Abstract

Stress birefringence can be found in gradient-index (GRIN) materials because they contain a variation in composition. GRIN glass fabricated by ion exchange may contain stress from two different processes. These include a size difference between the exchange and the diffusing ions and a variation in the thermal-expansion coefficient across the gradient region. The optical properties of the stressed material are polarization dependent, and therefore image quality is directly affected. We examine birefringence in GRIN rod lenses that have lengths more than ten times greater than their diameters. The effects are more easily observed in long rod lenses because of the large optical path lengths.

© 1999 Optical Society of America

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References

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  1. M. Mino, “Application of a gradient-index lens array to the office photocopier,” in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, 1979).
  2. J. D. Rees, “Office applications of gradient-index optics,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. D. Rees, eds., Proc. SPIE935, 27–51 (1988).
    [CrossRef]
  3. D. C. Leiner, “Miniature optics in the hospital operating room,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. D. Rees, eds., Proc. SPIE935, 52–62 (1988).
    [CrossRef]
  4. V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).
  5. J. M. Brot, “Assessment of the optical performances of radial gradient-index lenses,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 451–456 (1986).
    [CrossRef]
  6. W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC type,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 156–167 (1994).
    [CrossRef]
  7. W. A. Wozniak, “Residual birefringence in the gradient-index lenses,” Opt. Appl. 19, 429–437 (1989).
  8. A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
    [CrossRef]
  9. C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
    [CrossRef]
  10. G. W. Scherer, “Stress-induced index profile distortion in optical waveguides,” Appl. Opt. 19, 2000–2006 (1980).
    [CrossRef] [PubMed]
  11. P. L. Chu, T. Whitbread, “Measurement of stresses in optical fiber and preform,” Appl. Opt. 21, 4241–4245 (1982).
    [CrossRef] [PubMed]
  12. M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
    [CrossRef]
  13. A. L. Zijlstra, A. J. Burggraaf, “Fracture phenomena and strength properties of chemically and physically strengthened glass. I. General survey of strength and fracture behaviour of strengthened glass,” J. Non-Cryst. Solids 1, 49–68 (1968).
    [CrossRef]
  14. T. H. Tomkinson, D. T. Moore, “Interferometric chromatic dispersion measurements of long, gradient-index rod lenses in the visible and the near infrared,” Appl. Opt. 38, 5355–5364 (1999).
    [CrossRef]
  15. Gradient Lens Corporation, 207 Tremont Street, Rochester, New York, 14608.
  16. Nippon Sheet Glass America, 27 World’s Fair Drive, Somerset, New Jersey, 08873.
  17. A. Y. Sane, A. R. Cooper, “Stress buildup and relaxation during ion exchange strengthening of glass,” J. Am. Ceram. Soc. 70, 86–89 (1987).
    [CrossRef]

1999

1990

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

1989

W. A. Wozniak, “Residual birefringence in the gradient-index lenses,” Opt. Appl. 19, 429–437 (1989).

1987

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

A. Y. Sane, A. R. Cooper, “Stress buildup and relaxation during ion exchange strengthening of glass,” J. Am. Ceram. Soc. 70, 86–89 (1987).
[CrossRef]

1986

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

1982

1980

1968

A. L. Zijlstra, A. J. Burggraaf, “Fracture phenomena and strength properties of chemically and physically strengthened glass. I. General survey of strength and fracture behaviour of strengthened glass,” J. Non-Cryst. Solids 1, 49–68 (1968).
[CrossRef]

1964

M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
[CrossRef]

Brandenburg, A.

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

Brot, J. M.

J. M. Brot, “Assessment of the optical performances of radial gradient-index lenses,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 451–456 (1986).
[CrossRef]

Burggraaf, A. J.

A. L. Zijlstra, A. J. Burggraaf, “Fracture phenomena and strength properties of chemically and physically strengthened glass. I. General survey of strength and fracture behaviour of strengthened glass,” J. Non-Cryst. Solids 1, 49–68 (1968).
[CrossRef]

Carnera, A.

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

Chu, P. L.

Cooper, A. R.

A. Y. Sane, A. R. Cooper, “Stress buildup and relaxation during ion exchange strengthening of glass,” J. Am. Ceram. Soc. 70, 86–89 (1987).
[CrossRef]

De Bernadi, C.

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

Garfinkel, H. M.

M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
[CrossRef]

Kosyakov, V. I.

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

Leiner, D. C.

D. C. Leiner, “Miniature optics in the hospital operating room,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. D. Rees, eds., Proc. SPIE935, 52–62 (1988).
[CrossRef]

Mino, M.

M. Mino, “Application of a gradient-index lens array to the office photocopier,” in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, 1979).

Mochel, E. L.

M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
[CrossRef]

Moore, D. T.

Morasca, S.

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

Morra, M.

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

Nordberg, M. E.

M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
[CrossRef]

Olcott, J. S.

M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
[CrossRef]

Pechenkin, I. V.

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

Rees, J. D.

