Abstract

A Fresnel-like structure is required for various kinds of applications, such as contact lenses in the biomedical field, solar concentrators in the energy industry, wave-front correctors for display technology, and beam shaping for illumination systems. In this report, the author provides a simple iterative algorithm that can generate prism structures on arbitrary curved surfaces in an analytical form. Using this algorithm, a spreadsheet program can easily generate the profile of prism structures for optical software simulation. Moreover, a noniterative formulation is derived in order to reduce the design procedures. Comparisons between iterative and noniterative formulations prove the feasibility and robustness of the present approach.

© 2012 Optical Society of America

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References

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  1. M. Shirayanagi, “Progressive multi-focal ophthalmic lens,” U. S. patent 4,950,057 (1990).
  2. A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
    [CrossRef]
  3. L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
    [CrossRef]
  4. K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
    [CrossRef]
  5. J. Y. Joo, D. K. Woo, S. S. Park, and S. K. Lee, “Fabrication of LED based ultra slim optical pointing device,” in 2010 IEEE International Conference on Optical MEMS and Nanophotonics (IEEE, 2010).
  6. N. A. Kelly and T. L. Gibson, “Improved photovoltaic energy output for cloudy conditions with a solar tracking system,” Solar Energy 83, 2092–2102, (2009).
    [CrossRef]
  7. Z. C. Shen, Y. Lu, and J. Y. Lu, “Fresnel lens solar concentrator design and spectral distribution on focus surface,” Opt. Rev. 18, 398–402, (2011).
    [CrossRef]
  8. I. R. Cole and R. Gottschalg, “Modeling solar flux distributions for Fresnel lens CPV systems,” in Proceedings of 7th Photovoltaic Science Application and Technology Conference; (Solar Energy Society, 2011).
  9. C. J. Ou, J. R. Bai, and J. S. Chen, “Fresnel structure on arbitrary curved surface for angular compensating of solar tracking device,” in Technical Digest of 7th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2010).
  10. C. J. Ou, C. M. Ou, and Y. Y. Liu, “Investigation of prism array angular tolerance for Fresnel-like prism structure surface design with arbitrary based surface profiles,” in Technical Digest of 8th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2012).
  11. P. T. Saunders, An Introduction to Catastrophe Theory(Cambridge University, 1995).

2012 (1)

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

2011 (2)

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Z. C. Shen, Y. Lu, and J. Y. Lu, “Fresnel lens solar concentrator design and spectral distribution on focus surface,” Opt. Rev. 18, 398–402, (2011).
[CrossRef]

2009 (1)

N. A. Kelly and T. L. Gibson, “Improved photovoltaic energy output for cloudy conditions with a solar tracking system,” Solar Energy 83, 2092–2102, (2009).
[CrossRef]

2004 (1)

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Ali, M.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Bai, J. R.

C. J. Ou, J. R. Bai, and J. S. Chen, “Fresnel structure on arbitrary curved surface for angular compensating of solar tracking device,” in Technical Digest of 7th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2010).

Chen, J. S.

C. J. Ou, J. R. Bai, and J. S. Chen, “Fresnel structure on arbitrary curved surface for angular compensating of solar tracking device,” in Technical Digest of 7th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2010).

Chen, K.

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Cole, I. R.

I. R. Cole and R. Gottschalg, “Modeling solar flux distributions for Fresnel lens CPV systems,” in Proceedings of 7th Photovoltaic Science Application and Technology Conference; (Solar Energy Society, 2011).

Gibson, T. L.

N. A. Kelly and T. L. Gibson, “Improved photovoltaic energy output for cloudy conditions with a solar tracking system,” Solar Energy 83, 2092–2102, (2009).
[CrossRef]

Gottschalg, R.

I. R. Cole and R. Gottschalg, “Modeling solar flux distributions for Fresnel lens CPV systems,” in Proceedings of 7th Photovoltaic Science Application and Technology Conference; (Solar Energy Society, 2011).

Jing, L.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

Joo, J. Y.

J. Y. Joo, D. K. Woo, S. S. Park, and S. K. Lee, “Fabrication of LED based ultra slim optical pointing device,” in 2010 IEEE International Conference on Optical MEMS and Nanophotonics (IEEE, 2010).

Kelly, N. A.

N. A. Kelly and T. L. Gibson, “Improved photovoltaic energy output for cloudy conditions with a solar tracking system,” Solar Energy 83, 2092–2102, (2009).
[CrossRef]

Klonner, M.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Lee, S. K.

J. Y. Joo, D. K. Woo, S. S. Park, and S. K. Lee, “Fabrication of LED based ultra slim optical pointing device,” in 2010 IEEE International Conference on Optical MEMS and Nanophotonics (IEEE, 2010).

Li, E.

