Abstract

A systematic approach for the aberration correction of zoom systems is presented. It is assumed that the powers and movements of the components of the zoom systems are known. Each component is considered as a system of thin lenses in contact. An evolutionary algorithm is developed to explore the multivariate hyperspace of design variables formed by spherical aberration, central coma, and longitudinal chromatic aberration of each component for infinite conjugate. The primary aberrations for each component at any zoom position are deduced from three central aberration coefficients of the component for infinite conjugate using conjugate shift formulas. Overall system aberrations of the zoom systems are determined by using stop shift formulas. In most of the zoom lens systems it is important to achieve stability in the primary aberrations of the system over the zoom range. This is facilitated by proper formulation of the merit function for the optimization process. Investigations have been carried out on four-component zoom lenses, and an ab initio structure of a four-component zoom lens is presented.

© 2013 Optical Society of America

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References

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  1. L. N. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
    [CrossRef]
  2. S. Pal and L. N. Hazra, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 501441–1443 (2010).
  3. S. Pal and L. N. Hazra, “Structural design of four-component optically compensated zoom lenses: use of evolutionary programming,” Optik 123, 1534–1541 (2012).
    [CrossRef]
  4. S. Pal and L. N. Hazra, “Structural design of mechanically compensated zoom lenses by evolutionary programming,” Opt. Eng. 51, 063001 (2012).
    [CrossRef]
  5. A. Mikš and J. Novák, “Estimation of accuracy of optical measuring systems with respect to object distance,” Opt. Express 19, 14300–14314 (2011).
    [CrossRef]
  6. K. Yamaji, “Design of zoom lenses,” Prog. Opt. VI, 105–170 (1967).
    [CrossRef]
  7. T. H. Jamieson, “Thin-lens theory of zoom system,” J. Mod. Opt. 17, 565–584 (1970).
  8. H. H. Hopkins, “An analytical technique for stable aberration correction in zoom systems,” Proc. SPIE 399, 100–133 (1983).
    [CrossRef]
  9. M. Salter, “Zoom lens aberration correction algorithm,” Proc. SPIE 4487, 76–82 (2001).
    [CrossRef]
  10. A. Mikš, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47, 6088–6098 (2008).
    [CrossRef]
  11. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).
  12. M. I. Khan and J. Macdonald, “Cemented doublets: a method for rapid design,” J. Mod. Opt. 29, 807–822 (1982).
  13. L. N. Hazra, “Structural design of multicomponent lens systems,” Appl. Opt. 23, 4440–4443 (1984).
    [CrossRef]
  14. 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]
  15. S. Chatterjee and L. N. Hazra, “Structural design of cemented triplets by genetic algorithm,” Opt. Eng. 43, 432–440 (2004).
    [CrossRef]
  16. H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).
  17. H. H. Hopkins and V. V. Rao, “Systematic design of two component objectives,” J. Mod. Opt. 17, 497–514 (1970).
  18. D. E. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

2012 (2)

S. Pal and L. N. Hazra, “Structural design of four-component optically compensated zoom lenses: use of evolutionary programming,” Optik 123, 1534–1541 (2012).
[CrossRef]

S. Pal and L. N. Hazra, “Structural design of mechanically compensated zoom lenses by evolutionary programming,” Opt. Eng. 51, 063001 (2012).
[CrossRef]

2011 (1)

2010 (2)

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, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 501441–1443 (2010).

2008 (1)

2004 (1)

S. Chatterjee and L. N. Hazra, “Structural design of cemented triplets by genetic algorithm,” Opt. Eng. 43, 432–440 (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]

2001 (1)

M. Salter, “Zoom lens aberration correction algorithm,” Proc. SPIE 4487, 76–82 (2001).
[CrossRef]

1984 (1)

1983 (1)

H. H. Hopkins, “An analytical technique for stable aberration correction in zoom systems,” Proc. SPIE 399, 100–133 (1983).
[CrossRef]

1982 (1)

M. I. Khan and J. Macdonald, “Cemented doublets: a method for rapid design,” J. Mod. Opt. 29, 807–822 (1982).

1970 (2)

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

H. H. Hopkins and V. V. Rao, “Systematic design of two component objectives,” J. Mod. Opt. 17, 497–514 (1970).

1967 (1)

K. Yamaji, “Design of zoom lenses,” Prog. Opt. VI, 105–170 (1967).
[CrossRef]

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]

Chatterjee, S.

S. Chatterjee and L. N. Hazra, “Structural design of cemented triplets by genetic algorithm,” Opt. Eng. 43, 432–440 (2004).
[CrossRef]

Chretien, H.

