Abstract

This work deals with a theoretical analysis of zoom lenses with a fixed distance between focal points. Equations are derived for the primary (paraxial) design of the basic parameters of a three-element zoom lens. It is shown that the number of optical elements for such a lens must be larger than two.

© 2012 Optical Society of America

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References

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  1. A. Mikš, Applied Optics (Czech Technical University, 2009).
  2. M. Herzberger, Modern Geometrical Optics (Interscience, 1958).
  3. A. D. Clark, Zoom Lenses (Hilger, 1973).
  4. K. Yamaji, in Progress in Optics, E. Wolf, ed. (North-Holland, 1967), Vol. 6, pp. 105–170.
  5. A. Mikš, J. Novák, and P. Novák, Appl. Opt. 47, 6088 (2008).
    [CrossRef]
  6. G. Wooters and E. W. Silvertooth, J. Opt. Soc. Am. 55, 347 (1965).
    [CrossRef]
  7. A. V. Grinkevich, J. Opt. Technol. 73, 343 (2006).
    [CrossRef]
  8. K. Tanaka, Proc. SPIE 3129, 13 (1997).
    [CrossRef]
  9. K. Tanaka, Proc. SPIE 3749, 286 (1999).
    [CrossRef]
  10. S. Pal and L. Hazra, Appl. Opt. 50, 1434 (2011).
    [CrossRef]
  11. L. N. Hazra and S. Pal, Proc. SPIE 7786, 778607 (2010).
    [CrossRef]
  12. M. Berek, Grundlagen der praktischen Optik (de Gruyter, 1970).
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), Chap. 8.

2011 (1)

2010 (1)

L. N. Hazra and S. Pal, Proc. SPIE 7786, 778607 (2010).
[CrossRef]

2008 (1)

2006 (1)

1999 (1)

K. Tanaka, Proc. SPIE 3749, 286 (1999).
[CrossRef]

1997 (1)

K. Tanaka, Proc. SPIE 3129, 13 (1997).
[CrossRef]

1965 (1)

Berek, M.

M. Berek, Grundlagen der praktischen Optik (de Gruyter, 1970).

Clark, A. D.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), Chap. 8.

Grinkevich, A. V.

Hazra, L.

Hazra, L. N.

L. N. Hazra and S. Pal, Proc. SPIE 7786, 778607 (2010).
[CrossRef]

Herzberger, M.

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

Mikš, A.

A. Mikš, J. Novák, and P. Novák, Appl. Opt. 47, 6088 (2008).
[CrossRef]

A. Mikš, Applied Optics (Czech Technical University, 2009).

Novák, J.

Novák, P.

Pal, S.

S. Pal and L. Hazra, Appl. Opt. 50, 1434 (2011).
[CrossRef]

L. N. Hazra and S. Pal, Proc. SPIE 7786, 778607 (2010).
[CrossRef]

Silvertooth, E. W.

Tanaka, K.

K. Tanaka, Proc. SPIE 3749, 286 (1999).
[CrossRef]

K. Tanaka, Proc. SPIE 3129, 13 (1997).
[CrossRef]

Wooters, G.

Yamaji, K.

K. Yamaji, in Progress in Optics, E. Wolf, ed. (North-Holland, 1967), Vol. 6, pp. 105–170.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Technol. (1)

Proc. SPIE (3)

K. Tanaka, Proc. SPIE 3129, 13 (1997).
[CrossRef]

K. Tanaka, Proc. SPIE 3749, 286 (1999).
[CrossRef]

L. N. Hazra and S. Pal, Proc. SPIE 7786, 778607 (2010).
[CrossRef]

Other (6)

M. Berek, Grundlagen der praktischen Optik (de Gruyter, 1970).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), Chap. 8.

A. Mikš, Applied Optics (Czech Technical University, 2009).

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

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

K. Yamaji, in Progress in Optics, E. Wolf, ed. (North-Holland, 1967), Vol. 6, pp. 105–170.

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Figures (2)

Fig. 1.
Fig. 1.

Three-element optical system (ξ, object plane; ξ, image plane; F, object focal point; F, image focal point).

Fig. 2.
Fig. 2.

Double-sided telecentric zoom lens.

Tables (1)

Tables Icon

Table 1. Example of Three-Element Zoom Systema

Equations (25)

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φ=1/f=γ,sF=δ/γ,sF=α/γ,s=(δ1/m)/γ,s=(mα)/γ,
α=d1d2φ1φ2d2(φ1+φ2)d1φ1+1,γ=[d1d2φ1φ2φ3d2φ3(φ1+φ2)d1φ1(φ2+φ3)+φ1+φ2+φ3],δ=d1d2φ2φ3d1(φ2+φ3)d2φ3+1,
sF+d1+sF=D.
d1=(2Dφ)/φ1φ2.
φ=γ=φ1+φ2d1φ1φ2.
d1=(φ1+φ2φ)/φ1φ2.
φ2+Pφ+Q=0,
P=Dφ1φ22(φ1+φ2),Q=φ12+φ22.
sF+d1+d2+sF=D.
d1d2(φ1φ2+φ2φ3)d1(φ1+φ2+φ3φ)d2(φ1+φ2+φ3φ)φD+2=0.
d1d2φ1φ2φ3d1φ1(φ2+φ3)d2φ3(φ1+φ2)+φ1+φ2+φ3φ=0.
d22(A3B1A1A4)+d2[A4(A2A3B1)+A1B2]+A42A2B2=0,
A1=φ1φ2φ3,A2=φ1(φ2+φ3),A3=φ3(φ1+φ2),A4=pφ,p=φ1+φ2+φ3,B1=φ1φ2+φ2φ3,B2=2φD.
d1=a0/a1,a1=d2A1A2,a0=d2A3+A4.
P=φ1/n1+φ2/n2+φ3/n3=(φ1+φ2+φ3)/n=p/n,
n=(φ1+φ2+φ3)/(φ1/n1+φ2/n2+φ3/n3).
φ1=φ3,φ2=2φ1.
b2d12+b1d1+b0=0,
b2=φ12(2φ1d21),b1=3φ12d2+(2φ1d21)(φ12d2φ12D),b0=φ12d22+φ12d2D2.
d2=D/2±(D/2)22f12.
D22f12.82f1.
d22c2+d2c1+c0=0,
c2=2φ13(2φ1φ),c1=2φ13(Dφ2)4φφ12,c0=φ2φ12(Dφ2).
d1=(φ/φ12d2)/(12φ1d2).
φ=1/f=(1/2f1)[D/f1±(D/f1)28],d1=f12/f.

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