Abstract

Zoom lenses with a fixed distance between focal points are analyzed. Formulas are derived for the primary design of basic parameters of a four-component zoom lens. It is also demonstrated that a three-component zoom lens can be analyzed using derived formulas. Zoom lenses with such a design can be used in a 4-f system with variable magnification or as a part of a double side telecentric lenses with variable magnification.

© 2012 Optical Society of America

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References

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  1. M. Herzberger, Modern Geometrical Optics (Interscience, 1958).
  2. M. Herzberger, “Gaussian optics and Gaussian brackets,” J. Opt. Soc. Am. 33, 651–652 (1943).
    [CrossRef]
  3. A. D. Clark, Zoom Lenses (Adam Hilger, 1973).
  4. K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol. 6, E. Wolf, ed. (North-Holland, 1967), pp. 105–170.
  5. A. Mikš, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47, 6088–6098 (2008).
    [CrossRef]
  6. G. Wooters and E. W. Silvertooth, “Optically compensated zoom lens,” J. Opt. Soc. Am. 55, 347–351 (1965).
    [CrossRef]
  7. A. V. Grinkevich, “Version of an objective with variable focal length,” J. Opt. Technol. 73, 343–345 (2006).
    [CrossRef]
  8. K. Tanaka, “Recent development of zoom lenses,” Proc. SPIE 3129, 13–22 (1997).
    [CrossRef]
  9. K. Tanaka, “General paraxial analysis of mechanically compensated zoom lenses,” Proc. SPIE 3749, 286–287(1999).
    [CrossRef]
  10. S. Pal and L. Hazra, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 50, 1434–1441 (2011).
    [CrossRef]
  11. L. Hazra and S. Pal, “A novel approach for structural synthesis of zoom systems,” Proc. SPIE 7786, 778607 (2010).
    [CrossRef]
  12. R. J. Pegis and W. G. Peck, “First-order design theory for linearly compensated zoom systems,” J. Opt. Soc. Am. 52, 905–909 (1962).
    [CrossRef]
  13. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Courier Dover Publications, 2000).
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  15. H. Gross, F. Blechinger, and B. Achtner, “Survey of optical instruments,” in Handbook of Optical Systems, Vol. 4, H. Gross, ed. (Wiley-VCH, 2008).
  16. K. Lenhardt, “Optical measurement techniques with telecentric lenses,” http://www.schneiderkreuznach.com/knowhow_e.htm .

2011 (1)

2010 (1)

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

2008 (1)

2006 (1)

1999 (1)

K. Tanaka, “General paraxial analysis of mechanically compensated zoom lenses,” Proc. SPIE 3749, 286–287(1999).
[CrossRef]

1997 (1)

K. Tanaka, “Recent development of zoom lenses,” Proc. SPIE 3129, 13–22 (1997).
[CrossRef]

1965 (1)

1962 (1)

1943 (1)

Achtner, B.

H. Gross, F. Blechinger, and B. Achtner, “Survey of optical instruments,” in Handbook of Optical Systems, Vol. 4, H. Gross, ed. (Wiley-VCH, 2008).

Blechinger, F.

H. Gross, F. Blechinger, and B. Achtner, “Survey of optical instruments,” in Handbook of Optical Systems, Vol. 4, H. Gross, ed. (Wiley-VCH, 2008).

Clark, A. D.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grinkevich, A. V.

Gross, H.

H. Gross, F. Blechinger, and B. Achtner, “Survey of optical instruments,” in Handbook of Optical Systems, Vol. 4, H. Gross, ed. (Wiley-VCH, 2008).

Hazra, L.

S. Pal and L. Hazra, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 50, 1434–1441 (2011).
[CrossRef]

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

Herzberger, M.

Korn, G. A.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Courier Dover Publications, 2000).

Korn, T. M.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Courier Dover Publications, 2000).

Mikš, A.

Novák, J.

Novák, P.

Pal, S.

S. Pal and L. Hazra, “Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming,” Appl. Opt. 50, 1434–1441 (2011).
[CrossRef]

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

Peck, W. G.

Pegis, R. J.

Silvertooth, E. W.

Tanaka, K.

K. Tanaka, “General paraxial analysis of mechanically compensated zoom lenses,” Proc. SPIE 3749, 286–287(1999).
[CrossRef]

K. Tanaka, “Recent development of zoom lenses,” Proc. SPIE 3129, 13–22 (1997).
[CrossRef]

Wooters, G.

Yamaji, K.

K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol. 6, E. Wolf, ed. (North-Holland, 1967), pp. 105–170.

Appl. Opt. (2)

J. Opt. Soc. Am. (3)

J. Opt. Technol. (1)

Proc. SPIE (3)

K. Tanaka, “Recent development of zoom lenses,” Proc. SPIE 3129, 13–22 (1997).
[CrossRef]

K. Tanaka, “General paraxial analysis of mechanically compensated zoom lenses,” Proc. SPIE 3749, 286–287(1999).
[CrossRef]

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

Other (7)

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

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

K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol. 6, E. Wolf, ed. (North-Holland, 1967), pp. 105–170.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Courier Dover Publications, 2000).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

H. Gross, F. Blechinger, and B. Achtner, “Survey of optical instruments,” in Handbook of Optical Systems, Vol. 4, H. Gross, ed. (Wiley-VCH, 2008).

