Abstract

Two different types of Gauss lens design, which effectively eliminate primary chromatic aberration, are presented using an efficient genetic algorithm (GA). The current GA has to deal with too many targets in optical global optimization so that the performance is not much improved. Generally speaking, achromatic aberrations have a great relationship with variable glass sets for all elements. For optics whose design is roughly convergent, glass sets for optics will play a significant role in axial and lateral color aberration. Therefore better results might be derived from the optimal process of eliminating achromatic aberration, which could be carried out by finding feasible glass sets in advance. As an alternative, we propose a new optimization process by using a GA and involving theories of geometrical optics in order to select the best optical glass combination. Two Gauss-type lens designs are employed in this research. First, a telephoto lens design is sensitive to axial aberration because of its long focal length, and second, a wide-angle Gauss design is complicated by lateral color aberration at the extreme corners because Gauss design is well known not to deal well with wide-angle problems. Without numbers of higher chief rays passing the element, it is difficult to correct lateral color aberration altogether for the Gauss design. The results and conclusions show that the attempts to eliminate primary chromatic aberrations were successful.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Levenberg, "A method for the solution of certain problems in least squares," Q. Appl. Math. 2, 164-168 (1994).
  2. D. Vasiljevic, "Optimization of the Cooke triplet with the various evolution strategies and the damped least squares," Proc. SPIE 3780, 207-215 (1999).
    [CrossRef]
  3. D. Vasiljevic and J. Golobic, "Comparison of the classical damped least squares and genetic algorithm in the optimization of the doublet," in Proceedings of the First Workshop on Soft Computing (Nagoya, Japan, 1996), pp. 200-204.
  4. K. E. Moore, "Algorithm for global optimization of optical systems based upon genetic competition," Proc. SPIE 3780, 40-47 (1999).
    [CrossRef]
  5. J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 6342, 63420M (2006).
    [CrossRef]
  6. M. Isshiki, D. C. Sinclair, and S. Kaneko, "Lens design: global optimization of both performance and tolerance sensitivity," Proc. SPIE 6342, 63420N (2006).
    [CrossRef]
  7. J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 6342, 63420O (2006).
    [CrossRef]
  8. S. Banerjee and L. N. Hazra, "Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm," J. Mod. Opt. 49, 1111-1123 (2002).
    [CrossRef]
  9. D. C. Van Leijenhorst, C. B. Lucasius, and Jos M. Thijssen, "Optical design with the aid of a genetic algorithm," BioSystems 37, 177-187 (1996).
    [CrossRef]
  10. X. Chen and K. Yamamoto, "An experiment in genetic optimization in lens design," J. Mod. Opt. 44, 1693-1702 (1997).
    [CrossRef]
  11. I. Ono, S. Kobeyashi, and K. Yoshida, "Global and multiobjective optimization for lens design by real-coded genetic algorithms," Proc. SPIE 3482, 110-121 (1998).
  12. Y.-C. Fang and J. MacDonald, "Optimizing chromatic aberration calibration using a novel genetic algorithm," J. Mod. Opt. 53, 1411-1427 (2006).
    [CrossRef]
  13. W. J. Smith, Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000), pp. 61-89.
  14. L. Nigel, "Some applications of neural networks in optics and image processing," Ph.D. dissertation (University of Reading, 1998), pp. 9-47.
  15. J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975), pp. 88-94.
  16. D. E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison-Wesley, 1989), pp. 151-159.
  17. L. Davis, Handbook of Genetic Algorithms (Van Nostrand Reinhold, 1991).

2006

J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 6342, 63420M (2006).
[CrossRef]

M. Isshiki, D. C. Sinclair, and S. Kaneko, "Lens design: global optimization of both performance and tolerance sensitivity," Proc. SPIE 6342, 63420N (2006).
[CrossRef]

J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 6342, 63420O (2006).
[CrossRef]

Y.-C. Fang and J. MacDonald, "Optimizing chromatic aberration calibration using a novel genetic algorithm," J. Mod. Opt. 53, 1411-1427 (2006).
[CrossRef]

2002

S. Banerjee and L. N. Hazra, "Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm," J. Mod. Opt. 49, 1111-1123 (2002).
[CrossRef]

1999

D. Vasiljevic, "Optimization of the Cooke triplet with the various evolution strategies and the damped least squares," Proc. SPIE 3780, 207-215 (1999).
[CrossRef]

K. E. Moore, "Algorithm for global optimization of optical systems based upon genetic competition," Proc. SPIE 3780, 40-47 (1999).
[CrossRef]

1998

I. Ono, S. Kobeyashi, and K. Yoshida, "Global and multiobjective optimization for lens design by real-coded genetic algorithms," Proc. SPIE 3482, 110-121 (1998).

