Abstract

The sphere lens with a spherical gradient-index (GRIN) was prepared for the first time by two modified suspension polymerization techniques. The index change of the 0.05–3.0-mm diam GRIN sphere was 0.02–0.04, and the index profile was almost quadratic. The optimum condition minimizing the spherical aberration of the GRIN sphere embedded in a certain substrate was confirmed. Furthermore, 1-D and 2-D GRIN sphere lens arrays were fabricated.

© 1986 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).
  2. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).
  3. S. P. Morgan, “General Solution of the Luneberg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
    [CrossRef]
  4. K. Kikuchi, T. Morikawa, J. Shimada, K. Sakurai, “Cladded Radially Inhomogeneous Sphere Lenses,” Appl. Opt. 20, 388 (1981).
    [CrossRef] [PubMed]
  5. Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN Plastic Lens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985), paper B1.
  6. Y. Koike, Y. Ohtsuka, “Precise Nondestructive Method of Measuring Refractive-Index Distribution of Spherical GRIN lens by Interferometry,” in Technical Digest, Topical Meeting on Gradient Index Optical Imaging Systems, Palermo, Italy (1985), paper H1.
  7. H. M. Presby, I. P. Kaminow, “Binary Silica Optical Fibers: Refractive Index and Profile Dispersion Measurements,” Appl. Opt. 15, 3029 (1976).
    [CrossRef] [PubMed]
  8. M. Ikeda, M. Tateda, H. Yoshikiyo, “Refractive Index Profile of a Graded-Index Fiber: Measurement by a Reflection Method,” Appl. Opt. 14, 814 (1975).
    [CrossRef] [PubMed]
  9. A. M. Hunter, P. W. Schreiber, “Mach-Zehnder Data Reduction Method for Refractively Inhomogeneous Test Objects,” Appl. Opt. 14, 634 (1975).
    [CrossRef]
  10. Y. Ohtsuka, Y. Koike, “Determination of the Refractive Index Profile of Light-Focusing Rods: Accuracy of a Method Using Interphako Interference Microscopy,” Appl. Opt. 19, 2866 (1980).
    [CrossRef] [PubMed]
  11. Y. Ohtsuka, Y. Shimizu, “Radial Distribution of the Refractive Index in Light-Focusing Rods: Determination Using Interphako Interference Microscopy,” Appl. Opt. 16, 1050 (1977).
    [PubMed]

1981 (1)

1980 (1)

1977 (1)

1976 (1)

1975 (2)

1958 (1)

S. P. Morgan, “General Solution of the Luneberg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Hunter, A. M.

Ikeda, M.

Kaminow, I. P.

Kikuchi, K.

Koike, Y.

Y. Ohtsuka, Y. Koike, “Determination of the Refractive Index Profile of Light-Focusing Rods: Accuracy of a Method Using Interphako Interference Microscopy,” Appl. Opt. 19, 2866 (1980).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN Plastic Lens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985), paper B1.

Y. Koike, Y. Ohtsuka, “Precise Nondestructive Method of Measuring Refractive-Index Distribution of Spherical GRIN lens by Interferometry,” in Technical Digest, Topical Meeting on Gradient Index Optical Imaging Systems, Palermo, Italy (1985), paper H1.

Marchand, E. W.

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

Morgan, S. P.

S. P. Morgan, “General Solution of the Luneberg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
[CrossRef]

Morikawa, T.

Ohtsuka, Y.

Y. Ohtsuka, Y. Koike, “Determination of the Refractive Index Profile of Light-Focusing Rods: Accuracy of a Method Using Interphako Interference Microscopy,” Appl. Opt. 19, 2866 (1980).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Shimizu, “Radial Distribution of the Refractive Index in Light-Focusing Rods: Determination Using Interphako Interference Microscopy,” Appl. Opt. 16, 1050 (1977).
[PubMed]

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN Plastic Lens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985), paper B1.

Y. Koike, Y. Ohtsuka, “Precise Nondestructive Method of Measuring Refractive-Index Distribution of Spherical GRIN lens by Interferometry,” in Technical Digest, Topical Meeting on Gradient Index Optical Imaging Systems, Palermo, Italy (1985), paper H1.

Presby, H. M.

Sakurai, K.

Schreiber, P. W.

Shimada, J.

Shimizu, Y.

Sumi, Y.

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN Plastic Lens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985), paper B1.

Tateda, M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Yoshikiyo, H.