J. D. Rees, “Office applications of gradient-index optics,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. D. Rees, eds., Proc. SPIE935, 27–51 (1988).
[CrossRef]

Sadikov, S. N.

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

Sane, A. Y.

A. Y. Sane, A. R. Cooper, “Stress buildup and relaxation during ion exchange strengthening of glass,” J. Am. Ceram. Soc. 70, 86–89 (1987).
[CrossRef]

Scarano, D.

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

Scherer, G. W.

Smirnova, D. V.

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

Tomkinson, T. H.

Tukhvatulin, A. Sh.

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

Whitbread, T.

Wozniak, W. A.

W. A. Wozniak, “Residual birefringence in the gradient-index lenses,” Opt. Appl. 19, 429–437 (1989).

W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC type,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 156–167 (1994).
[CrossRef]

Zijlstra, A. L.

A. L. Zijlstra, A. J. Burggraaf, “Fracture phenomena and strength properties of chemically and physically strengthened glass. I. General survey of strength and fracture behaviour of strengthened glass,” J. Non-Cryst. Solids 1, 49–68 (1968).
[CrossRef]

Appl. Opt.

J. Am. Ceram. Soc.

A. Y. Sane, A. R. Cooper, “Stress buildup and relaxation during ion exchange strengthening of glass,” J. Am. Ceram. Soc. 70, 86–89 (1987).
[CrossRef]

M. E. Nordberg, E. L. Mochel, H. M. Garfinkel, J. S. Olcott, “Strengthening by ion exchange,” J. Am. Ceram. Soc. 47, 215–219 (1964).
[CrossRef]

J. Lightwave Technol.

A. Brandenburg, “Stress in ion-exchanged glass waveguides,” J. Lightwave Technol. LT-4, 1580–1593 (1986).
[CrossRef]

J. Non-Cryst. Solids

C. De Bernadi, S. Morasca, D. Scarano, A. Carnera, M. Morra, “Compositional and stress-optical effects in glass waveguides: comparison between K-Na and Ag-Na ion exchange,” J. Non-Cryst. Solids 119, 195–204 (1990).
[CrossRef]

A. L. Zijlstra, A. J. Burggraaf, “Fracture phenomena and strength properties of chemically and physically strengthened glass. I. General survey of strength and fracture behaviour of strengthened glass,” J. Non-Cryst. Solids 1, 49–68 (1968).
[CrossRef]

Opt. Appl.

W. A. Wozniak, “Residual birefringence in the gradient-index lenses,” Opt. Appl. 19, 429–437 (1989).

Opt. Spektrosk.

V. I. Kosyakov, I. V. Pechenkin, S. N. Sadikov, D. V. Smirnova, A. Sh. Tukhvatulin, “Longitudinal spherical aberration and birefringence in polymer gradient lenses,” Opt. Spektrosk. 62, 900–904 (1987).

Other

J. M. Brot, “Assessment of the optical performances of radial gradient-index lenses,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 451–456 (1986).
[CrossRef]

W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC type,” in Nonconventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 156–167 (1994).
[CrossRef]

M. Mino, “Application of a gradient-index lens array to the office photocopier,” in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, 1979).

J. D. Rees, “Office applications of gradient-index optics,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. D. Rees, eds., Proc. SPIE935, 27–51 (1988).
[CrossRef]

D. C. Leiner, “Miniature optics in the hospital operating room,” in Gradient-Index Optics and Miniature Optics, D. C. Leiner, J. D. Rees, eds., Proc. SPIE935, 52–62 (1988).
[CrossRef]

Gradient Lens Corporation, 207 Tremont Street, Rochester, New York, 14608.

Nippon Sheet Glass America, 27 World’s Fair Drive, Somerset, New Jersey, 08873.

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Figures (7)

Fig. 1
Fig. 1

Vertically polarized light at normal incidence on birefringent GRIN rod. Rays in the tangential (yz) plane focus at a different point than rays in the sagittal (xz) plane.

Fig. 2
Fig. 2

PSF (a) outside the tangential and the sagittal foci and (b) several millimeters farther beyond foci.

Fig. 3
Fig. 3

PSF in Fig. 2(b) through crossed polarizers.

Fig. 4
Fig. 4

Phase-stepping Twyman–Green interferometer used to measure OPD. PZT, piezoelectric transducer; BFL, back focal length.

Fig. 5
Fig. 5

EG-13 sample fabrication conditions and OPD measurements made with vertically and horizontally polarized He–Ne laser source. Dashed curves indicate vertical polarization; solid curves indicate horizontal polarization.

Fig. 6
Fig. 6

EG-14 sample fabrication conditions and OPD measurements made with vertically and horizontally polarized He–Ne laser source. Dashed curves indicate vertical polarization; solid curves indicate horizontal polarization. Rod aperture is normalized.

Fig. 7
Fig. 7

OPD measurement for NSG relay lens.

Equations (3)

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OPDr, λ=λ2π ϕr, λ,
Wr=-OPDr
Nr=N00+N10r2+N20r4+,

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