Abstract

An approach for ab initio synthesis of the thin lens structure of linearly compensated zoom lenses is reported. This method uses evolutionary programming that explores the available configuration space formed by powers of the individual components, the intercomponent separations, and the relative movement parameters of the moving components. Useful thin lens structures of optically and linearly compensated zoom lens systems are obtained by suitable formulation of the merit function of optimization. This paper reports our investigations on three-component zoom lens structures. Illustrative numerical results are presented.

© 2011 Optical Society of America

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References

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  1. D. Clark, Zoom Lenses (Hilger, 1973).
  2. M. Laikin, Lens Design (Dekker, 2001).
  3. R. Kingslake, “The development of the zoom lens,” J. SMPTE 69, 534–544 (1960).
  4. E. Betensky, “Zoom lens principles and types,” in Lens Design, Vol. CR41 of SPIE Critical Review Series (SPIE, 1992), pp. 88–116.
  5. T. H. Jamieson, “Thin-lens theory of zoom systems,” J. Mod. Opt. 17, 565–584 (1970).
    [CrossRef]
  6. A. Mikš, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47, 6088–6098 (2008).
    [CrossRef] [PubMed]
  7. K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol.  VI, E.Wolf, ed. (North-Holland, 1967), pp. 107–170.
  8. K. Tanaka, “Paraxial theory of lens design in terms of Gaussian brackets,” in Progress in Optics, Vol.  XXIII, E.Wolf, ed. (North-Holland, 1984), pp. 65–111.
  9. X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
    [CrossRef]
  10. F. G. Back and H. Lowen, “The basic theory of varifocal lenses with linear movement and optical compensation,” J. Opt. Soc. Am. 44, 684–691 (1954).
    [CrossRef]
  11. L. Bergstein, “General theory of optically compensated varifocal systems,” J. Opt. Soc. Am. 48154–171 (1958).
    [CrossRef]
  12. A. Mikš and J. Novák, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18, 6797–6810(2010).
    [CrossRef] [PubMed]
  13. D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43, 8–9 (2004).
    [CrossRef]
  14. R. J. Pegis and W. G. Peck, “First-order design theory for linearly compensated zoom systems,” J. Opt. Soc. Am. 52, 905–911 (1962).
    [CrossRef]
  15. G. Wooters and E. W. Silvertooth, “Optically compensated zoom lens,” J. Opt. Soc. Am. 55, 347–351 (1965).
    [CrossRef]
  16. I. Rechenberg, Evolutionsstrategie: Optimeirung Technischer System nach Prinzipen der Biologischen Evolution (Frommen-Holzboog Verlag, 1973).
  17. D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley, 1989).
  18. L. N. Hazra, “Structural design of multi-component lens systems,” Appl. Opt. 23, 4440–4443 (1984).
    [CrossRef] [PubMed]
  19. L. N. Hazra and S. Banerjee, “Genetic algorithm in structural design of Cooke triplet lenses,” Proc. SPIE 3737, 172–179(1999).
    [CrossRef]
  20. 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]
  21. S. Chatterjee and L. N. Hazra, “Structural design of a lens component with prespecified aberration targets by evolutionary algorithm ,” Proc. SPIE 6668, 66680S (2007).
    [CrossRef]
  22. S. Pal and L. N. Hazra, “Structural design of optically compensated zoom lenses using genetic algorithm,” Proc. SPIE 7429, 742910 (2009).
    [CrossRef]
  23. L. N. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
    [CrossRef]
  24. http://en.wikipedia.org/wiki/Floor_and_ceiling_functions.
  25. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  26. H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

2010 (2)

L. N. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
[CrossRef]

A. Mikš and J. Novák, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express 18, 6797–6810(2010).
[CrossRef] [PubMed]

2009 (1)

S. Pal and L. N. Hazra, “Structural design of optically compensated zoom lenses using genetic algorithm,” Proc. SPIE 7429, 742910 (2009).
[CrossRef]

2008 (1)

2007 (1)

S. Chatterjee and L. N. Hazra, “Structural design of a lens component with prespecified aberration targets by evolutionary algorithm ,” Proc. SPIE 6668, 66680S (2007).
[CrossRef]

2005 (1)

X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
[CrossRef]

2004 (1)

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43, 8–9 (2004).
[CrossRef]

2002 (1)

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 (1)

L. N. Hazra and S. Banerjee, “Genetic algorithm in structural design of Cooke triplet lenses,” Proc. SPIE 3737, 172–179(1999).
[CrossRef]

1984 (1)

1970 (1)

T. H. Jamieson, “Thin-lens theory of zoom systems,” J. Mod. Opt. 17, 565–584 (1970).
[CrossRef]

1965 (1)

1962 (1)

1960 (1)

R. Kingslake, “The development of the zoom lens,” J. SMPTE 69, 534–544 (1960).

1958 (1)

1954 (1)

Back, F. G.

