Abstract

Studies on evaluating and measuring aberrations of rod lenses which have mostly parabolic distribution of refractive index have been reviewed. Some efforts at reducing aberrations by controlling the fabrication process are also summarized.

© 1982 Optical Society of America

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References

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  1. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).
  2. A. D. Pearson, W. D. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
    [CrossRef]
  3. K. Kobayashi, R. Ishikawa, K. Minemura, S. Sugimoto, Fiber and Integrated Optics (Crane, Trenton, N.J., 1979); T. Uchida, S. Sugimoto, in Technical Digest, ECOC (Genoa, 1978); S.Sugimoto Sugimoto, K. Kobayashi, S. Matsushita, Trans. IECE Jpn. 61, 1114 (1968), in Japanese.
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  8. T. Miyazawa, K. Okada, T. Kubo, I. Kitano, K. Nishizawa, K. Iga, Appl. Opt. 19, 1113 (1980).
    [CrossRef] [PubMed]
  9. K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington D.C., 1981), paper MC1.
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  11. K. Iga, Appl. Opt. 19, 1039 (1980).
    [CrossRef] [PubMed]
  12. T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
    [CrossRef]
  13. K. Maeda, J. Hamasaki, J. Opt. Soc. Am. 67, 1672 (1977).
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  15. N. Yamamoto, K. Iga, Appl. Opt. 19, 1101 (1980).
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  17. K. Kikuchi, S. Ishihara, H. Shimizu, J. Shimada, Appl. Opt. 19, 1076 (1980).
    [CrossRef] [PubMed]
  18. E. G. Rawson, D. R. Herriott, J. McKenna, Appl. Oct. 9, 753 (1970).
    [CrossRef]
  19. Y. Ohtsuka, T. Senga, H. Yasuda, Appl. Phys. Lett. 25, 659 (1974).
    [CrossRef]
  20. K. Nishizawa, Appl. Opt. 19, 1052 (1980).
    [CrossRef] [PubMed]
  21. L. Gregorka, D. T. Moore, Appl. Opt. 19, 1096 (1980).
    [CrossRef] [PubMed]
  22. W. E. Martin, Appl. Opt. 13, 2112 (1974).
    [CrossRef] [PubMed]
  23. Y. Kokubun, K. Iga, Trans. IECE Jpn. E60, 702 (1977).
  24. Y. Kokubun, K. Iga, Appl. Opt. 19, 846 (1980).
    [CrossRef] [PubMed]
  25. Y. Kokubun, K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington D.C., 1981).
  26. M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 814 (1975).
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  27. T. Okoshi, K. Hotate, Appl. Opt. 15, 2756 (1976).
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  28. H. M. Presby, D. Marcuse, Appl. Opt. 18, 671 (1979).
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    [CrossRef]
  30. K. Iga, K. Yokomori, Trans. IECE Jpn. C58, 283 (1975).
  31. K. Iga, N. Yamamoto, Y. Matsumura, Trans. IECE Jpn. E60, 239 (1977).
  32. K. Iga, N. Yamamoto, IECE Jpn. National Convention Record (1977), p. 856.

1980 (12)

1979 (1)

1977 (4)

K. Iga, N. Yamamoto, Y. Matsumura, Trans. IECE Jpn. E60, 239 (1977).

K. Iga, N. Yamamoto, IECE Jpn. National Convention Record (1977), p. 856.

K. Maeda, J. Hamasaki, J. Opt. Soc. Am. 67, 1672 (1977).
[CrossRef]

Y. Kokubun, K. Iga, Trans. IECE Jpn. E60, 702 (1977).

1976 (1)

1975 (3)

K. Iga, K. Yokomori, Trans. IECE Jpn. C58, 283 (1975).

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

M. Ikeda, M. Tateda, H. Yoshikiyo, Appl. Opt. 14, 814 (1975).
[CrossRef] [PubMed]

1974 (2)

Y. Ohtsuka, T. Senga, H. Yasuda, Appl. Phys. Lett. 25, 659 (1974).
[CrossRef]

W. E. Martin, Appl. Opt. 13, 2112 (1974).
[CrossRef] [PubMed]

1973 (1)

T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
[CrossRef]

1971 (1)

1970 (1)

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

1969 (1)

A. D. Pearson, W. D. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[CrossRef]

1966 (1)

Y. Suematsu, K. Iga, Trans. IECE Jpn. 49, 1645 (1966).

Adams, M. J.