1997

X. Chen and K. Yamamoto, "An experiment in genetic optimization in lens design," J. Mod. Opt. 44, 1693-1702 (1997).
[CrossRef]

1996

D. C. Van Leijenhorst, C. B. Lucasius, and Jos M. Thijssen, "Optical design with the aid of a genetic algorithm," BioSystems 37, 177-187 (1996).
[CrossRef]

1994

K. Levenberg, "A method for the solution of certain problems in least squares," Q. Appl. Math. 2, 164-168 (1994).

Banerjee, S.

S. Banerjee and L. N. Hazra, "Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm," J. Mod. Opt. 49, 1111-1123 (2002).
[CrossRef]

Chen, X.

X. Chen and K. Yamamoto, "An experiment in genetic optimization in lens design," J. Mod. Opt. 44, 1693-1702 (1997).
[CrossRef]

Davis, L.

L. Davis, Handbook of Genetic Algorithms (Van Nostrand Reinhold, 1991).

Fang, Y.-C.

Y.-C. Fang and J. MacDonald, "Optimizing chromatic aberration calibration using a novel genetic algorithm," J. Mod. Opt. 53, 1411-1427 (2006).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison-Wesley, 1989), pp. 151-159.

Golobic, J.

D. Vasiljevic and J. Golobic, "Comparison of the classical damped least squares and genetic algorithm in the optimization of the doublet," in Proceedings of the First Workshop on Soft Computing (Nagoya, Japan, 1996), pp. 200-204.

Hazra, L. N.

S. Banerjee and L. N. Hazra, "Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm," J. Mod. Opt. 49, 1111-1123 (2002).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975), pp. 88-94.

Isshiki, M.

M. Isshiki, D. C. Sinclair, and S. Kaneko, "Lens design: global optimization of both performance and tolerance sensitivity," Proc. SPIE 6342, 63420N (2006).
[CrossRef]

Kaneko, S.

M. Isshiki, D. C. Sinclair, and S. Kaneko, "Lens design: global optimization of both performance and tolerance sensitivity," Proc. SPIE 6342, 63420N (2006).
[CrossRef]

Kobeyashi, S.

I. Ono, S. Kobeyashi, and K. Yoshida, "Global and multiobjective optimization for lens design by real-coded genetic algorithms," Proc. SPIE 3482, 110-121 (1998).

Levenberg, K.

K. Levenberg, "A method for the solution of certain problems in least squares," Q. Appl. Math. 2, 164-168 (1994).

Lucasius, C. B.

D. C. Van Leijenhorst, C. B. Lucasius, and Jos M. Thijssen, "Optical design with the aid of a genetic algorithm," BioSystems 37, 177-187 (1996).
[CrossRef]

MacDonald, J.

Y.-C. Fang and J. MacDonald, "Optimizing chromatic aberration calibration using a novel genetic algorithm," J. Mod. Opt. 53, 1411-1427 (2006).
[CrossRef]

McGuire, J. P.

J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 6342, 63420O (2006).
[CrossRef]

Moore, K. E.

K. E. Moore, "Algorithm for global optimization of optical systems based upon genetic competition," Proc. SPIE 3780, 40-47 (1999).
[CrossRef]

Nigel, L.

L. Nigel, "Some applications of neural networks in optics and image processing," Ph.D. dissertation (University of Reading, 1998), pp. 9-47.

Ono, I.

I. Ono, S. Kobeyashi, and K. Yoshida, "Global and multiobjective optimization for lens design by real-coded genetic algorithms," Proc. SPIE 3482, 110-121 (1998).

Rogers, J. R.

J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 6342, 63420M (2006).
[CrossRef]

Sinclair, D. C.

M. Isshiki, D. C. Sinclair, and S. Kaneko, "Lens design: global optimization of both performance and tolerance sensitivity," Proc. SPIE 6342, 63420N (2006).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000), pp. 61-89.