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

Goldberg, D. E.

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

Hazra, L. N.

S. Pal and L. N. Hazra, “Structural design of four-component optically compensated zoom lenses: use of evolutionary programming,” Optik 123, 1534–1541 (2012).
[CrossRef]

S. Pal and L. N. Hazra, “Structural design of mechanically compensated zoom lenses by evolutionary programming,” Opt. Eng. 51, 063001 (2012).
[CrossRef]

S. Pal and L. N. Hazra, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 501441–1443 (2010).

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

S. Chatterjee and L. N. Hazra, “Structural design of cemented triplets by genetic algorithm,” Opt. Eng. 43, 432–440 (2004).
[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, “Structural design of multicomponent lens systems,” Appl. Opt. 23, 4440–4443 (1984).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “An analytical technique for stable aberration correction in zoom systems,” Proc. SPIE 399, 100–133 (1983).
[CrossRef]

H. H. Hopkins and V. V. Rao, “Systematic design of two component objectives,” J. Mod. Opt. 17, 497–514 (1970).

Jamieson, T. H.

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

Khan, M. I.

M. I. Khan and J. Macdonald, “Cemented doublets: a method for rapid design,” J. Mod. Opt. 29, 807–822 (1982).

Macdonald, J.

M. I. Khan and J. Macdonald, “Cemented doublets: a method for rapid design,” J. Mod. Opt. 29, 807–822 (1982).

Mikš, A.

Novák, J.

Novák, P.

Pal, S.

S. Pal and L. N. Hazra, “Structural design of mechanically compensated zoom lenses by evolutionary programming,” Opt. Eng. 51, 063001 (2012).
[CrossRef]

S. Pal and L. N. Hazra, “Structural design of four-component optically compensated zoom lenses: use of evolutionary programming,” Optik 123, 1534–1541 (2012).
[CrossRef]

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, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 501441–1443 (2010).

Rao, V. V.

H. H. Hopkins and V. V. Rao, “Systematic design of two component objectives,” J. Mod. Opt. 17, 497–514 (1970).

Salter, M.

M. Salter, “Zoom lens aberration correction algorithm,” Proc. SPIE 4487, 76–82 (2001).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).

Yamaji, K.

K. Yamaji, “Design of zoom lenses,” Prog. Opt. VI, 105–170 (1967).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (4)

H. H. Hopkins and V. V. Rao, “Systematic design of two component objectives,” J. Mod. Opt. 17, 497–514 (1970).

M. I. Khan and J. Macdonald, “Cemented doublets: a method for rapid design,” J. Mod. Opt. 29, 807–822 (1982).

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

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]

Opt. Eng. (2)

S. Chatterjee and L. N. Hazra, “Structural design of cemented triplets by genetic algorithm,” Opt. Eng. 43, 432–440 (2004).
[CrossRef]

S. Pal and L. N. Hazra, “Structural design of mechanically compensated zoom lenses by evolutionary programming,” Opt. Eng. 51, 063001 (2012).
[CrossRef]

Opt. Express (1)

Optik (1)

S. Pal and L. N. Hazra, “Structural design of four-component optically compensated zoom lenses: use of evolutionary programming,” Optik 123, 1534–1541 (2012).
[CrossRef]

Proc. SPIE (3)

H. H. Hopkins, “An analytical technique for stable aberration correction in zoom systems,” Proc. SPIE 399, 100–133 (1983).
[CrossRef]

M. Salter, “Zoom lens aberration correction algorithm,” Proc. SPIE 4487, 76–82 (2001).
[CrossRef]

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

Prog. Opt. (1)

K. Yamaji, “Design of zoom lenses,” Prog. Opt. VI, 105–170 (1967).
[CrossRef]

Other (3)

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

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

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).

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Figures (6)

Fig. 1.
Fig. 1.

Imaging of an object (a) at infinity and (b) at a finite axial location, O* by a thin lens component of power k in air. A stop is placed on the lens. PMR, paraxial marginal ray; PPR, paraxial pupil ray.

Fig. 2.
Fig. 2.

Variation of four primary monochromatic aberrations of the zoom lens with zoom position, predicted by the optimization algorithm. Spherical aberration, coma, and astigmatism are expressed in λ0. Distortion is expressed in percentage.

Fig. 3.
Fig. 3.

Variation of two primary chromatic aberrations of the zoom lens with zoom position, predicted by the optimization algorithm. The longitudinal chromatic aberration is expressed in λ0 and the transverse chromatic aberration is expressed in percentage.