I. Sasaki, D. N. Payne, M. J. Adams, Electron. Lett. 16, 219 (1980).
[CrossRef]

French, W. D.

A. D. Pearson, W. D. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[CrossRef]

Furukawa, M.

T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
[CrossRef]

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).

Gregorka, L.

Hamasaki, J.

Hatate, Y.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, Trans. IECE Jpn. IE80, 72 (1980).

Herriott, D. R.

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

Hotate, K.

Iga, K.

Y. Kokubun, K. Iga, Appl. Opt. 19, 846 (1980).
[CrossRef] [PubMed]

N. Yamamoto, K. Iga, Appl. Opt. 19, 1101 (1980).
[CrossRef] [PubMed]

K. Iga, Appl. Opt. 19, 1039 (1980).
[CrossRef] [PubMed]

T. Miyazawa, K. Okada, T. Kubo, I. Kitano, K. Nishizawa, K. Iga, Appl. Opt. 19, 1113 (1980).
[CrossRef] [PubMed]

K. Iga, N. Yamamoto, Y. Matsumura, Trans. IECE Jpn. E60, 239 (1977).

K. Iga, N. Yamamoto, IECE Jpn. National Convention Record (1977), p. 856.

Y. Kokubun, K. Iga, Trans. IECE Jpn. E60, 702 (1977).

K. Iga, K. Yokomori, Trans. IECE Jpn. C58, 283 (1975).

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Y. Suematsu, K. Iga, Trans. IECE Jpn. 49, 1645 (1966).

Y. Kokubun, K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington D.C., 1981).

K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington D.C., 1981), paper MC1.

Ikeda, M.

Ishihara, S.

Ishikawa, R.

K. Kobayashi, R. Ishikawa, K. Minemura, S. Sugimoto, Fiber and Integrated Optics (Crane, Trenton, N.J., 1979); T. Uchida, S. Sugimoto, in Technical Digest, ECOC (Genoa, 1978); S.Sugimoto Sugimoto, K. Kobayashi, S. Matsushita, Trans. IECE Jpn. 61, 1114 (1968), in Japanese.

Kanzaki, M.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, Trans. IECE Jpn. IE80, 72 (1980).

Kawazu, M.

Kikuchi, K.

Kitano, I.

T. Miyazawa, K. Okada, T. Kubo, I. Kitano, K. Nishizawa, K. Iga, Appl. Opt. 19, 1113 (1980).
[CrossRef] [PubMed]

T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
[CrossRef]

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).

Kitano, T.

T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
[CrossRef]

Kobayashi, K.

K. Kobayashi, R. Ishikawa, K. Minemura, S. Sugimoto, Fiber and Integrated Optics (Crane, Trenton, N.J., 1979); T. Uchida, S. Sugimoto, in Technical Digest, ECOC (Genoa, 1978); S.Sugimoto Sugimoto, K. Kobayashi, S. Matsushita, Trans. IECE Jpn. 61, 1114 (1968), in Japanese.

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).

Kokubun, Y.

Y. Kokubun, K. Iga, Appl. Opt. 19, 846 (1980).
[CrossRef] [PubMed]

Y. Kokubun, K. Iga, Trans. IECE Jpn. E60, 702 (1977).

Y. Kokubun, K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington D.C., 1981).

Komiya, K.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, Trans. IECE Jpn. IE80, 72 (1980).

Kubo, T.

Maeda, K.

Marcuse, D.

Martin, W. E.

Matsumura, H.

T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
[CrossRef]

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).

Matsumura, Y.

K. Iga, N. Yamamoto, Y. Matsumura, Trans. IECE Jpn. E60, 239 (1977).

Matsushita, K.

McKenna, J.

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

Minemura, K.