Thijssen, Jos M.

D. C. Van Leijenhorst, C. B. Lucasius, and Jos M. Thijssen, "Optical design with the aid of a genetic algorithm," BioSystems 37, 177-187 (1996).
[CrossRef]

Van Leijenhorst, D. C.

D. C. Van Leijenhorst, C. B. Lucasius, and Jos M. Thijssen, "Optical design with the aid of a genetic algorithm," BioSystems 37, 177-187 (1996).
[CrossRef]

Vasiljevic, D.

D. Vasiljevic, "Optimization of the Cooke triplet with the various evolution strategies and the damped least squares," Proc. SPIE 3780, 207-215 (1999).
[CrossRef]

D. Vasiljevic and J. Golobic, "Comparison of the classical damped least squares and genetic algorithm in the optimization of the doublet," in Proceedings of the First Workshop on Soft Computing (Nagoya, Japan, 1996), pp. 200-204.

Yamamoto, K.

X. Chen and K. Yamamoto, "An experiment in genetic optimization in lens design," J. Mod. Opt. 44, 1693-1702 (1997).
[CrossRef]

Yoshida, K.

I. Ono, S. Kobeyashi, and K. Yoshida, "Global and multiobjective optimization for lens design by real-coded genetic algorithms," Proc. SPIE 3482, 110-121 (1998).

BioSystems

D. C. Van Leijenhorst, C. B. Lucasius, and Jos M. Thijssen, "Optical design with the aid of a genetic algorithm," BioSystems 37, 177-187 (1996).
[CrossRef]

J. Mod. Opt.

X. Chen and K. Yamamoto, "An experiment in genetic optimization in lens design," J. Mod. Opt. 44, 1693-1702 (1997).
[CrossRef]

Y.-C. Fang and J. MacDonald, "Optimizing chromatic aberration calibration using a novel genetic algorithm," J. Mod. Opt. 53, 1411-1427 (2006).
[CrossRef]

S. Banerjee and L. N. Hazra, "Structural design of broken contact doublets with prespecified aberration targets using genetic algorithm," J. Mod. Opt. 49, 1111-1123 (2002).
[CrossRef]

Proc. SPIE

D. Vasiljevic, "Optimization of the Cooke triplet with the various evolution strategies and the damped least squares," Proc. SPIE 3780, 207-215 (1999).
[CrossRef]

K. E. Moore, "Algorithm for global optimization of optical systems based upon genetic competition," Proc. SPIE 3780, 40-47 (1999).
[CrossRef]

J. R. Rogers, "Using global synthesis to find tolerance-insensitive design forms," Proc. SPIE 6342, 63420M (2006).
[CrossRef]

M. Isshiki, D. C. Sinclair, and S. Kaneko, "Lens design: global optimization of both performance and tolerance sensitivity," Proc. SPIE 6342, 63420N (2006).
[CrossRef]

J. P. McGuire, Jr., "Designing easily manufactured lenses using a global method," Proc. SPIE 6342, 63420O (2006).
[CrossRef]

Q. Appl. Math.

K. Levenberg, "A method for the solution of certain problems in least squares," Q. Appl. Math. 2, 164-168 (1994).

Other

D. Vasiljevic and J. Golobic, "Comparison of the classical damped least squares and genetic algorithm in the optimization of the doublet," in Proceedings of the First Workshop on Soft Computing (Nagoya, Japan, 1996), pp. 200-204.

W. J. Smith, Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000), pp. 61-89.

L. Nigel, "Some applications of neural networks in optics and image processing," Ph.D. dissertation (University of Reading, 1998), pp. 9-47.

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975), pp. 88-94.

D. E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning (Addison-Wesley, 1989), pp. 151-159.

L. Davis, Handbook of Genetic Algorithms (Van Nostrand Reinhold, 1991).

I. Ono, S. Kobeyashi, and K. Yoshida, "Global and multiobjective optimization for lens design by real-coded genetic algorithms," Proc. SPIE 3482, 110-121 (1998).

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 (11)

Fig. 1
Fig. 1

(Color online) Mobile phone lens of a Cooke triplet (a) without and (b) with a GA process.

