Abstract

A simple method to obtain the fourth-order coefficient of the series expansion for the radial distribution of a lenslike medium is described. The coefficient is obtained by measuring the position of a discontinuity of the far-field intensity pattern. The relation between the coefficient and this position is calculated by using either the ray theory or the wave theory. By using a ray model, the position of the discontinuity and the macroscopic intensity distribution is easily obtained.

© 1978 Optical Society of America

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  1. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).
  2. M. Ikeda, "Propagation of multimode fibers with graded core index," IEEE J. Quantum Electron. QE-10, 362–371 (1974).
  3. J. Hamasaki and K. Maeda, "Correction of image through lenslike medium by means of holography," 1974 National Conv. Rec. of IECE, Japan 1182.
  4. R. Olshansky and D. B. Keck, "Pulse broadening in graded-index optical fibers," Appl. Opt. 15, 483–491 (1976).
  5. T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).
  6. Y. Suematsu and K. Furuya, "Measuring methods of characteristics in a lenslike medium stressed on spotsize divergence and group delay, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE-70, 39 (1970).
  7. E. G. Rawson and R. G. Murray, "Interferometric measurement of SELFOC dielectric constant coefficients to sixth order," IEEE J. Quantum Electron. QE-9, 1114–1118 (1973).
  8. M. Ikeda, M. Tateda, and H. Yoshikiyo, "Refractive index profile of a graded index fiber: Measurement by a reflection method," Appl. Opt. 14, 814–815 (1975).
  9. K. Terazawa, Sugaku Gairon (Iwanami, Tokyo, 1959).
  10. H. Matsumura and T. Kitano, "Geometrical analysis in a lens-medium with the fourth order aberration, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE70, 37 (1970).
  11. S. Kawakami and J. Nishizawa, "An optical waveguide with the optimum distribution of refractive index with reference to waveform distortion," IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).
  12. J. Hamasaki, "Gaussian wave in spatial frequency domain," Seisan Kenkyu 24, 12–18 (1972).
  13. K. Maeda, "Research on image transmission characteristics of lens-like medium," Ph. D. thesis, University of Tokyo (1976).

1976 (1)

1975 (1)

1974 (1)

M. Ikeda, "Propagation of multimode fibers with graded core index," IEEE J. Quantum Electron. QE-10, 362–371 (1974).

1973 (2)

T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).

E. G. Rawson and R. G. Murray, "Interferometric measurement of SELFOC dielectric constant coefficients to sixth order," IEEE J. Quantum Electron. QE-9, 1114–1118 (1973).

1972 (1)

J. Hamasaki, "Gaussian wave in spatial frequency domain," Seisan Kenkyu 24, 12–18 (1972).

1970 (3)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

Y. Suematsu and K. Furuya, "Measuring methods of characteristics in a lenslike medium stressed on spotsize divergence and group delay, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE-70, 39 (1970).

H. Matsumura and T. Kitano, "Geometrical analysis in a lens-medium with the fourth order aberration, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE70, 37 (1970).

1968 (1)

S. Kawakami and J. Nishizawa, "An optical waveguide with the optimum distribution of refractive index with reference to waveform distortion," IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).

Furukawa, M.

T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

Furuya, K.

Y. Suematsu and K. Furuya, "Measuring methods of characteristics in a lenslike medium stressed on spotsize divergence and group delay, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE-70, 39 (1970).

Hamasaki, J.

J. Hamasaki, "Gaussian wave in spatial frequency domain," Seisan Kenkyu 24, 12–18 (1972).

J. Hamasaki and K. Maeda, "Correction of image through lenslike medium by means of holography," 1974 National Conv. Rec. of IECE, Japan 1182.

Ikeda, M.

M. Ikeda, M. Tateda, and H. Yoshikiyo, "Refractive index profile of a graded index fiber: Measurement by a reflection method," Appl. Opt. 14, 814–815 (1975).