Fig. 4.
Fig. 4.

Final zoom lens system (a) at wide angle, (b) at an intermediate, and (c) at telephoto zoom position. The second and the third components (shaded) are moving components. An aperture stop is placed between two moving components at a fixed axial position.

Fig. 5.
Fig. 5.

Variation of four primary monochromatic aberrations of the zoom lens with zoom position, when each zoom component is replaced by thick lens elements. Spherical aberration, coma, and astigmatism are expressed in λ0. Distortion is expressed in percentage.

Fig. 6.
Fig. 6.

Variation of two primary chromatic aberrations of the zoom lens with zoom position, when each zoom component is replaced by thick lens elements. The longitudinal chromatic aberration is expressed in λ0 and the transverse chromatic aberration is expressed in percentage.

Tables (7)

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Table 1. Thin Lens Structure of a Four-Component Zoom Lens

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Table 2. Target Values for Spherical Aberration, Central Coma, and Longitudinal Chromatic Aberrations in λ0 for Four Components of the Zoom Lens

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Table 3. Curvatures (c), Separations (d), and Materials of a Cemented Doublet Used as the First Component of the Zoom Lens, for hiR=10

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Table 4. Curvatures (c), Separations (d), and Materials of a Triplet Lens Used as the Second Component of the Zoom Lens, for hiR=10

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Table 5. Curvatures (c), Separations (d), and Materials of a Triplet Lens Used as the Third Component of the Zoom Lens, for hiR=10

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Table 6. Curvatures (c), Separations (d), and Materials of a Cemented Doublet Used as the Fourth Component of the Zoom Lens, for hiR=5

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Table 7. Intercomponent Separations (d3, d8, d9, and d14) for Different Zoom Positions

Equations (36)

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

S1=14h4k3{n0+2n0(n01)2(X2(n021)n0+2Y)2+n02(n01)2n0n0+2Y2},
S2=12h2k2H{n0+2n0(n01)X2n0+1n0Y},
S3=H2k,
S4=H2P0.63H2k,
S5=0,
C1=h2kδn0n01,
C2=0,
X=(c1+c2)/(c1c2);Y=(u+u)/(uu),
S1h*=(h*h)4S1,
S2h*=(h*h)2S2,
C1h*=(h*h)2C1,
S1Y*=S1+4δE¯S2+6δE¯2S3+2δE¯2S4+4δE¯3S5+δE¯4S6+H[δE¯Δ(u2)+3δE¯2Δ(uu¯)+3δE¯3Δ(u¯2)],
S2Y*=S2+3δE¯S3+δE¯S4+3δE¯2S5+δE¯3S6+H[δE¯Δ(uu¯)+2δE¯2Δ(u¯2)],
δE¯=h*hh¯=δhh¯.
Δ(u2)=u2u2;Δ(uu¯)=uu¯uu¯;Δ(u¯2)=u¯2u¯2.
S1Y*=S1+4δE¯S2+4.26δE¯2H2k+δE¯Hh2k2,
S2Y*=S2+2.63δE¯H2k.
S˜1i=1mλ0S1i8,
S˜2i=1mλ0S2i2,
C˜1i=1mλ0C1i2,
lGi=log2xmaxixminiεi,
lC=i=1MlGi,
S^1iZ1=(hiZ1hiR)4S1i,S^2iZ1=(hiZ1hiR)2S2i,C^1iZ1=(hiZ1hiR)2C1i,
S1iZ1=S^1iZ1+4δE¯iZ1S^2iZ1+4.26δE¯iZ1H2k2+δE¯iZ1Hhi2Z1k2,
S2iZ1=S^2iZ1+2.63δE¯iZ1H2k,
C1iZ1=C^1iZ1.
S1Z1=i=1NS1iZ1,
S2Z1=i=1NS2iZ1+i=1NEiZ1S2iZ1,
S3Z1=H2i=1Nki+2i=1NEiZ1S2iZ1+i=1NEi2Z1S1iZ1,
S5Z1=(3+0.63)H2i=1NEiZ1ki+3i=1NEi2Z1S2iZ1+i=1NEi3Z1S1iZ1.
C1Z1=i=1NC1iZ1,
C2Z1=i=1NEiZ1C1iZ1,
EiZ1=h¯iZ1hiZ1,
Φ=p=2P[i=1i45ωiM×|SiZ1SiZp|+j=12ωjC×|CjZ1CjZp|]+ω0Ml=15|SlZ1|+ω0Cm=12|CmZ1|,
Ψ=11+Φ.
hiR=5×|Telhi|5,

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