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]

L. N. Hazra and S. Banerjee, “Genetic algorithm in structural design of Cooke triplet lenses,” Proc. SPIE 3737, 172–179(1999).
[CrossRef]

Bergstein, L.

Betensky, E.

E. Betensky, “Zoom lens principles and types,” in Lens Design, Vol. CR41 of SPIE Critical Review Series (SPIE, 1992), pp. 88–116.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Chatterjee, S.

S. Chatterjee and L. N. Hazra, “Structural design of a lens component with prespecified aberration targets by evolutionary algorithm ,” Proc. SPIE 6668, 66680S (2007).
[CrossRef]

Cheng, X.

X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
[CrossRef]

Clark, D.

D. Clark, Zoom Lenses (Hilger, 1973).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Hao, Q.

X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
[CrossRef]

Hazra, L. N.

L. N. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
[CrossRef]

S. Pal and L. N. Hazra, “Structural design of optically compensated zoom lenses using genetic algorithm,” Proc. SPIE 7429, 742910 (2009).
[CrossRef]

S. Chatterjee and L. N. Hazra, “Structural design of a lens component with prespecified aberration targets by evolutionary algorithm ,” Proc. SPIE 6668, 66680S (2007).
[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]

L. N. Hazra and S. Banerjee, “Genetic algorithm in structural design of Cooke triplet lenses,” Proc. SPIE 3737, 172–179(1999).
[CrossRef]

L. N. Hazra, “Structural design of multi-component lens systems,” Appl. Opt. 23, 4440–4443 (1984).
[CrossRef] [PubMed]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

Jamieson, T. H.

T. H. Jamieson, “Thin-lens theory of zoom systems,” J. Mod. Opt. 17, 565–584 (1970).
[CrossRef]

Kingslake, R.

R. Kingslake, “The development of the zoom lens,” J. SMPTE 69, 534–544 (1960).

Laikin, M.

M. Laikin, Lens Design (Dekker, 2001).

Lowen, H.

Martinez, T.

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43, 8–9 (2004).
[CrossRef]

Mikš, A.

Novák, J.

Novák, P.

Pal, S.

L. N. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
[CrossRef]

S. Pal and L. N. Hazra, “Structural design of optically compensated zoom lenses using genetic algorithm,” Proc. SPIE 7429, 742910 (2009).
[CrossRef]

Peck, W. G.

Pegis, R. J.

Rechenberg, I.

I. Rechenberg, Evolutionsstrategie: Optimeirung Technischer System nach Prinzipen der Biologischen Evolution (Frommen-Holzboog Verlag, 1973).

Sasian, J. M.

X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
[CrossRef]

Silvertooth, E. W.

Tanaka, K.

K. Tanaka, “Paraxial theory of lens design in terms of Gaussian brackets,” in Progress in Optics, Vol.  XXIII, E.Wolf, ed. (North-Holland, 1984), pp. 65–111.

Wang, Y.

X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
[CrossRef]

Wick, D. V.

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43, 8–9 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Wooters, G.

Yamaji, K.

K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol.  VI, E.Wolf, ed. (North-Holland, 1967), pp. 107–170.

Appl. Opt. (2)

J. Mod. Opt. (2)

T. H. Jamieson, “Thin-lens theory of zoom systems,” J. Mod. Opt. 17, 565–584 (1970).
[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]

J. Opt. Soc. Am. (4)

J. SMPTE (1)

R. Kingslake, “The development of the zoom lens,” J. SMPTE 69, 534–544 (1960).

Opt. Eng. (2)

X. Cheng, Y. Wang, Q. Hao, and J. M. Sasian, “Expert system for generating initial layout of zoom systems with multiple moving lens group,” Opt. Eng. 44, 1–8 (2005).
[CrossRef]

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43, 8–9 (2004).
[CrossRef]

Opt. Express (1)

Proc. SPIE (3)

S. Pal and L. N. Hazra, “Structural design of optically compensated zoom lenses using genetic algorithm,” Proc. SPIE 7429, 742910 (2009).
[CrossRef]

L. N. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
[CrossRef]

L. N. Hazra and S. Banerjee, “Genetic algorithm in structural design of Cooke triplet lenses,” Proc. SPIE 3737, 172–179(1999).
[CrossRef]

Structural design of a lens component with prespecified aberration targets by evolutionary algorithm (1)

S. Chatterjee and L. N. Hazra, “Structural design of a lens component with prespecified aberration targets by evolutionary algorithm ,” Proc. SPIE 6668, 66680S (2007).
[CrossRef]

Other (10)

I. Rechenberg, Evolutionsstrategie: Optimeirung Technischer System nach Prinzipen der Biologischen Evolution (Frommen-Holzboog Verlag, 1973).

