Abstract

Some formulas of importance in lens design and evaluation have been derived on a planar lens with spherically symmetric quadratic index profile. Also a nondestructive evaluation method of the focusing constant in the index profile has been developed by the method of least squares.

© 1983 Optical Society of America

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References

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  1. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, Appl. Opt. 21, 3456 (1982).
    [CrossRef] [PubMed]
  2. M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, Jpn. J. Appl. Phys. 20, L296 (1981).
    [CrossRef]
  3. G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.
  4. The examples are Maxwell’s fisheye lens and Luneburg lens.
  5. H.A. Buchdahl, J. Opt. Soc. Am. 63, 46 (1973).
    [CrossRef]
  6. K. Iga, M. Oikawa, J. Banno, Appl. Opt. 21, 3451 (1982).
    [CrossRef] [PubMed]
  7. T. Sakamoto, Kogaku (Jpn. J. Opt.) 12, 38 (1983).
  8. T. Sakamoto, submitted for publication.
  9. H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
    [CrossRef]

1983

T. Sakamoto, Kogaku (Jpn. J. Opt.) 12, 38 (1983).

1982

1981

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

1973

1971

H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
[CrossRef]

Banno, J.

Buchdahl, H.A.

Furukawa, M.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
[CrossRef]

Iga, K.

Khoe, G. D.

G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Kita, H.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
[CrossRef]

Kitano, I.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
[CrossRef]

Knepperss, D.

G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Kock, H. G.

G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Kokubun, Y.

Luijendik, J. A.

G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Misawa, S.

Nishizawa, K.

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Oikawa, M.

Sakamoto, T.

T. Sakamoto, Kogaku (Jpn. J. Opt.) 12, 38 (1983).

T. Sakamoto, submitted for publication.

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Uchida, T.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
[CrossRef]

van en Brekel, C. H. J.

G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

Yamamoto, N.

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Appl. Opt.

J. Am. Ceram. Soc.

H. Kita, I. Kitano, T. Uchida, M. Furukawa, J. Am. Ceram. Soc. 54, 321 (1971).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

M. Oikawa, K. Iga, T. Sanada, N. Yamamoto, K. Nishizawa, Jpn. J. Appl. Phys. 20, L296 (1981).
[CrossRef]

Kogaku (Jpn. J. Opt.)

T. Sakamoto, Kogaku (Jpn. J. Opt.) 12, 38 (1983).

Other

T. Sakamoto, submitted for publication.

G. D. Khoe, H. G. Kock, J. A. Luijendik, C. H. J. van en Brekel, D. Knepperss, in Technical Digest, Seventh European Conference on Optical Communication, Copenhagen (1981), paper 7.6.

The examples are Maxwell’s fisheye lens and Luneburg lens.

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Figures (3)

Fig. 1
Fig. 1

Notation of the parameters: xi, initial ray height; l, distance from the exit face; xl, axial deviation of the ray observed at the distance l; t, lens thickness; a, lens radius; lf, paraxial focal length; sT, transverse spherical aberration; sL, longitudinal spherical aberration.

Fig. 2
Fig. 2

Spherical aberration of the spherical gradient-index planar lens; n0 = 1.55 and gt = 0.200.

Fig. 3
Fig. 3

Numerical aperture and paraxial focal length; n0 = 1.55.

Equations (14)

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n 2 ( r , z ) = n 0 2 [ 1 - g 2 ( r 2 + z 2 ) ] ,
g x ( z ) = g x i 1 - ( g z ) 2 1 - ( g x i ) 2 ,
g x = g x t + g l n t d x d z | z = t - 1 + ( 1 - n t 2 ) ( d x d z | z = t - ) 2 ,
g x t = g x i 1 - ( g t ) 2 - ( g x i ) 3 ( g t ) 2 2 1 - ( g t ) 2 + O ( 5 ) .
g x l = g x i 1 - ( g t ) 2 - ( g x i ) 3 ( g t ) 2 2 1 - ( g t ) 2 + g l n 0 { - g x i g t - ( g x i ) 3 ½ g t [ n 0 2 ( g t ) 2 + 1 ] } + O ( 5 ) .
g l f n 0 = 1 - ( g t ) 2 g t .
g s T = g x l l = l f
g s T = ( g x i ) 3 n 0 2 ( g t ) 4 - n 0 2 ( g t ) 2 - 1 2 1 - ( g t ) 2 + O ( 5 ) .
g s L n 0 = g l x l = 0 - g l f
g s L n 0 = ( g x i ) 2 n 0 2 ( g t ) 4 - n 0 2 ( g t ) 2 - 1 2 g t 1 - ( g t ) 2 + O ( 4 ) .
sin θ = n t d x d z | z = t - 1 + ( d x d z | z = t - ) 2
y = a ( g ) x
ɛ 2 = k ( a x k - y k ) 2
g ^ = - 2 l n 0 t a ^ - t 2 + t 4 + 4 ( l n 0 t ) 2 + 4 l n 0 t 3 a ^ 2 l n 0 t ,

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