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Liao, Y.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Lingley, A. R.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Lipsanen, H.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Liu, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

Liu, Y. Y.

C. J. Ou, C. M. Ou, and Y. Y. Liu, “Investigation of prism array angular tolerance for Fresnel-like prism structure surface design with arbitrary based surface profiles,” in Technical Digest of 8th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2012).

Lu, J. Y.

Z. C. Shen, Y. Lu, and J. Y. Lu, “Fresnel lens solar concentrator design and spectral distribution on focus surface,” Opt. Rev. 18, 398–402, (2011).
[CrossRef]

Lu, Y.

Z. C. Shen, Y. Lu, and J. Y. Lu, “Fresnel lens solar concentrator design and spectral distribution on focus surface,” Opt. Rev. 18, 398–402, (2011).
[CrossRef]

Lu, Z.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

Mirjalili, R.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Otis, B. P.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Ou, C. J.

C. J. Ou, J. R. Bai, and J. S. Chen, “Fresnel structure on arbitrary curved surface for angular compensating of solar tracking device,” in Technical Digest of 7th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2010).

C. J. Ou, C. M. Ou, and Y. Y. Liu, “Investigation of prism array angular tolerance for Fresnel-like prism structure surface design with arbitrary based surface profiles,” in Technical Digest of 8th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2012).

Ou, C. M.

C. J. Ou, C. M. Ou, and Y. Y. Liu, “Investigation of prism array angular tolerance for Fresnel-like prism structure surface design with arbitrary based surface profiles,” in Technical Digest of 8th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2012).

Park, S. S.

J. Y. Joo, D. K. Woo, S. S. Park, and S. K. Lee, “Fabrication of LED based ultra slim optical pointing device,” in 2010 IEEE International Conference on Optical MEMS and Nanophotonics (IEEE, 2010).

Parviz, B. A.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Saunders, P. T.

P. T. Saunders, An Introduction to Catastrophe Theory(Cambridge University, 1995).

Shen, T.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Shen, Z. C.

Z. C. Shen, Y. Lu, and J. Y. Lu, “Fresnel lens solar concentrator design and spectral distribution on focus surface,” Opt. Rev. 18, 398–402, (2011).
[CrossRef]

Shirayanagi, M.

M. Shirayanagi, “Progressive multi-focal ophthalmic lens,” U. S. patent 4,950,057 (1990).

Sopanen, M.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Suihkonen, S.

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Wang, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Woo, D. K.

J. Y. Joo, D. K. Woo, S. S. Park, and S. K. Lee, “Fabrication of LED based ultra slim optical pointing device,” in 2010 IEEE International Conference on Optical MEMS and Nanophotonics (IEEE, 2010).

Wu, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

Wu, J.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

Yang, F.

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Yang, Z.

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Zhang, Y.

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Zhao, H.

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

Int. J. Photoenergy (1)

L. Jing, H. Liu, H. Zhao, Z. Lu, H. Wu, H. Wang, and J. Wu, “Design of novel compound Fresnel lens for high-performance photovoltaic concentrator,” Int. J. Photoenergy 2012, 630692 (2012).
[CrossRef]

J. Micromech. Microeng. (1)

A. R. Lingley, M. Ali, Y. Liao, R. Mirjalili, M. Klonner, M. Sopanen, S. Suihkonen, T. Shen, B. P. Otis, H. Lipsanen, and B. A. Parviz, “A single-pixel wireless contact lens display,” J. Micromech. Microeng. 21, 125014–125021 (2011).
[CrossRef]

Opt. Rev. (1)

Z. C. Shen, Y. Lu, and J. Y. Lu, “Fresnel lens solar concentrator design and spectral distribution on focus surface,” Opt. Rev. 18, 398–402, (2011).
[CrossRef]

Proc. SPIE (1)

K. Chen, Z. Yang, H. Wang, E. Li, F. Yang, and Y. Zhang, “PSD-based Shack-Hartmann wavefront sensor,” Proc. SPIE 5639, 87–94 (2004).
[CrossRef]

Solar Energy (1)

N. A. Kelly and T. L. Gibson, “Improved photovoltaic energy output for cloudy conditions with a solar tracking system,” Solar Energy 83, 2092–2102, (2009).
[CrossRef]

Other (6)

J. Y. Joo, D. K. Woo, S. S. Park, and S. K. Lee, “Fabrication of LED based ultra slim optical pointing device,” in 2010 IEEE International Conference on Optical MEMS and Nanophotonics (IEEE, 2010).

M. Shirayanagi, “Progressive multi-focal ophthalmic lens,” U. S. patent 4,950,057 (1990).

I. R. Cole and R. Gottschalg, “Modeling solar flux distributions for Fresnel lens CPV systems,” in Proceedings of 7th Photovoltaic Science Application and Technology Conference; (Solar Energy Society, 2011).