D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

http://en.wikipedia.org/wiki/Floor_and_ceiling_functions.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol.  VI, E.Wolf, ed. (North-Holland, 1967), pp. 107–170.

K. Tanaka, “Paraxial theory of lens design in terms of Gaussian brackets,” in Progress in Optics, Vol.  XXIII, E.Wolf, ed. (North-Holland, 1984), pp. 65–111.

E. Betensky, “Zoom lens principles and types,” in Lens Design, Vol. CR41 of SPIE Critical Review Series (SPIE, 1992), pp. 88–116.

D. Clark, Zoom Lenses (Hilger, 1973).

M. Laikin, Lens Design (Dekker, 2001).

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Figures (7)

Fig. 1
Fig. 1

Thin lens structure of a three-component linearly compensated zoom lens system.

Fig. 2
Fig. 2

Chromosome representing a three-component linearly compensated zoom structure.

Fig. 3
Fig. 3

Axial shift Δ of the image plane with change in power over ( k Tel , k WA ): Δ max , maximum axial shift of the image plane over the zoom range.

Fig. 4
Fig. 4

Axial shift of the image plane for a 2 × linearly compensated zoom when the object is at infinity.

Fig. 5
Fig. 5

Axial shift of the image plane for a 3 × linearly compensated zoom when the object is at infinity.

Fig. 6
Fig. 6

Axial shift of the image plane for a 5 × linearly compensated zoom when the object is at infinity.

Fig. 7
Fig. 7

Axial shift of the image plane for a 2 × linearly compensated zoom when the object is at a distance of 20 f WA .

Tables (6)

Tables Icon

Table 1 Linearly Compensated Zoom Systems a

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Table 2 Linearly Compensated Zoom Systems a

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Table 3 Linearly Compensated Zoom Systems

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Table 4 Optically Compensated Zoom Systems a

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Table 5 Optically Compensated Zoom Systems a

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Table 6 Optically Compensated Zoom Systems a

Equations (18)

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k ˜ i = ( 1 m ) ( k i k WA ) ,
d ˜ i = k WA d i ,
m = f Tel f WA = k WA k Tel ,
d 1 * = d 1 z d 2 * = d 2 + r 1 z d 3 * = d 3 r 1 z d 4 * = d 4 + r 2 z d N 1 * = d N 1 + ( 1 ) N 1 r n ^ 1 z .
n ^ = N 2 , for   even   N = N + 1 2 , for   odd   N .
l i gene = log 2 x i max x i min ε i ,
l chr = i = 1 2 ( N 1 ) + n ^ l i gene .
u i + 1 u i = h i k i h i + 1 = h i d i u i + 1 ,
f eq = h 1 u 4 .
d 1 * = d 1 Z R d 2 * = d 2 + r 1 Z R d 3 * = d 3 r 1 Z R d 4 * = d 4 + r 2 Z R ... d N 1 * = d N 1 + ( 1 ) N 1 r n ^ 1 Z R .
f min = f eq R , if     | f WA f eq R | < | f WA f eq L | = f eq L , if   | f WA f eq L | < | f WA f eq R | .
f max = f eq R , if     f min = f eq L = f eq L , if     f min = f eq R .
f max = f eq R , if   | f Tel f eq R | < | f Tel f eq L | = f eq L , if     | f Tel f eq L | < | f Tel f eq R | .
f min = f eq R , if     | f WA f eq R | < | f WA f eq L | = f eq L , if   | f WA f eq L | < | f WA f eq R | .
Φ = ω 1 × ( 1 f min f WA ) 2 + ω 2 × m 2 ( 1 f max f Tel ) 2 + ω 3 × ( Δ max f WA ) 2 ,
Φ = Φ + ω 4 × ( L sys T L sys f WA ) 2 if     L sys T < L sys = Φ if     L sys T L sys ,
Ψ = 1 1 + Φ .
g = i PopSize ( H D ) i PopSize × l chr ,

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