Abstract

This study investigates the role of gradient-index materials in the design of Cooke triplets for use as 35-mm format photographic objectives. Cooke triplet designs are presented with different types of gradient-index profiles. Both linear axial and shallow radial gradients are shown to provide effective control of spherical aberration and astigmatism. In particular, a Cooke triplet with a combination of both linear axial and radial gradients attains performance comparable to a six-element double Gauss lens. In virtually all cases, the use of gradient-index components improves the Cooke triplets’ performance significantly.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. P. Bowen et al., “Radial Gradient-Index Eyepiece Design,” Appl. Opt. 27, 3170–3176 (1988).
    [CrossRef] [PubMed]
  2. L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, 993–998 (1982).
    [CrossRef] [PubMed]
  3. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 345.
  4. Code V is a proprietary product of Optical Research Associates, Pasadena, CA.
  5. P. J. Sands, “Third-Order Aberrations of Inhomogeneous Lenses,” J. Opt. Soc. Am. 60, 1436–1443 (1970).
    [CrossRef]
  6. D. T. Moore, “Aberration Correction Using Index Gradients,” M. S. Thesis, U. Rochester (1970), p. 53.
  7. P. J. Sands, “Inhomogeneous Lenses, III. Paraxial Optics,” J. Opt. Soc. Am. 61, 879–885 (1971).
    [CrossRef]
  8. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 94.
  9. R. W. Wood, Physical Optics (Macmillan, New York, 1934), p. 88.
  10. W. Mandler, Proc. Soc. Photo-Opt. Instrum. Eng. 237, 222 (1980).

1988 (1)

1982 (1)

1980 (1)

W. Mandler, Proc. Soc. Photo-Opt. Instrum. Eng. 237, 222 (1980).

1971 (1)

1970 (1)

Atkinson, L. G.

Bowen, J. P.

Houde-Walter, S. N.

Mandler, W.

W. Mandler, Proc. Soc. Photo-Opt. Instrum. Eng. 237, 222 (1980).

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 94.

Moore, D. T.

Ryan, D. P.

Sands, P. J.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 345.

Stagaman, J. M.

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, 1934), p. 88.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. Mandler, Proc. Soc. Photo-Opt. Instrum. Eng. 237, 222 (1980).

Other (5)

E. W. Marchand, Gradient Index Optics (Academic, New York, 1978), p. 94.

R. W. Wood, Physical Optics (Macmillan, New York, 1934), p. 88.

D. T. Moore, “Aberration Correction Using Index Gradients,” M. S. Thesis, U. Rochester (1970), p. 53.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 345.

Code V is a proprietary product of Optical Research Associates, Pasadena, CA.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Abbreviated glass map where each line indicates the crown/flint glass pair and the resulting error function value associated with that lens.

Fig. 2
Fig. 2

Abbreviated glass map where each line indicates the crown/flint glass pair and the resulting error function value associated with that lens.

Fig. 3
Fig. 3

Abbreviated glass map where each line indicates the crown/flint glass pair and the resulting error function value associated with that lens.

Fig. 4
Fig. 4

(a) Layout; (b) ray aberration plots; and (c) field curves for lens 2 from Table II.

Fig. 5
Fig. 5

(a) Layout; (b) ray aberration plots; and (c) field curves for lens 2 from Table III.

Fig. 6
Fig. 6

(a) Layout; (b) ray aberration plots; and (c) field curves for the f/2.8 GRIN triplet with a linear axial gradient in the first element and a radial gradient in the last element. The corresponding six-digit glass code is given for each element and the Δn for the two GRIN elements.

Fig. 7
Fig. 7

(a) MTF for Mandler’s 1975 double Gauss optimized at f/2.8; (b) MTF for GRIN triplet optimized at f/2.8.

Tables (3)

Tables Icon

Table I Glass Pairs for the Homogeneous Lenses Studied

Tables Icon

Table II Linear Axial Gradients in First and Third Elements

Tables Icon

Table III Shallow Radial Gradients in First and Third Elements

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

N ( z , r ) = N 0 ( z ) + N 1 ( z ) r 2 + N 2 ( z ) r 4 + ,
N i ( z ) = N i 0 + N i 1 z + N i 2 z 2 + ,
N ( z ) = N 00 + N 01 z + N 02 z 2 + , V 0 i N 0 i , d N 0 i , f - N 0 i , c ,             i 0 ,
N ( r ) = N 00 + N 10 r 2 + N 20 r 4 + , V i 0 N i 0 , d N i 0 , f - N i 0 , c ,             i 0 ,
σ i = - a i n k u a k             i = 1 , 5
a 1 = a + κ y a 4 ,             a = N 0 2 ( N 0 N 0 - 1 ) y a i a 2 ( i a + u a ) ,
a 2 = q a + κ y a 3 y b ,             κ = - 1 2 c 2 Δ ( N 01 ) ,
a 3 = q 2 a + κ y a 2 y b 2 ,
σ i = - 1 n k n a K ( a i + a i * )             i = 1 , 5
a 1 * = 1 2 ( N 00 y a u a 3 ) + 0 t ( 4 N 20 y a 4 - 1 2 N 00 u a 4 ) d z ,
a 2 * = 1 2 ( N 00 y a u a 2 u b ) + 0 t ( 4 N 20 y a 3 y b - 1 4 N 00 u a 3 u b ) d z ,
a 3 * = 1 2 ( N 00 y a u a u b 2 ) + 0 t ( 4 N 20 y a 2 y a 2 - 1 4 N 00 u a 2 u b 2 ) d z ,
Φ g = - 2 N 10 t ,
σ 4 H 2 n k u a k ( Φ g 2 N 00 2 ) ,

Metrics