M. Ikeda, "Propagation of multimode fibers with graded core index," IEEE J. Quantum Electron. QE-10, 362–371 (1974).

Kawakami, S.

S. Kawakami and J. Nishizawa, "An optical waveguide with the optimum distribution of refractive index with reference to waveform distortion," IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).

Keck, D. B.

Kitano, I.

T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

Kitano, T.

T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).

H. Matsumura and T. Kitano, "Geometrical analysis in a lens-medium with the fourth order aberration, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE70, 37 (1970).

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

Maeda, K.

K. Maeda, "Research on image transmission characteristics of lens-like medium," Ph. D. thesis, University of Tokyo (1976).

J. Hamasaki and K. Maeda, "Correction of image through lenslike medium by means of holography," 1974 National Conv. Rec. of IECE, Japan 1182.

Matsumura, H.

T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

H. Matsumura and T. Kitano, "Geometrical analysis in a lens-medium with the fourth order aberration, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE70, 37 (1970).

Murray, R. G.

E. G. Rawson and R. G. Murray, "Interferometric measurement of SELFOC dielectric constant coefficients to sixth order," IEEE J. Quantum Electron. QE-9, 1114–1118 (1973).

Nishizawa, J.

S. Kawakami and J. Nishizawa, "An optical waveguide with the optimum distribution of refractive index with reference to waveform distortion," IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).

Olshansky, R.

Rawson, E. G.

E. G. Rawson and R. G. Murray, "Interferometric measurement of SELFOC dielectric constant coefficients to sixth order," IEEE J. Quantum Electron. QE-9, 1114–1118 (1973).

Suematsu, Y.

Y. Suematsu and K. Furuya, "Measuring methods of characteristics in a lenslike medium stressed on spotsize divergence and group delay, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE-70, 39 (1970).

Tateda, M.

Terazawa, K.

K. Terazawa, Sugaku Gairon (Iwanami, Tokyo, 1959).

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

Yoshikiyo, H.

Appl. Opt. (2)

IEEE J. Quantum Electron. (4)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, "Optical characteristics of a light-focusing fiber guide and its applications, " IEEE J. Quantum Electron. QE-6, 606–612 (1970).

M. Ikeda, "Propagation of multimode fibers with graded core index," IEEE J. Quantum Electron. QE-10, 362–371 (1974).

T. Kitano, H. Matsumura, M. Furukawa, and I. Kitano, "Measurement of fourth-order aberration in a lens-like medium," IEEE J. Quantum Electron. QE-9, 967–971 (1973).

E. G. Rawson and R. G. Murray, "Interferometric measurement of SELFOC dielectric constant coefficients to sixth order," IEEE J. Quantum Electron. QE-9, 1114–1118 (1973).

IEEE Trans. Microwave Theory Tech. (1)

S. Kawakami and J. Nishizawa, "An optical waveguide with the optimum distribution of refractive index with reference to waveform distortion," IEEE Trans. Microwave Theory Tech. MTT-16, 814–818 (1968).

Rep. Tech. Group on Quantum Electron. (2)

Y. Suematsu and K. Furuya, "Measuring methods of characteristics in a lenslike medium stressed on spotsize divergence and group delay, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE-70, 39 (1970).

H. Matsumura and T. Kitano, "Geometrical analysis in a lens-medium with the fourth order aberration, " IECE of Japan, Rep. Tech. Group on Quantum Electron. QE70, 37 (1970).

Seisan Kenkyu (1)

J. Hamasaki, "Gaussian wave in spatial frequency domain," Seisan Kenkyu 24, 12–18 (1972).

Other (3)

K. Maeda, "Research on image transmission characteristics of lens-like medium," Ph. D. thesis, University of Tokyo (1976).

K. Terazawa, Sugaku Gairon (Iwanami, Tokyo, 1959).

J. Hamasaki and K. Maeda, "Correction of image through lenslike medium by means of holography," 1974 National Conv. Rec. of IECE, Japan 1182.

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