K. Kobayashi, R. Ishikawa, K. Minemura, S. Sugimoto, Fiber and Integrated Optics (Crane, Trenton, N.J., 1979); T. Uchida, S. Sugimoto, in Technical Digest, ECOC (Genoa, 1978); S.Sugimoto Sugimoto, K. Kobayashi, S. Matsushita, Trans. IECE Jpn. 61, 1114 (1968), in Japanese.

Miyazawa, T.

Moore, D. T.

Nishizawa, K.

Ogura, Y.

Ohtsuka, Y.

Y. Ohtsuka, T. Senga, H. Yasuda, Appl. Phys. Lett. 25, 659 (1974).
[CrossRef]

Okada, K.

Okoshi, T.

Paxton, K. B.

Payne, D. N.

I. Sasaki, D. N. Payne, M. J. Adams, Electron. Lett. 16, 219 (1980).
[CrossRef]

Pearson, A. D.

A. D. Pearson, W. D. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[CrossRef]

Presby, H. M.

Rawson, E. G.

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

A. D. Pearson, W. D. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[CrossRef]

Sakayori, T.

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Sasaki, I.

I. Sasaki, D. N. Payne, M. J. Adams, Electron. Lett. 16, 219 (1980).
[CrossRef]

Senga, T.

Y. Ohtsuka, T. Senga, H. Yasuda, Appl. Phys. Lett. 25, 659 (1974).
[CrossRef]

Shimada, J.

Shimizu, H.

Streifer, W.

Suematsu, Y.

Y. Suematsu, K. Iga, Trans. IECE Jpn. 49, 1645 (1966).

Sugimoto, S.

K. Kobayashi, R. Ishikawa, K. Minemura, S. Sugimoto, Fiber and Integrated Optics (Crane, Trenton, N.J., 1979); T. Uchida, S. Sugimoto, in Technical Digest, ECOC (Genoa, 1978); S.Sugimoto Sugimoto, K. Kobayashi, S. Matsushita, Trans. IECE Jpn. 61, 1114 (1968), in Japanese.

Tateda, M.

Tomlinson, W. J.

Toyama, M.

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).

Yamamoto, N.

N. Yamamoto, K. Iga, Appl. Opt. 19, 1101 (1980).
[CrossRef] [PubMed]

K. Iga, N. Yamamoto, IECE Jpn. National Convention Record (1977), p. 856.

K. Iga, N. Yamamoto, Y. Matsumura, Trans. IECE Jpn. E60, 239 (1977).

Yamashita, T.

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, Trans. IECE Jpn. IE80, 72 (1980).

Yasuda, H.

Y. Ohtsuka, T. Senga, H. Yasuda, Appl. Phys. Lett. 25, 659 (1974).
[CrossRef]

Yokomori, K.

K. Iga, K. Yokomori, Trans. IECE Jpn. C58, 283 (1975).

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Yoshikiyo, H.

Appl. Oct. (1)

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

Appl. Opt. (15)

Appl. Phys. Lett. (3)

A. D. Pearson, W. D. French, E. G. Rawson, Appl. Phys. Lett. 15, 76 (1969).
[CrossRef]

K. Iga, K. Yokomori, T. Sakayori, Appl. Phys. Lett. 26, 578 (1975).
[CrossRef]

Y. Ohtsuka, T. Senga, H. Yasuda, Appl. Phys. Lett. 25, 659 (1974).
[CrossRef]

Electron. Lett. (1)

I. Sasaki, D. N. Payne, M. J. Adams, Electron. Lett. 16, 219 (1980).
[CrossRef]

IECE Jpn. National Convention Record (1)

K. Iga, N. Yamamoto, IECE Jpn. National Convention Record (1977), p. 856.

IEEE J. Quantum Electron. (1)

T. Kitano, H. Matsumura, M. Furukawa, I. Kitano, IEEE J. Quantum Electron. QE-9, 967 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Trans. IECE Jpn. (5)

Y. Suematsu, K. Iga, Trans. IECE Jpn. 49, 1645 (1966).

K. Komiya, M. Kanzaki, Y. Hatate, T. Yamashita, Trans. IECE Jpn. IE80, 72 (1980).

K. Iga, K. Yokomori, Trans. IECE Jpn. C58, 283 (1975).

K. Iga, N. Yamamoto, Y. Matsumura, Trans. IECE Jpn. E60, 239 (1977).

Y. Kokubun, K. Iga, Trans. IECE Jpn. E60, 702 (1977).

Other (4)

Y. Kokubun, K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems, (Optical Society of America, Washington D.C., 1981).

