## Light diffraction by concentrator Fresnel lenses |

Optics Express, Vol. 22, Issue S3, pp. A686-A704 (2014)

http://dx.doi.org/10.1364/OE.22.00A686

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### Abstract

Fresnel lenses are widely used in concentrating photovoltaic (CPV) systems as primary optical elements focusing sunlight onto small solar cells or onto entrance apertures of secondary optical elements attached to the solar cells. Calculations using the Young-Maggi-Rubinowicz theory of diffraction yield analytical expressions for the amount of light spilling outside these target areas due to diffraction at the edges of the concentrator Fresnel lenses. Explicit equations are given for the diffraction loss due to planar Fresnel lenses with small prisms and due to arbitrarily shaped Fresnel lenses. Furthermore, the cases of illumination by monochromatic, polychromatic, totally spatially coherent and partially spatially coherent light (e.g. from the solar disc) are treated, resulting in analytical formulae. Examples using realistic values show losses due to diffraction of up to several percent.

© 2014 Optical Society of America

## 1. Introduction

1. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 42),” Prog. Photovolt. Res. Appl. **21**(1), 827–837 (2013). [CrossRef]

2. G. Zubi, J. L. Bernal-Agustin, and G. V. Fracastoro, “High concentration photovoltaic systems applying IIIV cells,” Renew. Sustain. Energy Rev. **13**(9), 2645–2652 (2009). [CrossRef]

*f*is the focal length of the Fresnel lens) [3

3. J. R. Egger, “Use Of Fresnel Lenses In Optical Systems: Some Advantages And Limitations,” Proc. SPIE **193**, 63–69 (1979). [CrossRef]

4. A. Davis and F. Kühnlenz, “Optical design using Fresnel lenses,” Optik Photonik **2**(4), 52–55 (2007). [CrossRef]

5. F. Duerr, Y. Meuret, and H. Thienpont, “Miniaturization of Fresnel lenses for solar concentration: a quantitative investigation,” Appl. Opt. **49**(12), 2339–2346 (2010). [CrossRef] [PubMed]

6. F. Duerr, Y. Meuret, and H. Thienpont, “Down scaling of micro-structured Fresnel lenses for solar concentration: a quantitative investigation,” Proc. SPIE **7725**, 772509 (2010). [CrossRef]

## 2. Edge radii of mass-manufactured Fresnel lenses

## 3. Application of Kirchhoff’s Integral Theorem to Fresnel Lenses

*inward directed*normal of the surface element

## 4. Diffraction loss for idealized Fresnel lenses under coherent illumination

11. T. Young, “On the theory of light and colours,” Philos. Trans. R. Soc. Lond. **92**(0), 12–48 (1802). [CrossRef]

8. G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Annalen der Physik **254**(4), 663–695 (1883). [CrossRef]

13. A. Rubinowicz, “Zur Kirchhoffschen Beugungstheorie,” Annalen der Physik **378**(5-6), 339–364 (1924). [CrossRef]

14. A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Annalen der Physik **358**(12), 257–278 (1917). [CrossRef]

16. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part I,” J. Opt. Soc. Am. **52**(6), 615–622 (1962). [CrossRef]

17. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part II,” J. Opt. Soc. Am. **52**(6), 626–636 (1962). [CrossRef]

13. A. Rubinowicz, “Zur Kirchhoffschen Beugungstheorie,” Annalen der Physik **378**(5-6), 339–364 (1924). [CrossRef]

17. K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part II,” J. Opt. Soc. Am. **52**(6), 626–636 (1962). [CrossRef]

## 5. Diffraction loss for realistic Fresnel lenses under polychromatic illumination

## 6. Diffraction loss under partially coherent illumination

*i*th edge. It is determined by the half-angle

*i*th diffracting edge (Fig. 6). For a flat concentrator Fresnel lens with a planar entrance surface, the light is refracted on entry to and exit from the lens. For small angles of incidence and

*n*as the refractive index,

*i*edges, Eq. (26) results.

