Abstract

Two different aspherical singlets, four types of axial gradient-index singlet, and one radial gradient-index singlet achieving the same performance are toleranced for thickness, curvatures, base index, and special coefficient (aspheric or gradient) sensitivities. The results show that the singlet with the most relaxed tolerances has a linear axial gradient which extends through the lens, followed in order by a singlet with a parabolic radial gradient, a singlet with an aspheric surface on the front, and a singlet with a parabolic axial gradient crossing the first surface.

© 1990 Optical Society of America

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References

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  1. W. L. Wolfe, “Optical Materials,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, Eds. (Office of Naval Research, Department of the Navy, Washington DC, 1978), pp. 7.1–7.137.
  2. code v, Optical Research Associates, Pasadena, CA.
  3. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  4. P. J. Sands, “Inhomogeneous Lenses, IV, Aberrations of Lenses with Axial Index Distributions,” J. Opt. Soc. Am. 61, 1086–1091 (1971).
    [CrossRef]
  5. D. T. Moore, P. J. Sands, “Third-Order Aberrations of Inhomogeneous Lenses with Cylindrical Index Distributions,” J. Opt. Soc. Am. 61, 1195–1201 (1971).
    [CrossRef]
  6. D. T. Moore, J. R. Zinter, “Infrared Gradient-Index Design,” Photonics Spectra 22 (7), 117–122 (1988).

1988 (1)

D. T. Moore, J. R. Zinter, “Infrared Gradient-Index Design,” Photonics Spectra 22 (7), 117–122 (1988).

1971 (2)

Moore, D. T.

Sands, P. J.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

Wolfe, W. L.

W. L. Wolfe, “Optical Materials,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, Eds. (Office of Naval Research, Department of the Navy, Washington DC, 1978), pp. 7.1–7.137.

Zinter, J. R.

D. T. Moore, J. R. Zinter, “Infrared Gradient-Index Design,” Photonics Spectra 22 (7), 117–122 (1988).

J. Opt. Soc. Am. (2)

Photonics Spectra (1)

D. T. Moore, J. R. Zinter, “Infrared Gradient-Index Design,” Photonics Spectra 22 (7), 117–122 (1988).

Other (3)

W. L. Wolfe, “Optical Materials,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, Eds. (Office of Naval Research, Department of the Navy, Washington DC, 1978), pp. 7.1–7.137.

code v, Optical Research Associates, Pasadena, CA.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

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Figures (4)

Fig. 1
Fig. 1

Layout of the optimized spherical homogeneous lens. The 10-mm thick lens has the following characteristics: R1 = 51.62 mm, R2 = 67.23 mm, FNO = 1, EFL = 50 mm, and half field of view = 1°.

Fig. 2
Fig. 2

Ray aberration plot for the optimized homogeneous lens.

Fig. 3
Fig. 3

Ray aberration plot for the optimized special lenses. All the lenses have similar ray aberration plots. The differences can only be detected in the third-order aberration contributions.

Fig. 4
Fig. 4

Tolerances on the different lens parameters. The curves show the Strehl ratio as a function of the percent change in (a) the first surface thickness, (b) the sag for aspheric lenses or the index change for the GRIN lenses, (c) the base index following the first surface, (d) the curvature of the first surface, and (e) the curvature of the second surface.

Tables (2)

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Table I Data for the Optimized Lenses

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Table II Tolerancing: Absolute Range of Permissible Change

Equations (3)

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z = c r 2 1 + 1 - ( κ + 1 ) c 2 r 2 + d r 4 + e r 6 + f r 8 + ,
N ( ρ , z ) = N 00 + N 01 z + N 02 z 2 + N 03 z 3 + + N 10 ( z ) r 2 + N 20 ( z ) r 4 + ,
Φ g = - 2 N 10 T ,

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