K. Iga, in Digest of Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington D.C., 1981), paper MC1.

K. Kobayashi, R. Ishikawa, K. Minemura, S. Sugimoto, Fiber and Integrated Optics (Crane, Trenton, N.J., 1979); T. Uchida, S. Sugimoto, in Technical Digest, ECOC (Genoa, 1978); S.Sugimoto Sugimoto, K. Kobayashi, S. Matsushita, Trans. IECE Jpn. 61, 1114 (1968), in Japanese.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, H. Matsumura, in Technical Digest, Conference on Laser Engineering and Applications (Optical Society of America, Washington, D.C., 1969).

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Figures (14)

Fig. 1
Fig. 1

Expression of index distribution.

Fig. 2
Fig. 2

(a) Intensity distribution of the beam astigmatically converted through flow-type gas lens. The ratio win/w0 was much greater than unity. (b) Mode conversion was reduced by making win/w0 close to unity.

Fig. 3
Fig. 3

Measurement of beam position and shape after being transmitted through a Selfoc lens. x0 is the position of the incident beam.

Fig. 4
Fig. 4

Change of sinusoidal trajectory of the ray inside a plastic distributed-index rod lens: (a) xin = 0.1 mm; (b) 0.4 mm; (c) 0.8 mm; and (d) Ωvs xin.

Fig. 5
Fig. 5

Evaluation of aberration by the imaging method.

Fig. 6
Fig. 6

Focused spot from an experimental Selfoc lens.

Fig. 7
Fig. 7

Focused spot diameter vs the numerical aperture of a lens.

Fig. 8
Fig. 8

Relation between the expansion coefficients in index distribution and the normalized diffusion time D T 2 / r 0 2, where D is the diffusion constant, T2 the diffusion time, and r0 the radius rod.

Fig. 9
Fig. 9

Measured longitudinal aberration of experimental Selfoc lenses against the ion exchange time.

Fig. 10
Fig. 10

Optimum diffusion-exchange and heat-treatment condition. Fourth- and sixth-order coefficients h4 and h6 have optimum values for low aberration within the superimposed region indicated by the arrow. T2 and T3 are the diffusion and heat-treatment time, respectively, D is the diffusion constant, and r0 is the radius of a lens.

Fig. 11
Fig. 11

Chromatic aberration and ND in plastic materials.

Fig. 12
Fig. 12

Measurement of chromatic aberration in rod lenses.

Fig. 13
Fig. 13

Schematic of the gradient-index schlieren system.

Fig. 14
Fig. 14

(a) Compensation of chromatic aberration by use of paired lenses; and (b) achromatization condition.

Tables (1)

Tables Icon

Table I Measuring Methods of Refractive-index Distribution

Equations (3)

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n 2 ( r ) = n 2 ( 0 ) [ 1 - ( g r ) 2 + h 4 ( g r ) 4 + h 4 ( g r ) 6 + ] ( r a ) , = n 2 2 ( r a ) ,
x ( z ) = x i cos Ω z + ( x ˙ i / Ω ) sin Ω z ,
Ω / g = 1 - ( 3 / 4 ) ( h 4 - 2 / 3 ) [ ( g x i ) 2 + x ˙ i 2 ] - ( 3 / 4 ) ( h 4 - 2 / 3 ) [ 21 ( g x i ) 4 + 46 ( g x i ) 2 x ˙ i 2 + 17 x ˙ i 4 ] / 12 - [ ( 3 / 4 ) ( h 4 - 2 / 3 ) ] 2 [ 7 ( g x i ) 4 + 46 ( g x i ) 2 x ˙ i 2 + 23 x ˙ i 4 ] / 12 - ( 15 / 16 ) ( h 6 + 17 / 45 ) [ ( g x i ) 2 + x ˙ i 2 ] 2 .

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