T. E. Tietz, “Theoretical Considerations on Performance Characteristics of Solar Furnaces.” Stanford Research Institute, Report No. 3, Technical Report No. 1, S.R.I. Project No. CV-1410 under Air Force Contract No. AF 18(600)-1499.

Eyer, J. A.

N. S. Kapany, J. A. Eyer, R. E. Keim, J. Opt. Soc. Am. 46, 872 (1956); ibid. 47, 423 (1957).
[Crossref]

Glaser, P. E.

P. E. Glaser, J. Electrochem. Soc. 107, 226 (1960).
[Crossref]

P. E. Glaser, J. Solar, Energy Sci. Eng. 1, 63 (1957).

Hiester, N. K.

R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
[Crossref]

E. Loh, P. Duwez, N. K. Hiester, T. E. Tietz, “Theoretical Considerations on Performance Characteristics of Solar Furnaces.” Stanford Research Institute, Report No. 3, Technical Report No. 1, S.R.I. Project No. CV-1410 under Air Force Contract No. AF 18(600)-1499.

Kapany, N. S.

N. S. Kapany, J. A. Eyer, R. E. Keim, J. Opt. Soc. Am. 46, 872 (1956); ibid. 47, 423 (1957).
[Crossref]

Keim, R. E.

N. S. Kapany, J. A. Eyer, R. E. Keim, J. Opt. Soc. Am. 46, 872 (1956); ibid. 47, 423 (1957).
[Crossref]

Loh, E.

R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
[Crossref]

E. Loh, P. Duwez, N. K. Hiester, T. E. Tietz, “Theoretical Considerations on Performance Characteristics of Solar Furnaces.” Stanford Research Institute, Report No. 3, Technical Report No. 1, S.R.I. Project No. CV-1410 under Air Force Contract No. AF 18(600)-1499.

Potter, R. J.

Solar, J.

P. E. Glaser, J. Solar, Energy Sci. Eng. 1, 63 (1957).

Tietz, T. E.

E. Loh, P. Duwez, N. K. Hiester, T. E. Tietz, “Theoretical Considerations on Performance Characteristics of Solar Furnaces.” Stanford Research Institute, Report No. 3, Technical Report No. 1, S.R.I. Project No. CV-1410 under Air Force Contract No. AF 18(600)-1499.

Williamson, D. E.

Energy Sci. Eng. (1)

P. E. Glaser, J. Solar, Energy Sci. Eng. 1, 63 (1957).

J. Electrochem. Soc. (1)

P. E. Glaser, J. Electrochem. Soc. 107, 226 (1960).
[Crossref]

J. Opt. Soc. Am. (3)

R. J. Potter, J. Opt. Soc. Am. 51, 1079 (1961).
[Crossref]

N. S. Kapany, J. A. Eyer, R. E. Keim, J. Opt. Soc. Am. 46, 872 (1956); ibid. 47, 423 (1957).
[Crossref]

D. E. Williamson, J. Opt. Soc. Am. 42, 712 (1952).
[Crossref]

J. Solar Energy Sci. Eng. (1)

R. E. de la Rue, E. Loh, J. L. Brenner, N. K. Hiester, J. Solar Energy Sci. Eng. 1, 94 (1957).
[Crossref]

Other (1)

E. Loh, P. Duwez, N. K. Hiester, T. E. Tietz, “Theoretical Considerations on Performance Characteristics of Solar Furnaces.” Stanford Research Institute, Report No. 3, Technical Report No. 1, S.R.I. Project No. CV-1410 under Air Force Contract No. AF 18(600)-1499.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a light pipe in a solar or arc imaging surface.

Fig. 2
Fig. 2

Schematic diagram of light pipe operation.

Fig. 3
Fig. 3

The light rays that terminate at x = x0 for arbitrary y in the sample plane. 1, Path of a light ray that is not reflected; 2-2, path of a light ray that is reflected once; 2-2′, path of ray 2-2 in the absence of the kaleidoscope; 3-3 and 3-3′ are similar to 2-2 and 2-2′.

Fig. 4
Fig. 4

Flux intensity vs light pipe dimensions.

Fig. 5
Fig. 5

Reflection efficiencies for several light pipes.

Fig. A.1
Fig. A.1

Reflections in a light pipe with circular cross section.