Fig. 2
Fig. 2

(Color online) Modulation transfer function (MTF) of a mobile phone lens (a) without and (b) with a GA process.

Fig. 3
Fig. 3

(Color online) Diagram of chromatic aberration.

Fig. 4
Fig. 4

Relationship between lateral aberration and stop.

Fig. 5
Fig. 5

(Color online) Gauss lens with (a) a telephoto lens and (b) a wide-angle lens.

Fig. 6
Fig. 6

Flow diagram of the GA.

Fig. 7
Fig. 7

(Color online) The average object values of 10 GA rounds for (a) a telephoto lens and (b) a wide-angle lens.

Fig. 8
Fig. 8

(Color online) Best object value among 10 GA rounds for (a) a telephoto lens and (b) a wide-angle lens.

Fig. 9
Fig. 9

(Color online) Best object value of a telephoto lens with pop_size x generation = 10 6 for two different mutation probabilities of (a) Pm = 0.2 and (b) Pm = 0.4.

Fig. 10
Fig. 10

(Color online) Best object value of a wide-angle lens with pop_size x generation = 10 6 for two different mutation probabilities of (a) Pm = 0.2 and (b) Pm = 0.4.

Fig. 11
Fig. 11

(Color online) Average mean object value of 10 GA rounds with three different mutation probabilities running 100 generations for (a) a telephoto lens and (b) a wide-angle lens.

Tables (3)

Tables Icon

Table 1 Lens Data of the Simulation of the Telephoto Lens and the Wide-Angle Lens

Tables Icon

Table 2 First Five Best Glass Sets of Running GA for Telephoto Lenses

Tables Icon

Table 3 First Five Best Glass Sets of Running GA for Wide-Angle Lenses

Equations (20)

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

C L = A 1 h 1 Δ ( δ n / n ) 1 + A 2 h 2 Δ ( δ n / n ) 2 ,
A 1 h 1 Δ ( δ n / n ) 1 ( t h e f i r s t f a c e a x i a l c h o r o m a t i c a b e r r a t i o n ) ,
A 2 h 2 Δ ( δ n / n ) 2 ( t h e sec o n d f a c e a x i a l c h o r o m a t i c a b e r r a t i o n ) ,
h 1 = h 2 = h ( b e i n g o n l y a g l a s s m e d i u m ) ,
( δ n / n ) 1 = δ n / n 0 : Δ ( δ n / n ) 2 = 0 δ n / n ( l i g h t r a y s e n t e r t h e f i r s t l e n s f r o m t h e a i r m e di u m a n d e m e r g e f r o m t h e sec o n d l e n s into t h e     a i r medium on the other side ) .
C L = h ( δ n / n ) ( A 1 A 2 ) A 1 = h c 1 + u 1 , A 2 = h c 2 + u 2 ,
C L = h ( δ n / n ) ( h c 1 + u 1 h c 2 u 2 ) = h ( δ n / n ) [ h ( c 1 c 2 ) + ( u 1 u 2 ) ]
= h 2 ( δ n / n ) [ K ( n 1 ) + K ] = h 2 K ( δ n / n ) ( n n 1 )
= h 2 K ( n 1 n V ) ( n n 1 )
= h 2 K / V .
C T = A ¯ A C L = h ¯ h ( h 2 K V ) = h ¯ h K V ,
A = n ( h c + u ) A ¯ = n ( h ¯ c + u ¯ ) ( re f r a c t i v e var i a n t ) ,
H E = h ¯ h ( c e n t r i f u g a l p a r a m e t e r ) .
K 1 + K 2 + K 3 = 1 ,
h = constant K 1 V 1 + K 2 V 2 + K 3 V 3 = 0.
T c h C = y i p n k u k ( Δ n n n Δ n ) lateral   chromatic aberration   ( vertical   direction ) ,
T A c h C = y i n k u k ( Δ n n n Δ n ) transverse chromatic   aberration ( vertical   direction ) ,
L A c h C = T A c h C u k longitudinal chromatic   aberration ( horizontal   direction ) .
o b j _ v a l u e ( i ) = w L | AX | + w T | LAT | ,
p ( i ) = ( m a x o b j _ v a l u e ( i ) ) / [ n = 1 p o p _ s i z e m a x o b j _ v a l u e ( n ) ] ,

Metrics