## 7. Conclusion

## Acknowledgments

## References and links

1. | M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 42),” Prog. Photovolt. Res. Appl. |

2. | G. Zubi, J. L. Bernal-Agustin, and G. V. Fracastoro, “High concentration photovoltaic systems applying IIIV cells,” Renew. Sustain. Energy Rev. |

3. | J. R. Egger, “Use Of Fresnel Lenses In Optical Systems: Some Advantages And Limitations,” Proc. SPIE |

4. | A. Davis and F. Kühnlenz, “Optical design using Fresnel lenses,” Optik Photonik |

5. | F. Duerr, Y. Meuret, and H. Thienpont, “Miniaturization of Fresnel lenses for solar concentration: a quantitative investigation,” Appl. Opt. |

6. | F. Duerr, Y. Meuret, and H. Thienpont, “Down scaling of micro-structured Fresnel lenses for solar concentration: a quantitative investigation,” Proc. SPIE |

7. | M. Born and E. Wolf, |

8. | G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Annalen der Physik |

9. | G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin |

10. | W. Hoßfeld, |

11. | T. Young, “On the theory of light and colours,” Philos. Trans. R. Soc. Lond. |

12. | G. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in un mezzo isotropo,” Ann. Math. |

13. | A. Rubinowicz, “Zur Kirchhoffschen Beugungstheorie,” Annalen der Physik |

14. | A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Annalen der Physik |

15. | P. B. S. Kumar and G. S. Ranganath, “Geometrical theory of diffraction,” Pramana |

16. | K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part I,” J. Opt. Soc. Am. |

17. | K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part II,” J. Opt. Soc. Am. |

18. | S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater. |

19. | J. W. Goodman, |

20. | W. H. Carter, “Coherence theory,” in |

21. | K. K. Sharma, |

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(220.1770) Optical design and fabrication : Concentrators

**ToC Category:**

Solar Concentrators

**History**

Original Manuscript: January 13, 2014

Revised Manuscript: February 14, 2014

Manuscript Accepted: February 19, 2014

Published: March 26, 2014

**Citation**

Thorsten Hornung and Peter Nitz, "Light diffraction by concentrator Fresnel lenses," Opt. Express **22**, A686-A704 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S3-A686

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### References

- M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 42),” Prog. Photovolt. Res. Appl.21(1), 827–837 (2013). [CrossRef]
- G. Zubi, J. L. Bernal-Agustin, and G. V. Fracastoro, “High concentration photovoltaic systems applying IIIV cells,” Renew. Sustain. Energy Rev.13(9), 2645–2652 (2009). [CrossRef]
- J. R. Egger, “Use Of Fresnel Lenses In Optical Systems: Some Advantages And Limitations,” Proc. SPIE193, 63–69 (1979). [CrossRef]
- A. Davis and F. Kühnlenz, “Optical design using Fresnel lenses,” Optik Photonik2(4), 52–55 (2007). [CrossRef]
- F. Duerr, Y. Meuret, and H. Thienpont, “Miniaturization of Fresnel lenses for solar concentration: a quantitative investigation,” Appl. Opt.49(12), 2339–2346 (2010). [CrossRef] [PubMed]
- F. Duerr, Y. Meuret, and H. Thienpont, “Down scaling of micro-structured Fresnel lenses for solar concentration: a quantitative investigation,” Proc. SPIE7725, 772509 (2010). [CrossRef]
- M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
- G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Annalen der Physik254(4), 663–695 (1883). [CrossRef]
- G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin2, 641–669 (1882).
- W. Hoßfeld, Tageslichtsteuerung mit prismatischen Mikrostrukturen im Übergangsbereich von diffraktiver und geometrischer Optik (doctoral thesis, Albert-Ludwigs-Universität Freiburg im Breisgau, 2004).
- T. Young, “On the theory of light and colours,” Philos. Trans. R. Soc. Lond.92(0), 12–48 (1802). [CrossRef]
- G. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in un mezzo isotropo,” Ann. Math.16, 21–48 (1888).
- A. Rubinowicz, “Zur Kirchhoffschen Beugungstheorie,” Annalen der Physik378(5-6), 339–364 (1924). [CrossRef]
- A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Annalen der Physik358(12), 257–278 (1917). [CrossRef]
- P. B. S. Kumar and G. S. Ranganath, “Geometrical theory of diffraction,” Pramana37(6), 457–488 (1991). [CrossRef]
- K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part I,” J. Opt. Soc. Am.52(6), 615–622 (1962). [CrossRef]
- K. Miyamoto and E. Wolf, “Generalization of the Maggi-Rubinowicz Theory of the Boundary Diffraction Wave - Part II,” J. Opt. Soc. Am.52(6), 626–636 (1962). [CrossRef]
- S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, “Analysis of the dispersion of optical plastic materials,” Opt. Mater.29(11), 1481–1490 (2007). [CrossRef]
- J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).
- W. H. Carter, “Coherence theory,” in Handbook of Optics M. Bass, E. W. van Stryland, D. R. Williams, and W. L. Wolfe, eds. (McGraw-Hill, 1995, vol. 1).
- K. K. Sharma, Optics: Principles and Applications (Academic, 2006).

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