K. Lenhardt, “Optical measurement techniques with telecentric lenses,” http://www.schneiderkreuznach.com/knowhow_e.htm .

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Figures (1)

Fig. 1.
Fig. 1.

Four-component zoom lens.

Tables (2)

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Table 1. Parameters of the Four-Component Symmetrical Zoom Lensa

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Table 2. Parameters of the Three-Element Symmetrical Zoom Systema

Equations (37)

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α=[dN1,φN1,dN2,φN2,dN3,φN3,,d1,φ1,],β=[dN1,φN1,dN2,φN2,dN3,φN3,,d1],γ=[φN,dN1,φN1,dN2,φN2,dN3,,d1,φ1],δ=[φN,dN1,φN1,dN2,φN2,dN3,,d1],
[a1]=a1,[a1,a2]=a1a2+1,
[a1,a2,a3,,aN]=[a1,a2,a3,,aN2]+[a1,a2,a3,,aN1]aN,
[a1,a2,a3,,aN]=[aN,aN1,aN2,,a1],
[a1,,ak,,aN]=[a1,,ak1][ak+1,,aN]ak+[a1,,ak2,(ak1+ak+1),ak+2,,aN].
φ=γ,sF=δ/γ,sF=α/γ,s=βαsδγs,m=sγ+α=1δsγ,
φ=γ,δ+γ(d1+d2+d3)α=γD,
α=1d2(φ1+φ2φ1φ2d1)d3(φ1+φ2+φ3)φ1d1(1φ2d3φ3d3)+d2d3φ3(φ1+φ2φ1φ2d1),
γ=φ=(φ1+φ2+φ3+φ4)+φ1φ2d1+φ2φ3d2+φ3φ4d3+φ1φ3(d1+d2)+φ1φ4(d1+d2+d3)+φ2φ4(d2+d3)φ1φ2d1d2(φ3+φ4)φ1φ4d1d3(φ2+φ3)φ3φ4d2d3(φ1+φ2)φ1φ2φ3φ4d1d2d3,
δ=1d1(φ2+φ3+φ4)d2(φ3+φ4)d3φ4+d1d2(φ2φ3+φ2φ4)+d1d3(φ2φ4+φ3φ4)+d2d3φ3φ4(1φ2d1).
φ+γ=0,
δ+γ(d1+d2+d3)αγD=0,
δα=0,
P=φ1/n1+φ2/n2+φ3/n3+φ4/n4(φ1+φ2+φ3+φ4)/n=p/n,
α=φ1(d3d1)φ12d1(d2+2d3+φ1d2d3)+1,
γ=φ12d1(φ12d2d3+2d3φ11)φ12d3,
δ=φ1(d1d3)φ12d3(2d1+d2+φ1d1d2)+1.
φ+d3φ12(d1d2φ12+2d1φ11)d1φ12=0,
A2d32+A1d3+A0=0,
A2=φ12(d1d2φ12+2d1φ11),A1=φ12(D+2d1+2φ1d12+φ12d1d22+φ12d12d22φ1d1D+4φ1d1d2φ12d1d2D),A0=φ12d1(Dd1)2.
φ1(φ1d2+2)(d1d3)=0.
first solution, d1=d3;
second solution, d2=2/φ1.
R=c5d25+c4d24+c3d23+c2d22+c1d2+c0=0,
c5=φ2φ112,c4=2φφ111(5φ+2φ1φφ1D),c3=φ110(36φ24φ12+32φφ1+φ2φ12D216φ2φ1D),c2=2φ18(52φφ12+28φ2φ1+2φ312φ13+3φ2φ13D226φ2φ12D),c1=4φ17(40φφ12+8φ2φ1+4φ312φ13+3φ2φ13D220φ2φ12D),c0=φ16(96φφ1232φ13+16φ3+8φ2φ13D248φ2φ12D).
φ13(d2φ1+2)d322φ12d3+φ=0.
α=φ1(d1+d3)+1,
γ=φ12(d1+d3),
δ=φ1(d1+d3)+1.
Dφφ2/φ122=0,
φ1=φDφ2.
a0+a1d3=0,
a1=(d2φ14+2d1φ13)d1φ12,a0=φφ12d1.
b2d32+b1d3+b0=0,
b2=φ1(d1d2φ13+2d1φ12φ1),b1=φ12(2d1+D+2φ1d12+φ12d1d22+φ12d12d22φ1d1D+4φ1d1d2φ12d1d2D),b0=φ12d1Dφ12d122.
r3d13+r2d12+r1d1+r0=0,
r3=φ16(φ1d2+2)2(φ12d2+2φ1φ),r2=φ15(φ1d2+2)(3φ+6φ1+3φ12d2+φφ12d222φφ1D+4φφ1d2φφ12Dd2),r1=φ13(φ1d2+2)(φ2+4φ12+2φφ12φφ12D+φφ12d2),r0=φ12(φφ12Dφ22φ12).

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