Abstract

Solar concentrators made of a single refractive primary optics are limited to a concentration ratio of about 1000× [Opt. Express 19, A280 (2011)], due only to longitudinal chromatic aberration, while mirrors are limited to 46,000× by the angular size of the Sun. To reduce the chromatic aberration while keeping cost-effective systems for concentrated photovoltaics, a study of four different kinds of flat Fresnel doublets made of polycarbonates and polymethyl methacrylate is presented. It reveals that Fresnel doublets may have fewer optical losses than non-Fresnel doublets, with a lower lateral chromatic split allowing for even higher concentration ratio.

© 2011 Optical Society of America

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References

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  1. R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001), Chap. 1.
  2. A. W. Bett, F. Dimroth, and G. Siefer, in Concentrator Photovoltaics (Springer, 2007), Chap. 4.
  3. Spectrolab data sheets, www.spectrolab.com/DataSheets/PV/CPV/CDO-100-C3MJ.pdf.
  4. National Renewable Energy Laboratory AM 1.5 Standard Dataset, http://rredc.nrel.gov/solar/spectra/am1.5/, accessed on February 6, 2011.
  5. C. A. Gueymard, Sol. Energy 71, 325 (2001).
    [CrossRef]
  6. F. Languy, K. Fleury, C. Lenaerts, J. Loicq, D. Regaert, T. Thibert, and S. Habraken, Opt. Express 19, A280 (2011).
    [CrossRef] [PubMed]
  7. S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
    [CrossRef]
  8. R. Winston, J. Opt. Soc. Am. 60, 245 (1970).
    [CrossRef]
  9. S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
    [CrossRef]
  10. J.-T. Mäkinen and R. de Schipper, “Injection molding for solar concentrators,” presented at the Workshop on CPV Power Plants, Germany, 2007, http://www.concentrating-pv.org/marburg2007/papers.html.
  11. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 2003), p. 188.

2011

2007

A. W. Bett, F. Dimroth, and G. Siefer, in Concentrator Photovoltaics (Springer, 2007), Chap. 4.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
[CrossRef]

J.-T. Mäkinen and R. de Schipper, “Injection molding for solar concentrators,” presented at the Workshop on CPV Power Plants, Germany, 2007, http://www.concentrating-pv.org/marburg2007/papers.html.

2003

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 2003), p. 188.

2001

C. A. Gueymard, Sol. Energy 71, 325 (2001).
[CrossRef]

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001), Chap. 1.

2000

S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
[CrossRef]

1970

Andrei, A. H.

S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
[CrossRef]

Bett, A. W.

A. W. Bett, F. Dimroth, and G. Siefer, in Concentrator Photovoltaics (Springer, 2007), Chap. 4.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 2003), p. 188.

de Schipper, R.

J.-T. Mäkinen and R. de Schipper, “Injection molding for solar concentrators,” presented at the Workshop on CPV Power Plants, Germany, 2007, http://www.concentrating-pv.org/marburg2007/papers.html.

Dimroth, F.

A. W. Bett, F. Dimroth, and G. Siefer, in Concentrator Photovoltaics (Springer, 2007), Chap. 4.

Fleury, K.

Gueymard, C. A.

C. A. Gueymard, Sol. Energy 71, 325 (2001).
[CrossRef]

Habraken, S.

Ivanov, C. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
[CrossRef]

Jilinski, E. G.

S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
[CrossRef]

Kasarova, S. N.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
[CrossRef]

Languy, F.

Lenaerts, C.

Leutz, R.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001), Chap. 1.

Loicq, J.

Mäkinen, J.-T.

J.-T. Mäkinen and R. de Schipper, “Injection molding for solar concentrators,” presented at the Workshop on CPV Power Plants, Germany, 2007, http://www.concentrating-pv.org/marburg2007/papers.html.

Nikolov, I. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
[CrossRef]

Penna, J. L.

S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
[CrossRef]

Puliaev, S.

