Abstract

The design, fabrication, and properties of one of a new class of gradient-index lenses are reported. The lens is an f/2.25 GRIN singlet based on a nanolayered polymer composite material, designed to correct for spherical aberration. The light gathering and focusing properties of the polymer lens are compared to a homogeneous BK7 glass singlet with a similar f-number. The modulation transfer function of the polymer GRIN lens exceeded that of the homogeneous glass lens at all spatial frequencies and was as much as 3 times better at 5 cyc/mm. The weight of the polymer lens was approximately an order of magnitude less than the homogeneous glass lens.

© 2008 Optical Society of America

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References

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  1. D. A. Atchison, and G. Smith, "Continuous Gradient-Index and Shell Models of the Human Lens," Vision Res. 35, 2529-2538 (1995).
    [CrossRef] [PubMed]
  2. L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
    [CrossRef] [PubMed]
  3. H. von Helmholtz, A. Gullstrand, J. von Kries, and W. Nagel, Helmholtz's Treatise on Physiological Optics (The Optical Society of America, Rochester, N.Y., 1924).
  4. B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
    [CrossRef] [PubMed]
  5. L. Bergmann, C. Schaefer, and H. Niedrig, Optics of Waves and Particles (W. de Gruyter, Berlin; New York, 1999).
  6. G. L. Walls, The Vertebrate Eye and its Adaptive Radiation (Hafner Pub. Co., New York, 1963).
  7. W. S. Jagger, and P. J. Sands, "A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout," Vision Res. 36, 2623-2639 (1996).
    [CrossRef] [PubMed]
  8. Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
    [CrossRef]
  9. C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
    [CrossRef]
  10. J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
    [CrossRef]
  11. C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
    [CrossRef]
  12. J. A. Reynolds, and J. M. Hough, "Formulae for Dielectric Constant of Mixtures," Proc. Phys. Soc. London B 70, 769-775 (1957).
    [CrossRef]
  13. S. D. Fantone, "Optical Design with Spherical Index Gradients," Appl. Opt. 22, 1815-1819 (1983).
    [CrossRef] [PubMed]
  14. J. M. Gordon, "Spherical gradient-index lenses as perfect imaging and maximum power transfer devices," Appl. Opt. 39, 3825-3832 (2000).
    [CrossRef]
  15. Y. Koike, A. Kanemitsu, Y. Shioda, E. Nihei, and Y. Ohtsuka, "Spherical Gradient-Index Polymer Lens with Low Spherical-Aberration," Appl. Opt. 33, 3394-3400 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, CA, 1968).
  18. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge [England]; New York, 1992).
  19. A. Savitzky, and M. J. E. Golay, "Smoothing + Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627 (1964).
    [CrossRef]

2007 (1)

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

2002 (1)

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

2001 (1)

L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
[CrossRef] [PubMed]

2000 (3)

J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
[CrossRef]

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

J. M. Gordon, "Spherical gradient-index lenses as perfect imaging and maximum power transfer devices," Appl. Opt. 39, 3825-3832 (2000).
[CrossRef]

1997 (1)

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

1996 (1)

W. S. Jagger, and P. J. Sands, "A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout," Vision Res. 36, 2623-2639 (1996).
[CrossRef] [PubMed]

1995 (1)

D. A. Atchison, and G. Smith, "Continuous Gradient-Index and Shell Models of the Human Lens," Vision Res. 35, 2529-2538 (1995).
[CrossRef] [PubMed]

1994 (1)

1983 (1)

1977 (1)

1964 (1)

A. Savitzky, and M. J. E. Golay, "Smoothing + Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627 (1964).
[CrossRef]

1957 (1)

J. A. Reynolds, and J. M. Hough, "Formulae for Dielectric Constant of Mixtures," Proc. Phys. Soc. London B 70, 769-775 (1957).
[CrossRef]

Atchison, D. A.

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

D. A. Atchison, and G. Smith, "Continuous Gradient-Index and Shell Models of the Human Lens," Vision Res. 35, 2529-2538 (1995).
[CrossRef] [PubMed]

Augusteyn, R. C.

L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
[CrossRef] [PubMed]

Baer, E.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
[CrossRef]

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Ebeling, T.

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Fantone, S. D.

Garner, L. F.

L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
[CrossRef] [PubMed]

Golay, M. J. E.

A. Savitzky, and M. J. E. Golay, "Smoothing + Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627 (1964).
[CrossRef]

Gordon, J. M.

Hiltner, A.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
[CrossRef]

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Hough, J. M.

J. A. Reynolds, and J. M. Hough, "Formulae for Dielectric Constant of Mixtures," Proc. Phys. Soc. London B 70, 769-775 (1957).
[CrossRef]

Hsieh, A.

J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
[CrossRef]

Jagger, W. S.

W. S. Jagger, and P. J. Sands, "A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout," Vision Res. 36, 2623-2639 (1996).
[CrossRef] [PubMed]

Jin, Y.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

Kanemitsu, A.

Kerns, J.

J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
[CrossRef]

Koike, Y.

Moffat, B. A.

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

Moore, D. T.

Mueller, C.

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

Mueller, C. D.

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Nazarenko, S.

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Nihei, E.

Ohtsuka, Y.

Pope, J. M.

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

Reynolds, J. A.

