Abstract

Aberration of large numerical-aperture gradient-index lenses for optical pickup systems can be corrected with spherical surfaces whose curvatures are chosen corresponding to the measured values of the fourth- and sixth-order refractive-index coefficients.

© 1980 Optical Society of America

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References

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  1. K. Compaan, P. Kramer, Philips Tech. Rev. 33, 178 (1973).
  2. G. Bouwhuis, P. Burgstede, Philips Tech. Rev. 33, 186 (1973).
  3. K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).
  4. Y. Takeda, Y. Tsunoda, Appl. Opt. 17, 863 (1978).
    [CrossRef] [PubMed]
  5. G. Bouwhuis, J. J. M. Braat, Appl. Opt. 17, 1993 (1978).
    [CrossRef] [PubMed]
  6. H. H. Hopkins, J. Opt. Soc. Am. 69, 4 (1979).
    [CrossRef]
  7. A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
    [CrossRef]
  8. Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
    [CrossRef]
  9. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
    [CrossRef]
  10. K. Iga, N. Yamamoto, Appl. Opt. 16, 1305 (1977).
    [CrossRef] [PubMed]
  11. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).
  12. Y. Aoki, J. Opt. Soc. Am. 56, 1648 (1966).
    [CrossRef]
  13. E. G. Rawson, D. R. Herriott, J. McKenna, Appl. Opt. 9, 753 (1970).
    [CrossRef] [PubMed]
  14. These values (N.A. = 0.45 and b/a = 0.4) were derived with the diffraction integral for the SCOOP (self-coupled optical pickup)7-8 system. Because the finite aperture of the lens causes intensity modulation on the returned light, it cannot always be concluded that the larger the N.A. of the lens the better the system works. Details of the analysis will be published later.
  15. P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970).
    [CrossRef]
  16. D. T. Moore, J. Opt. Soc. Am. 61, 886 (1971).
    [CrossRef]
  17. D. T. Moore, P. J. Sands, U.S. Patent3, 729, 253.

1979 (1)

1978 (2)

1977 (1)

1976 (1)

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

1975 (1)

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

1973 (2)

K. Compaan, P. Kramer, Philips Tech. Rev. 33, 178 (1973).

G. Bouwhuis, P. Burgstede, Philips Tech. Rev. 33, 186 (1973).

1971 (1)

1970 (3)

E. G. Rawson, D. R. Herriott, J. McKenna, Appl. Opt. 9, 753 (1970).
[CrossRef] [PubMed]

P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970).
[CrossRef]

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

1966 (1)

Aoki, Y.

Bouwhuis, G.

G. Bouwhuis, J. J. M. Braat, Appl. Opt. 17, 1993 (1978).
[CrossRef] [PubMed]

G. Bouwhuis, P. Burgstede, Philips Tech. Rev. 33, 186 (1973).

Braat, J. J. M.

Burgstede, P.

G. Bouwhuis, P. Burgstede, Philips Tech. Rev. 33, 186 (1973).

Compaan, K.

K. Compaan, P. Kramer, Philips Tech. Rev. 33, 178 (1973).

Furukawa, M.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Herriott, D. R.

Hirasawa, K.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Hopkins, H. H.

Iga, K.

Kime, K.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Kitano, I.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Kondo, M.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Kramer, P.

K. Compaan, P. Kramer, Philips Tech. Rev. 33, 178 (1973).

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).

Matsumoto, H.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

McKenna, J.

Mitsuhashi, Y.

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

Miyazawa, T.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Moore, D. T.

D. T. Moore, J. Opt. Soc. Am. 61, 886 (1971).
[CrossRef]

D. T. Moore, P. J. Sands, U.S. Patent3, 729, 253.

Morikawa, T.

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

Okada, K.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Rawson, E. G.

Sakurai, K.

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

Sands, P. J.

P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970).
[CrossRef]

D. T. Moore, P. J. Sands, U.S. Patent3, 729, 253.

Sato, T.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Seko, A.

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

Shimada, J.

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

Susaki, W.

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

Takeda, Y.

Tsunoda, Y.

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

Yamamoto, N.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

A. Seko, Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, Appl. Phys. Lett. 27, 140 (1975).
[CrossRef]

IEEE J. Quantum Electron. (1)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumoto, IEEE J. Quantum Electron. QE-6, 606 (1970).
[CrossRef]

J. Opt. Soc. Am. (4)

Opt. Commun. (1)

Y. Mitsuhashi, T. Morikawa, K. Sakurai, A. Seko, J. Shimada, Opt. Commun. 17, 195 (1976).
[CrossRef]

Philips Tech. Rev. (2)

K. Compaan, P. Kramer, Philips Tech. Rev. 33, 178 (1973).

G. Bouwhuis, P. Burgstede, Philips Tech. Rev. 33, 186 (1973).

Other (4)

K. Okada, W. Susaki, M. Kondo, K. Hirasawa, T. Miyazawa, K. Kime, T. Sato, Preprint 1409, Sixty-First Convention of Audio Engineering Society (AES, New York, 1978).

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).

D. T. Moore, P. J. Sands, U.S. Patent3, 729, 253.

These values (N.A. = 0.45 and b/a = 0.4) were derived with the diffraction integral for the SCOOP (self-coupled optical pickup)7-8 system. Because the finite aperture of the lens causes intensity modulation on the returned light, it cannot always be concluded that the larger the N.A. of the lens the better the system works. Details of the analysis will be published later.

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Figures (7)

Fig. 1
Fig. 1

Geometry of the ray path in radial GRIN medium.

Fig. 2
Fig. 2

Point-to-point imaging system using a GRIN lens. Broken lines P.P. and V.P. represent the principal planes and the virtual-image plane, respectively.

Fig. 3
Fig. 3

Transverse aberration curves of the lens with flat surfaces. (a) Transverse aberration curves when h6 = 0 in the optical system shown in Fig. 2. (b) Transverse aberration curves when h6 = −0.22 in the same optical system.

Fig. 4
Fig. 4

Contour map of the aberration in the h4, h6 plane for a flat-surfaced GRIN lens. The aberration means the maximum value of the absolute transverse aberration for sinθ between θ and 0.45.

Fig. 5
Fig. 5

Contour map of residual spherical transverse aberration with curvatures Rs and Rd that make the aberration minimum. R0 in the figure represents a normalizing radius making an imaginary ray parallel to the optical axis at the back end of the lens focus on the back surface of the disk.

Fig. 6
Fig. 6

Contour map of the transverse aberration in the R0/Rs, R0/Rd plane, (a) h4, h6 = 0.9, 0.5. (b) h4, h6 = 1.0, 0.2.

Fig. 7
Fig. 7

Increase of N.A. of the GRIN lens by making the disk-side surface of the lens convex.

Tables (2)

Tables Icon

Table I Physical Parameters of Optical System Using GRIN Lens Adopted in Analyzing Transverse Aberration

Tables Icon

Table II Changes in Various Parameters in Optical System Corresponding to 0.6-μm Aberration

Equations (6)

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

n 2 ( r ) = n 0 2 [ 1 ( g r ) 2 + h 4 ( g r ) 4 + h 6 ( g r ) 6 ] ,
n ( r ) N = n i N i ,
r 2 d ϕ d z = 1 N i ( x i M i y i L i ) ,
z = r i r d r N i / { ( n ( r ) n i ) 2 + 1 r i 2 [ 1 ( r i r ) 2 ] × ( x i M i y i L i ) 2 N i 2 } 1 / 2 ,
r 2 d ϕ d z = 0 ,
z = r i r d r N i / { [ n ( r ) / n i ] 2 N i 2 } 1 / 2 ,

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