S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
[CrossRef]

Regaert, D.

Siefer, G.

A. W. Bett, F. Dimroth, and G. Siefer, in Concentrator Photovoltaics (Springer, 2007), Chap. 4.

Sultanova, N. G.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
[CrossRef]

Suzuki, A.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001), Chap. 1.

Thibert, T.

Winston, R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 2003), p. 188.

Astron. Astrophys. Suppl. Ser.

S. Puliaev, J. L. Penna, E. G. Jilinski, and A. H. Andrei, Astron. Astrophys. Suppl. Ser. 143, 265 (2000).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Mater.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 29, 1481 (2007).
[CrossRef]

Sol. Energy

C. A. Gueymard, Sol. Energy 71, 325 (2001).
[CrossRef]

Other

J.-T. Mäkinen and R. de Schipper, “Injection molding for solar concentrators,” presented at the Workshop on CPV Power Plants, Germany, 2007, http://www.concentrating-pv.org/marburg2007/papers.html.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 2003), p. 188.

R. Leutz and A. Suzuki, Nonimaging Fresnel Lenses (Springer, 2001), Chap. 1.

A. W. Bett, F. Dimroth, and G. Siefer, in Concentrator Photovoltaics (Springer, 2007), Chap. 4.

Spectrolab data sheets, www.spectrolab.com/DataSheets/PV/CPV/CDO-100-C3MJ.pdf.

National Renewable Energy Laboratory AM 1.5 Standard Dataset, http://rredc.nrel.gov/solar/spectra/am1.5/, accessed on February 6, 2011.

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Figures (6)

Fig. 1
Fig. 1

Evolution of the focal distance minimizing the maximum LCA to 0.0684% of the design focal distance (represented by the dotted line).

Fig. 2
Fig. 2

Four kinds of nF doublets [(1a) to (2b)] and their Fresnel equivalent [( 1 a ) to ( 2 b )]. Green coloration corresponds to PMMA and blue to PC (PC appears lighter in gray scale).

Fig. 3
Fig. 3

Both cases of TFT doublets with zoom on top teeth: with (a) top-converging lens and (b) back- converging lens. Zoom (ii) refers to open draft angle and (i) to closed draft angle.

Fig. 4
Fig. 4

(a) Schematic representation of the chromatic splitting on a single segment. Figures (b) and (c) are laterally stretched representations of both cases of TFT lenses.

Fig. 5
Fig. 5

FTT doublets: (a) PMMA top plus zoom on the intermediate teeth and (b) PC top.

Fig. 6
Fig. 6

Chromatic split for the Fresnel doublets and their equivalent nF doublets. The notation of the designs is in accordance with Fig. 2. (All figures have the same scale).

Tables (1)

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Table 1 Doublets Performance Comparison

Equations (7)

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n ( λ ) = A 1 + A 2 λ 2 + A 3 λ 2 + A 4 λ 4 + A 5 λ 6 + A 6 λ 8 .
d z 1 D ( 1 a ) = i = 2 i max h sin ( α i ) cos ( θ i ) cos ( α i θ i ) ,
i = 1 i max 1 h sin ( α i ) cos ( θ i ) cos ( α i θ i ) + e ( tan α max + tan γ max ) d z 1 D ( 1 b ) i = 1 i max 1 h sin ( α i ) cos ( θ i ) cos ( α i θ i ) + ( e + h ) ( tan α max + tan γ max ) .
s = ( sin ( θ r β ) sin ( θ r ) + sin ( θ b β ) sin ( θ b ) ) | P 1 P 2 | .
d z 1 D ( 2 a ) = i = 1 i max 1 h sin ( γ i ) cos ( θ i ) cos ( γ i θ i ) + e γ max .
d z 1 D ( 2 b ) = e β max .
C opt , 2 D = ( 2 R s ) 2 ( 1 d z 2 D π R 2 ) = ( 2 s * ) 2 ( 1 d z 2 D * ) .

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