Abstract

An axial gradient-index (GRIN) lens, where the refractive index varies along the optical axis of a convex lens, can reduce the spherical aberration compared with the conventional homogeneous lens. The transparent plastic axial GRIN material was successfully fabricated by chemical copolymerization and diffusion techniques. The depth of the gradient index was ~20 mm with the refractive-index change Δn = 0.07. By carrying out the ray tracing of the axial gradient index, the optimum refractive-index distribution reducing the spherical aberration was determined. If we assume that the axial GRIN lens was constructed from the sample experimentally obtained, it was theoretically confirmed that the spherical aberration of this lens would be remarkably improved.

© 1985 Optical Society of America

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References

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  1. D. T. Moore, “Design of Single-Element Gradient-Index Collimator,” J. Opt. Soc. Am. 67, 1137 (1977).
    [CrossRef]
  2. Y. Ohtsuka, Y. Koike, “Studies on the Light-Focusing Plastic Rod. 16: Mechanism of Gradient-Index Formation in Photocopolymerization of Multiple Monomer Systems,” Appl. Opt. 23, 1774 (1984).
    [CrossRef] [PubMed]
  3. Y. Koike, H. Hatanaka, Y. Ohtsuka, “Studies on the Light-Focusing Plastic Rod. 17: Plastic GRIN Rod Lens Prepared by Photocopolymerization of a Ternary Monomer System,” Appl. Opt. 23, 1779 (1984).
    [CrossRef] [PubMed]
  4. 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]
  5. Registered trade name of Carl Zeiss, Jena, East Germany.
  6. I. Kitano, K. Nishizawa, A. Momokita, “Diffusion Behavior of Doped Polarizable Ions in Glass During the Ion-Exchange Process,” Appl. Opt. 21, 1017 (1982).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 122.

1984 (2)

1982 (1)

1980 (1)

1977 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 122.

Hatanaka, H.

Kitano, I.

Koike, Y.

Momokita, A.

Moore, D. T.

Nishizawa, K.

Ohtsuka, Y.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 122.

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Figures (12)

Fig. 1
Fig. 1

Block diagram of the chemical copolymerization technique.

Fig. 2
Fig. 2

Change of copolymer composition with conversion P in the MMA–AN–VB system. Each mark (○,Δ,+,×) represents a copolymer composition at P = 5 wt.% (k = l,2…). MMA/AN/VB (wt./wt./wt.): A, 1/0/0; B, 1/1/3; C, 1/1.5/3; D, 1/2/3.

Fig. 3
Fig. 3

Block diagram of the diffusion technique: (a) vapor–phase diffusion; (b) liquid-phase diffusion.

Fig. 4
Fig. 4

Measurement of the axial-GRIN material by the partial splitting method by Interphako interference microscopy.

Fig. 5
Fig. 5

Refractive-index distributions of the samples prepared by the chemical copolymerization technique.

Fig. 6
Fig. 6

Index distributions of the samples prepared by the liquid-phase diffusion technique.

Fig. 7
Fig. 7

Index distribution of the sample by the vapor-phase diffusion technique.

Fig. 8
Fig. 8

Axial gradient-index lens.

Fig. 9
Fig. 9

Dependence of the longitudinal spherical aberration on β in Eq. (9) when d = 5 mm and Δn = 0.05: A, β = 0.8, ρ = 25.0 mm, ϕ = 30 mm; B, β = 1.0, ρ = 29.0 mm, ϕ = 32.6 mm; C, β = 1.5, ρ = 42.5 mm, ϕ = 40 mm.

Fig. 10
Fig. 10

Longitudinal spherical aberrations for β = 1.000 and β = 1.005; d = 5 mm and Δn = 0.05.

Fig. 11
Fig. 11

Index distribution of the sample fabricated by the liquid-phase diffusion technique.

Fig. 12
Fig. 12

Longitudinal spherical aberration δ of the lens with the index distribution of the sample in Fig. 11. ϕ (mm): A, 15.8; B, 16.5; C, 17.0. (Curve D is a homogeneous lens with a 15.8-mm diameter).

Equations (9)

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n ( z i ) = λ D t Δ R i + n base , z i = i · Δ z ,
d d s ( n d r d s ) = n ,
d d s ( n d x d s ) = 0 d d s ( n d y d s ) = 0 .
x d = z 0 d F ( z ) d z ,
F ( z ) = ( d x d s ) z = z 0 [ n ( z ) n ( z 0 ) ] 2 [ ( d x d s ) z = z 0 ] 2 ,
z 0 = ρ { 1 cos [ sin 1 ( x 0 ρ ) ] } .
δ = l l 0 = ( d + x d tan ψ ) l 0 ,
ψ = sin 1 [ n ( d ) sin | tan 1 F ( d ) | ] .
n ( z ) = n ( 0 ) ( 1 A z β ) ,

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