Abstract

Gradient-index materials will provide new valuable degrees of freedom for the lens designer. The gradient-index single element lens is studied in terms of its third-order aberration coefficients, ray-trace analysis, and wave-front error.

© 1977 Optical Society of America

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References

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  1. D. T. Moore, “Design of Singlets with Continuously Varying Indices of Refractions,” J. Opt. Soc. Am. 61, 886–894 (1971).
    [Crossref]
  2. D. T. Moore and P. J. Sands, “Optical System Comprising a Singlet Element Having a Continuously Varying Index of Refraction,” U. S. Patent No. 3 729 253, April1973.
  3. D. Malacara, “Two Lenses to Collimate Red Laser Light,” Appl. Opt. 4, 1652 (1965).
    [Crossref]
  4. D. T. Moore, “Aberration Correction Using Index Gradients,” M. S. thesis (University of Rochester, 1971) p. 1–16.
  5. D. T. Moore, “Ray Tracing in Gradient-Index Media,” J. Opt. Soc. Am. 65, 45 (1975).
    [Crossref]
  6. The design, evaluation, and tolerance analysis were carried out using the ADIOS Gradient-Index Lens Design Program.Information concerning the details of this program can be obtained by writing to the author of this paper.

1975 (1)

D. T. Moore, “Ray Tracing in Gradient-Index Media,” J. Opt. Soc. Am. 65, 45 (1975).
[Crossref]

1971 (1)

1965 (1)

Malacara, D.

Moore, D. T.

D. T. Moore, “Ray Tracing in Gradient-Index Media,” J. Opt. Soc. Am. 65, 45 (1975).
[Crossref]

D. T. Moore, “Design of Singlets with Continuously Varying Indices of Refractions,” J. Opt. Soc. Am. 61, 886–894 (1971).
[Crossref]

D. T. Moore, “Aberration Correction Using Index Gradients,” M. S. thesis (University of Rochester, 1971) p. 1–16.

D. T. Moore and P. J. Sands, “Optical System Comprising a Singlet Element Having a Continuously Varying Index of Refraction,” U. S. Patent No. 3 729 253, April1973.

Sands, P. J.

D. T. Moore and P. J. Sands, “Optical System Comprising a Singlet Element Having a Continuously Varying Index of Refraction,” U. S. Patent No. 3 729 253, April1973.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Other (3)

The design, evaluation, and tolerance analysis were carried out using the ADIOS Gradient-Index Lens Design Program.Information concerning the details of this program can be obtained by writing to the author of this paper.

D. T. Moore and P. J. Sands, “Optical System Comprising a Singlet Element Having a Continuously Varying Index of Refraction,” U. S. Patent No. 3 729 253, April1973.

D. T. Moore, “Aberration Correction Using Index Gradients,” M. S. thesis (University of Rochester, 1971) p. 1–16.

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Figures (13)

FIG. 1
FIG. 1

Spot diagram axial gradient singlet, f/4, fl = 20 cm, no tilt of gradient, diameter of airy disk is 4. 3 μm.

FIG. 2
FIG. 2

Spot diagram axial gradient singlet, f/4, fl = 20 cm, tilt of gradient relative to optical axis = 5 mrad.

FIG. 3
FIG. 3

Spot diagram axial gradient singlet, f/4, fl = 20 cm, tilt of gradient relative to optical axis = 10 mrad.

FIG. 4
FIG. 4

OPD plot, axial gradient singlet, f/4, fl = 20 cm, curve A tilt= 0. 0, curve B tilt = 0. 05 mrad, curve C tilt = 1 mrad.

FIG. 5
FIG. 5

OPD plot effect of variation of linear term, N01, of polynomial expansion of index of refraction profile. f/4 axial gradient singlet. Curve A, N01 = −0. 0303 cm−1; curve B, N01 = −0. 031 cm−1; curve C, N01 = −0. 033 cm−1; curve D, N01= −0. 035 cm−1; The OPD has been evaluated at an image plane such that the OPD is zero at edge of the aperture.

FIG. 6
FIG. 6

OPD plot, effect of quadratic term, N02, of polynomial expansion of index of refraction profile. f/4 axial gradient singlet. Curve A, N02 = 0. 0; curve B, N02 = 0. 001 cm−2; curve C, N02 = 0. 005 cm−2. OPD has been evaluated at an image plane such that the OPD is zero at edge of the aperture.

FIG. 7
FIG. 7

OPD plot; effect of cubic term, N03, of Polynomial expansion of index of refraction profile f/4 axial gradient singlet. Curve A, N03 = 0. 0; curve B, N03 = 0. 01 cm−3; curve c, N03 = 0. 025 cm−3; OPD has been evaluated at an image plane such that the OPD is zero at edge of the aperture.

FIG. 8
FIG. 8

Ray intercept plot: effect of various index profiles beyond maximum sag point of first surface. f/4 axial gradient singlet. Curve A, homogeneous; curve B, N = 1. 64 + 0. 03x; curve C, N = 1. 64 + 0. 03x + 0. 1x2.

FIG. 9
FIG. 9

OPD plot: Spherochromatism, f/4 axial gradient singlet. Curve A, base index at 0. 5145 μm, gradient profile at 0. 5145μm; curve B, base index at 0. 06328 μm, gradient profile at 0. 5145 μm; curve C, base index at 0. 6328 μm, gradient profile at 0. 6328 μm.

FIG. 10
FIG. 10

Transverse aberration plot for a single element f/5 lens, with radial gradient fl = 10. 0 cm. Index of refraction = 1. 522 + 0. 983r2 + 0. 03222r4 N30r6 + N40r8; σ1 = σ2 = σ3 = 0. 0; curve A: N30 = N40 = 0. 0; curve B: N30 ≠ 0. 0, N40 = 0. 0; curve C: N30 ≠ 0. 0, N40 ≠ 0. 0.

FIG. 11
FIG. 11

Transverse aberration plot for a single element f/5 collimator, with shallow radial gradient. fl = 10. 0 cm, index of refraction=1. 55 + 0. 000261r4 + N30r6. σ1 = σ2 = 0. 0. Curve A, N30 = 0. 0; curve B, N30 = +0. 000030 cm−6.

FIG. 12
FIG. 12

OPD: shallow radial gradient singlet f/5; curve A, tilt of gradient relative to optical axis = 0. 0; curve B, tilt of gradient = 5. 0 mrad; curve C, tilt of gradient = 10. 0 mrad; curve D, tilt of gradient = 50. 0 mrad.

FIG. 13
FIG. 13

OPD plot: shallow radial gradient singlet f/5; curve A, decentration of gradient relative to optical axis = 0. 0 cm; curve B, decentration = 0. 01 cm; curve C, decentration=0. 05 cm.

Tables (9)

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TABLE I A Parameters of f/4 axial gradient collimator.

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TABLE I B Third-order aberrations of f/4 collimator.

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TABLE II Tolerance analysis for f/4 axial gradient collimator.

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TABLE III Chromatic variation of index of refraction profile.

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TABLE IV A Parameters of f/5 radial gradient singlet.

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TABLE IV B Third-order aberrations of f/5 collimator.

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TABLE V A Parameters of f/5 shallow radial gradient collimator.

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TABLE V B Third-order aberrations of f/5 shallow radial gradient collimator.

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TABLE VI Tolerancing analysis for shallow radial gradient collimator.

Equations (3)

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N ( x ) = N 00 + N 01 x + N 02 x 2 + .
N ( ξ ) = N 00 + N 10 ξ + N 20 ξ 2 + ,
N = 1. 520600 0. 033444 x .