Equations (20)

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

I B ( r ) = ρ 0 I 0 f 2 [ 1 - ( 1 + r 2 / s 2 ) 1 / 2 ] 2 ( 4 a 4 ) ( 1 + r 2 / s 2 ) 1 / 2 ( r 4 ) ( s 2 ) ,
x = x 0 , a - x 0 , - ( a + x 0 ) , - ( 2 a - x 0 ) , 2 a + x 0 , 3 a - x 0 , - ( 3 a + x 0 ) ,
y = y 0 , a - y 0 , - ( a + y 0 ) , - ( 2 a - y 0 ) , 2 a + y 0 , 3 a - y 0 , - ( 3 a + y 0 ) , .
( x , y ) = ( x 0 ± 2 m a , y 0 ± 2 n a ) , [ - x 0 ± ( 2 m + 1 ) a , y 0 ± 2 n a ] [ x ± 2 m a , - y 0 ± ( 2 n + 1 ) a ] , [ - x 0 ± ( 2 m + 1 ) a , - y 0 ± ( 2 n + 1 ) a ]
I A ( x 0 , y 0 ) = ρ 0 I 0 ( f 2 / s 2 ) × i = 1 4 m , n are integers r i 2 s 2 tan 2 θ [ 1 - ( 1 + r i 2 ( m , n ) ) 1 / 2 ] 2 ( 4 s 4 ) ( ρ p m + n ) [ 1 + r i 2 ( m , n ) / s 2 ] 1 / 2 ( r i 4 ) ,
r 1 2 = ( x 0 ± 2 m a ) 2 + ( y 0 ± 2 n a ) 2 , r 2 2 = [ x 0 ± ( 2 m + 1 ) a ] 2 + ( y 0 ± 2 n a ) 2 , r 3 2 = ( x 0 ± 2 m a ) 2 + [ y 0 ± ( 2 n + 1 ) a ] 2 , r 4 2 = [ x 0 ± ( 2 m + 1 ) a ] 2 + [ y 0 ± ( 2 n + 1 ) a ] 2 ,
I A + = a 2 I A ( x 0 , y 0 ) ρ 0 I 0 π R 0 2 ,
lim a / s 0 f 2 a 2 π R 2 s 2 i = 1 4 r i 2 s 2 tan 2 θ [ 1 - ( 1 + r i 2 / s 2 ) 1 / 2 ] 2 ( 4 s 4 ) ( 1 + r i 2 / s 2 ) 1 / 2 ( r i 4 ) = lim a / s 0 2 f 2 a 2 R 0 2 s 2 r min ( s / a ) tan θ 4 r d r [ 1 + ( a 2 / s 2 ) ( r ) 2 ] 1 / 2 [ 1 + ( 1 + ( a 2 / s 2 ) r 2 ) 1 / 2 ] 2 = 1.
I A + ( x 0 , y 0 ) ( 1 + sec θ 0 ) 4 a 2 ( 2 tan θ 0 ) π s 2 0 π / 2 ρ p r ( sin ϕ + cos ϕ ) d ϕ × ( x 0 2 + y 0 2 ) 1 / 2 / a ( s / a ) tan θ s 4 a 4 r 4 { 1 - [ 1 + ( a 2 r 2 / s 2 ) ] 1 / 2 } 2 1 + ( a 2 r 2 / s 2 ) f ( ρ p ) r d r d ϕ ,
f ( ρ p ) = ρ p - ( x 0 + y 0 ) / a + ρ p ( x 0 - y ) / a + ρ p ( x 0 + y 0 ) / a + ρ p ( y 0 - x 0 ) / a
I A + = ( 1 + sec θ 0 ) 2 ( 2 tan θ 0 ) 2 f ( ρ p ) 1 + ( x 0 2 + y 0 2 ) 1 / 2 / s 2 sec θ 0 ρ p ( 4 / π ) ( s / a ) ( y 2 - 1 ) 1 / 2 d y ( y + 1 ) 2 ,
y = ( 1 + a 2 r 2 s 2 ) 1 / 2 .
I A + ( x 0 , y 0 ) ¼ ρ p ( 4 / π ) ( s / a ) [ 3 - 1 / 2 ln ( 2 + 3 ) ] [ f ( ρ p ) ] .
I r ( 0 ) = ( ρ 0 I 0 f 2 s 2 ) ( 1 + ) ,
= actual flux density - theoretical flux density theoretical flux density at r = 0.
I A ( 0 , 0 ) = ρ 0 I 0 f 2 S / s 2 .
I A ( 0 , 0 ) = ρ 0 I 0 f 2 ( + S ) / s 2 ,
S = m , n { 1 - [ 1 + ( m 2 a 2 + n 2 a 2 ) / s 2 ] 1 / 2 } 2 ρ p m + n 4 s 4 [ 1 + ( m 2 a 2 + n 2 a 2 ) / s 2 ] 1 / 2 ( m 2 a 2 + n 2 a 2 ) 2 .
δ 1 = I A - I A I A = S ( 1 + sec θ 0 2 tan θ 0 ) 2 ( 1 π ) ( a 2 s 2 ) ρ - π 4 s a ( 1.07 ) .
I ( r ) = I 0 { 1 s 2 + r 2 + n = 1 , 2 1 s 2 + ( 2 n r 0 + r ) 2 2 n r 0 + r r + n = 1 , 2 1 s 2 + ( 2 n r 0 - r ) 2 2 n r 0 - r r } ,

Metrics