Appl. Opt. (6)

J. Appl. Phys. (1)

S. P. Morgan, “General Solution of the Luneberg Lens Problem,” J. Appl. Phys. 29, 1358 (1958).
[CrossRef]

Other (4)

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN Plastic Lens,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy (1985), paper B1.

Y. Koike, Y. Ohtsuka, “Precise Nondestructive Method of Measuring Refractive-Index Distribution of Spherical GRIN lens by Interferometry,” in Technical Digest, Topical Meeting on Gradient Index Optical Imaging Systems, Palermo, Italy (1985), paper H1.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

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

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Figures (18)

Fig. 1
Fig. 1

Spherical GRIN sphere lenses prepared by the modified suspension polymerization technique.

Fig. 2
Fig. 2

Block diagram of preparation method I of the plastic GRIN sphere.

Fig. 3
Fig. 3

Block diagram of preparation method II of the plastic GRIN sphere.

Fig. 4
Fig. 4

Surface accuracy of the plastic GRIN sphere lens prepared by method I measured by a roundness measuring instrument.

Fig. 5
Fig. 5

Trajectory of the ray traversing the GRIN sphere lens.

Fig. 6
Fig. 6

Interference fringe pattern observed by shearing interferometry.

Fig. 7
Fig. 7

Representative spherical distribution of the refractive index in the plastic GRIN sphere prepared by method I in the DAP-3FMA monomer system: Ts = 90 °C; ts = 5 h; Td = 70 °C; and td = 1.5 h.

Fig. 8
Fig. 8

Index distribution of the GRIN sphere prepared by method II. A, EDMA-8FMA monomer system; B, DAP-3FMA.

Fig. 9
Fig. 9

Focusing of the GRIN sphere lens.

Fig. 10
Fig. 10

Bending angle of ray through the GRIN sphere in the medium with n2 when np = 1.50 and n0 = 1.53. The broken curve is for the homogeneous sphere with an index of 1.50.

Fig. 11
Fig. 11

Calculated TSA of the GRIN sphere in the medium with n2.

Fig. 12
Fig. 12

Relationship between l0/rp and Δn giving the minimum TSA in the medium with n2.

Fig. 13
Fig. 13

Relationship between n2 and Δn giving the minimum TSA.

Fig. 14
Fig. 14

Relationship between the n0 of the GRIN sphere and l0/rp giving the minimum aberration for np = 1.50.

Fig. 15
Fig. 15

TSA curve of the embedded GRIN sphere having a cladding shell.

Fig. 16
Fig. 16

Procedure to prepare 1-D and 2-D GRIN sphere lens arrays.

Fig. 17
Fig. 17

(a) The 1-D GRIN sphere lens array; (b) image through the 2-D GRIN sphere lens array.

Fig. 18
Fig. 18

Focused spot of collimated He–Ne laser through the GRIN sphere.

Equations (14)

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n ( r ) = n 0 [ 1 + ( r a ) 2 ] - 1 ,
n ( r ) = 2 - ( r r p ) 2 ,
Δ = P 0 P 1 n ( r ) d s - 2 n 2 · r p 2 - ρ 2 - n 2 ρ · tan ψ .
P 0 P 1 n ( r ) d s = 2 n p r p 2 - ( v ρ ) 2 - 2 n 2 ρ n p r p d ln n ( u ) d u · u 2 · d u u 2 - ( n 2 ρ ) 2 ,
ψ 0 = - 2 n 2 ρ n 2 ρ n p r p d ln n ( u ) d u d u u 2 - ( n 2 ρ ) 2 ,
ψ s = sin - 1 ( ρ / r p ) - sin - 1 ( v ρ / r p ) .
ψ = ψ 0 + 2 ψ s
n ( u ) = n p · exp ( - 1 π u / n 2 ( n p r p ) / n 2 { d Δ d ρ p + 2 n 2 [ sin - 1 ( ρ p r p ) - sin - 1 ( v ρ p r p ) ] } d ρ p ( n 2 ρ p ) 2 - u 2 ) ,
n ( u ) = n p · exp [ - 1 π u / n 2 r p d Δ d ρ p d ρ p ( n 2 ρ p ) 2 - u 2 ] .
d Δ d ρ p = λ D d R d ρ p = λ ρ p D y p d R d y p ,
θ = θ 0 + e r 0 r d r r n 2 r 2 - e 2 ;
e = ± n r sin α .
l = y / sin ψ ,
ψ = - 2 n 2 · y n 2 y n p r p d ln n ( u ) d u d u u 2 - ( n 2 y ) 2 + 2 [ sin - 1 ( y / r p ) - sin - 1 ( v y / r p ) ] ,

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