Abstract

A sphere lens with a spherical gradient index (GRIN) was prepared by the modified suspension polymerization technique. GRIN spheres with quadratic- and linear-index distributions were obtained by two different methods to confirm the effect of the GRIN profile on the focusing property of the sphere lens. It was confirmed in both theory and experiment that the spherical aberration of such GRIN spheres was remarkably decreased compared with that of a homogeneous sphere.

© 1994 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 4.
  2. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), Chap. 5.
  3. S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358–1368 (1958).
    [CrossRef]
  4. K. Kikuchi, T. Morikawa, J. Shimada, K. Sakurai, “Cladded radially inhomogeneous sphere lenses,” Appl. Opt. 20, 388–394 (1981).
    [CrossRef] [PubMed]
  5. J. Sochacki, “Stigmatic index-gradient doublet for microscope immersion objectives: a design,” Opt. Eng. 30, 103–110(1991).
    [CrossRef]
  6. Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN plastic lens,” presented at the Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy, 1985.
  7. Y. Koike, Y. Sumi, Y. Ohtsuka, “Spherical gradient-index sphere lens,” Appl. Opt. 25, 3356–3363 (1986).
    [CrossRef] [PubMed]

1991 (1)

J. Sochacki, “Stigmatic index-gradient doublet for microscope immersion objectives: a design,” Opt. Eng. 30, 103–110(1991).
[CrossRef]

1986 (1)

1981 (1)

1958 (1)

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358–1368 (1958).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 4.

Kikuchi, K.

Koike, Y.

Y. Koike, Y. Sumi, Y. Ohtsuka, “Spherical gradient-index sphere lens,” Appl. Opt. 25, 3356–3363 (1986).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN plastic lens,” presented at the Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy, 1985.

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), Chap. 5.

Morgan, S. P.

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358–1368 (1958).
[CrossRef]

Morikawa, T.

Ohtsuka, Y.

Y. Koike, Y. Sumi, Y. Ohtsuka, “Spherical gradient-index sphere lens,” Appl. Opt. 25, 3356–3363 (1986).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN plastic lens,” presented at the Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy, 1985.

Sakurai, K.

Shimada, J.

Sochacki, J.

J. Sochacki, “Stigmatic index-gradient doublet for microscope immersion objectives: a design,” Opt. Eng. 30, 103–110(1991).
[CrossRef]

Sumi, Y.

Y. Koike, Y. Sumi, Y. Ohtsuka, “Spherical gradient-index sphere lens,” Appl. Opt. 25, 3356–3363 (1986).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN plastic lens,” presented at the Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy, 1985.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 4.

Appl. Opt. (2)

J. Appl. Phys. (1)

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358–1368 (1958).
[CrossRef]

Opt. Eng. (1)

J. Sochacki, “Stigmatic index-gradient doublet for microscope immersion objectives: a design,” Opt. Eng. 30, 103–110(1991).
[CrossRef]

Other (3)

Y. Ohtsuka, Y. Koike, Y. Sumi, “Spherical GRIN plastic lens,” presented at the Topical Meeting on Gradient-Index Optical Imaging Systems, Palermo, Italy, 1985.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 4.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), Chap. 5.

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Figures (12)

Fig. 1
Fig. 1

Block diagram of preparation method I for a polymer GRIN sphere.

Fig. 2
Fig. 2

GRIN spheres with a diameter of 0.9 mm.

Fig. 3
Fig. 3

Block diagram of preparation method II for a polymer GRIN sphere.

Fig. 4
Fig. 4

Ray trajectory through a GRIN sphere lens.

Fig. 5
Fig. 5

Interference fringe pattern observed when a shearing interferometric technique is used.

Fig. 6
Fig. 6

Calculated TSA of a GRIN sphere (n 0 = 1.55, n p = 1.50) and a homogeneous sphere (n = 1.55) in the medium with n 2, which minimizes the TSA.

Fig. 7
Fig. 7

Refractive-index profiles of a GRIN sphere prepared with method I: linear-index distribution.

Fig. 8
Fig. 8

Refractive-index profiles of a GRIN sphere prepared with method II: quadratic-index distribution.

Fig. 9
Fig. 9

Calculated TSA of a prepared GRIN sphere and the homogeneous sphere of poly-BzMA (n = 1.568).

Fig. 10
Fig. 10

Focused spots of a collimated He–Ne laser through a sphere lens at a Gaussian focal point.

Fig. 11
Fig. 11

Ray trajectories through sphere lenses.

Fig. 12
Fig. 12

Refractive-index profile of a GRIN sphere prepared with method II and from the BzMA–MMA system.

Tables (1)

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Table 1 Properties of Polymers

Equations (9)

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Δ = P 0 P 1 n ( r ) d s - 2 n 2 ( r p 2 - ρ 2 ) 1 / 2 - n 2 ρ tan ψ .
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 ( ν ρ p r p ) ] } d ρ [ ( n 2 ρ p ) 2 - u 2 ] 1 / 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 ] 1 / 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 ) 1 / 2 ,
e = ± n r sin α .
l = ρ / sin ψ ,
ψ = - 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 ] 1 / 2 + 2 [ sin - 1 ( ρ / r p ) - sin - 1 ( ν ρ / r p ) ] ,
n ( r ) = n 0 - Δ n ( r / r p ) a .

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