J. A. Reynolds, and J. M. Hough, "Formulae for Dielectric Constant of Mixtures," Proc. Phys. Soc. London B 70, 769-775 (1957).
[CrossRef]

Sands, P. J.

W. S. Jagger, and P. J. Sands, "A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout," Vision Res. 36, 2623-2639 (1996).
[CrossRef] [PubMed]

Savitzky, A.

A. Savitzky, and M. J. E. Golay, "Smoothing + Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627 (1964).
[CrossRef]

Schuman, T. L.

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Shioda, Y.

Shirk, J. S.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

Smith, G.

L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
[CrossRef] [PubMed]

D. A. Atchison, and G. Smith, "Continuous Gradient-Index and Shell Models of the Human Lens," Vision Res. 35, 2529-2538 (1995).
[CrossRef] [PubMed]

Soerens, D.

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

Tai, H.

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

Topolkaraev, V.

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

Yao, S.

L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
[CrossRef] [PubMed]

Anal. Chem. (1)

A. Savitzky, and M. J. E. Golay, "Smoothing + Differentiation of Data by Simplified Least Squares Procedures," Anal. Chem. 36, 1627 (1964).
[CrossRef]

Appl. Opt. (3)

J. Appl. Polym. Sci. (3)

Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, "New class of bioinspired lenses with a gradient refractive index," J. Appl. Polym. Sci. 103, 1834-1841 (2007).
[CrossRef]

J. Kerns, A. Hsieh, A. Hiltner, and E. Baer, "Comparison of irreversible deformation and yielding in microlayers of polycarbonate with poly(methylmethacrylate) and poly(styrene-co-acrylonitrile)," J. Appl. Polym. Sci. 77, 1545-1557 (2000).
[CrossRef]

C. Mueller, V. Topolkaraev, D. Soerens, A. Hiltner, and E. Baer, "Breathable polymer films produced by the microlayer coextrusion process," J. Appl. Polym. Sci. 78, 816-828 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Polym. Eng. Sci. (1)

C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, "Novel structures by microlayer coextrusion - Talc-filled PP, PC/SAN, and HDPE/LLDPE," Polym. Eng. Sci. 37, 355-362 (1997).
[CrossRef]

Proc. Phys. Soc. London B (1)

J. A. Reynolds, and J. M. Hough, "Formulae for Dielectric Constant of Mixtures," Proc. Phys. Soc. London B 70, 769-775 (1957).
[CrossRef]

Vision Res. (4)

D. A. Atchison, and G. Smith, "Continuous Gradient-Index and Shell Models of the Human Lens," Vision Res. 35, 2529-2538 (1995).
[CrossRef] [PubMed]

L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, "Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods," Vision Res. 41, 973-979 (2001).
[CrossRef] [PubMed]

B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
[CrossRef] [PubMed]

W. S. Jagger, and P. J. Sands, "A wide-angle gradient index optical model of the crystalline lens and eye of the rainbow trout," Vision Res. 36, 2623-2639 (1996).
[CrossRef] [PubMed]

Other (5)

L. Bergmann, C. Schaefer, and H. Niedrig, Optics of Waves and Particles (W. de Gruyter, Berlin; New York, 1999).

G. L. Walls, The Vertebrate Eye and its Adaptive Radiation (Hafner Pub. Co., New York, 1963).

H. von Helmholtz, A. Gullstrand, J. von Kries, and W. Nagel, Helmholtz's Treatise on Physiological Optics (The Optical Society of America, Rochester, N.Y., 1924).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, CA, 1968).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge [England]; New York, 1992).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic for the fabrication of a plano-convex GRIN lens, starting from a heat-pressed GRIN sheet (top). The sheet is molded between concentric glass molds to form a meniscus shape (middle). After release from the molds, the concave surface is polished flat to the white dashed line to form the final lens (bottom).

Fig. 2.
Fig. 2.

Images of an Air Force resolution chart taken with the GRIN lens (left) and the glass lens (right). The colored bars represent the data displayed in Fig. 3, below. The slightly different sizes result from the different lens focal lengths: 41.0 mm for the GRIN lens and 38.2 mm for the glass lens.

Fig. 3.
Fig. 3.

Plots of the intensity as a function of position for the data from Fig. 3. The blue (red) curve is for the GRIN (glass) lens data. The horizontal scale is in pixels for the GRIN image (9.85 μm/pxl). The horizontal axis for the glass data was scaled to match the features in the GRIN image.

Fig. 4.
Fig. 4.

(a). The modulation transfer function (MTF) measured for the GRIN lens (blue) and the commercial glass lens (red.) The solid lines were extracted from an edge analysis of an imaged chart, while the dashed lines are MTFs extracted from a focused HeNe laser beam. The CCD had a pixel pitch of (8.53 x 9.85) μm. The units of the horizontal axis correspond to spatial frequency on the camera. (b) Comparison between measured (dashed) and simulated (solid) MTF data for the glass lens. The data curve is identical to the corresponding trace in (a).

Fig. 5.
Fig. 5.

The ratio of the GRIN to the homogeneous lens MTF. The solid line is the ratio from an edge analysis of a chart illuminated with incandescent light. The dashed line is from an analysis of a focused HeNe laser beam.

Tables (1)

Tables Icon

Table I. Design specifications for the f/2.25 GRIN lens.

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