C. J. Ou, J. R. Bai, and J. S. Chen, “Fresnel structure on arbitrary curved surface for angular compensating of solar tracking device,” in Technical Digest of 7th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2010).

C. J. Ou, C. M. Ou, and Y. Y. Liu, “Investigation of prism array angular tolerance for Fresnel-like prism structure surface design with arbitrary based surface profiles,” in Technical Digest of 8th International Conference on Optics-photonics Design and Fabrication (Japan Optical Society, 2012).

P. T. Saunders, An Introduction to Catastrophe Theory(Cambridge University, 1995).

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Figures (12)

Fig. 1.
Fig. 1.

Geometric configurations for generalized Fresnel-like prism structures.

Fig. 2.
Fig. 2.

Details and parameters of prism.

Fig. 3.
Fig. 3.

Generating profiles for a simple parabolic surface.

Fig. 4.
Fig. 4.

Simulation results and energy distribution on the focal plane F = 100 mm for the parabolic surface shown in Fig. 3.

Fig. 5.
Fig. 5.

Total internal reflection problems.

Fig. 6.
Fig. 6.

Profiles as a function of δ .

Fig. 7.
Fig. 7.

Generating profile for a more general surface with three prisms at location #1, #10, and #20.

Fig. 8.
Fig. 8.

Optical model using present method with the designed focal length F = 50 mm .

Fig. 9.
Fig. 9.

Simulation results and energy distribution on the focal plane F = 50 mm for the more general surface shown in Fig. 7.

Fig. 10.
Fig. 10.

Generated profiles for different focal lengths F .

Fig. 11.
Fig. 11.

Prism array angle β (degrees) by taking the focal length F (cm) as a control parameter.

Fig. 12.
Fig. 12.

Comparison between iterative and noniterative solutions for different focal lengths F .

Tables (2)

Tables Icon

Table 1. System Parameters for Parabolic Surface z ( x ) = 0.005 x 2

Tables Icon

Table 2. System Parameters for Parabolic Surface z ( x ) = 0.005 x 2 sin ( x 4 )

Equations (28)

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

z = z ( x ) .
w = tan ( x B L / 2 F z B ) .
x B = x 2 + x 3 2 , z B = z 2 + z 3 2 .
x 2 = x 1 + h A cos α z 2 = z 1 + h A sin α ,
x 3 = x 2 h B cos β z 3 = z 2 + h B sin β .
m P 1 d z d x | P 1 = tan ( α ) z 2 z 1 x 2 x 1 .
cos ( α ) = 1 tan 2 ( α ) + 1 = 1 m P 1 2 + 1 ,
sin ( α ) = 1 1 tan 2 α + 1 = 1 1 m P 1 2 + 1 .
z 2 = z 1 + m P 1 ( x 2 x 1 ) .
e cos β .
P 2 = ( x 2 , z 2 ) = ( x 1 + h A 1 m P 1 2 + 1 , z ( x 1 + h A 1 m P 1 2 + 1 ) ) ,
P 3 = ( x 3 , z 3 ) = ( x 2 h B e , z 2 + h B 1 e 2 ) .
n 0 sin a = n 1 sin b .
c = π b s .
α + β + π 2 + π 2 + s = 2 π .
c = α + β b .
n 1 sin c = n 0 sin d .
β = d w .
β = sin 1 ( n 1 n 0 sin ( α + β sin 1 ( n 0 n 1 sin a ) ) ) tan ( x B L / 2 F z B ) .
sin ( β + tan ( x B L / 2 F z B ) ) = n 1 n 0 sin ( β + α sin 1 ( n 0 n 1 sin a ) ) .
sin ( x + y ) = sin x cos y + cos x sin y ,
n 0 sin ( β ) cos ( w ) + n 0 cos ( β ) sin ( w ) = n 1 sin ( β ) cos ( K ) + n 1 cos ( β ) sin ( K ) ,
w tan ( x B L / 2 F z B ) , K α sin 1 ( n 0 n 1 sin a ) , and a = α + δ .
tan β = sin ( β ) cos ( β ) = n 1 sin ( K ) n 0 sin ( w ) n 0 cos ( w ) n 1 cos ( K ) .
β = tan 1 [ n 1 sin ( K ) n 0 sin ( w ) n 0 cos ( w ) n 1 cos ( K ) ] .
β = tan 1 [ n 1 sin ( α sin 1 ( n 0 n 1 sin ( α + δ ) ) ) n 0 sin ( tan ( x 2 L / 2 F z 2 ) ) n 0 cos ( tan ( x 2 L / 2 F z 2 ) ) n 1 cos ( α sin 1 ( n 0 n 1 sin ( α + δ ) ) ) ] .
z ( x ) = 0.005 x 2 .
z ( x ) = 0.005 x 2 sin ( x 4 ) .

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