Abstract

We present a theoretical method for analyzing the first-order optics of stabilized zoom lenses with two focal-length-variable elements. The zoom equations are established through the use of the Gaussian brackets method. This is done because the optical power of the focal-length-variable elements varies during the zooming process. The first and second derivatives and the Hessian matrix of the zoom equations with respect to the Gaussian parameters are determined using the equations. These parameters could represent the sensitivity of the zoom ratio of the system to changes in the corresponding system variables. We select the initial values of these system variables, i.e. the magnification of the focal-length-variable element and the structure parameters of the fixed lens group, to be close to the steepest gradient direction. Here the sensitivity of the system focal length is high with respect to variations in the zoom variables. This process leads to an increase in the zoom ratio of the zoom system. The results show successful four-group stabilized zoom lens designs with 2:1 and 5:1 zoom ratios, using two deformable mirrors as focal-length-variable elements. This system, with the inherent characteristics of a steepest gradient, could miniaturize zoom systems.

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References

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  1. K. Yamaji, “Design of zoom lenses,” in Progress in Optics, Vol. 6, E. Wolf, ed. (North-Holland, 1967), pp.105–170.
  2. S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
    [CrossRef]
  3. C. Tao, “The varifocal equation for a zoom system,” Kexue Tongbao22(Z1), 207–213 (1977).
  4. T. ChunKan, “Design of zoom system by the varifocal differential equation. I,” Appl. Opt.31(13), 2265–2273 (1992).
    [CrossRef] [PubMed]
  5. K. Tanaka, “Paraxial analysis of mechanically compensated zoom lenses. I: Four-component type,” Appl. Opt.21(12), 2174–2183 (1982).
    [CrossRef] [PubMed]
  6. K. Tanaka, “Paraxial theory in optical design in terms of gaussian brackets,” in Progress in Optics, Vol. 23, E. Wolf, Ed. (North-Holland, Amsterdam, 1986), pp.63–111.
  7. E. Betensky, “Forty years of modern zoom lens design,” Proc. SPIE586506 (2005).
    [CrossRef]
  8. S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
    [CrossRef]
  9. Q. Hao, X. Cheng, and Y. Song, “Zoom system of MOEMS elements,” PRC Patent 200810119431.4 (18 February 2008).
  10. P. Valley, M. Reza Dodge, J. Schwiegerling, G. Peyman, and N. Peyghambarian, “Nonmechanical bifocal zoom telescope,” Opt. Lett.35(15), 2582–2584 (2010).
    [CrossRef] [PubMed]
  11. R. Peng, J. Chen, C. Zhu, and S. Zhuang, “Design of a zoom lens without motorized optical elements,” Opt. Express15(11), 6664–6669 (2007).
    [CrossRef] [PubMed]
  12. Y. H. Lin, Y. L. Liu, and G. D. Su, “Optical zoom module based on two deformable mirrors for mobile device applications,” Appl. Opt.51(11), 1804–1810 (2012).
    [CrossRef] [PubMed]
  13. B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
    [CrossRef]
  14. A. Mikš and J. Novák, “Third-order aberrations of the thin refractive tunable-focus lens,” Opt. Lett.35(7), 1031–1033 (2010).
    [CrossRef] [PubMed]
  15. A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express18(7), 6797–6810 (2010).
    [CrossRef] [PubMed]
  16. A. Miks, J. Novak, and P. Novak, “Chromatic aberrations of thin refractive variable-focus lens,” Opt. Commun.285(10-11), 2506–2509 (2012).
    [CrossRef]
  17. M. Herzberger, “Gaussian optics and Gaussian brackets,” J. Opt. Soc. Am.33(12), 651–655 (1943).
    [CrossRef]

2012 (3)

Y. H. Lin, Y. L. Liu, and G. D. Su, “Optical zoom module based on two deformable mirrors for mobile device applications,” Appl. Opt.51(11), 1804–1810 (2012).
[CrossRef] [PubMed]

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

A. Miks, J. Novak, and P. Novak, “Chromatic aberrations of thin refractive variable-focus lens,” Opt. Commun.285(10-11), 2506–2509 (2012).
[CrossRef]

2010 (3)

2007 (2)

R. Peng, J. Chen, C. Zhu, and S. Zhuang, “Design of a zoom lens without motorized optical elements,” Opt. Express15(11), 6664–6669 (2007).
[CrossRef] [PubMed]

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

2005 (1)

E. Betensky, “Forty years of modern zoom lens design,” Proc. SPIE586506 (2005).
[CrossRef]

2004 (1)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

1992 (1)

1982 (1)

1977 (1)

C. Tao, “The varifocal equation for a zoom system,” Kexue Tongbao22(Z1), 207–213 (1977).

1943 (1)

Betensky, E.

E. Betensky, “Forty years of modern zoom lens design,” Proc. SPIE586506 (2005).
[CrossRef]

Chen, J.

ChunKan, T.

Deladi, S.

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

Dickensheets, D. L.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Greenfield, N. J.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Helwegen, I.

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

Hendriks, B. H. W.

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

Herzberger, M.

Kaylor, B. M.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Kuiper, S.

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

Lin, Y. H.

Liu, Y. L.

Miks, A.

A. Miks, J. Novak, and P. Novak, “Chromatic aberrations of thin refractive variable-focus lens,” Opt. Commun.285(10-11), 2506–2509 (2012).
[CrossRef]

A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express18(7), 6797–6810 (2010).
[CrossRef] [PubMed]

Mikš, A.

Moghimi, M. J.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Novak, J.

A. Miks, J. Novak, and P. Novak, “Chromatic aberrations of thin refractive variable-focus lens,” Opt. Commun.285(10-11), 2506–2509 (2012).
[CrossRef]

A. Miks and J. Novak, “Analysis of two-element zoom systems based on variable power lenses,” Opt. Express18(7), 6797–6810 (2010).
[CrossRef] [PubMed]

Novak, P.

A. Miks, J. Novak, and P. Novak, “Chromatic aberrations of thin refractive variable-focus lens,” Opt. Commun.285(10-11), 2506–2509 (2012).
[CrossRef]

Novák, J.

Peng, R.

Peyghambarian, N.

Peyman, G.

Reza Dodge, M.

Roos, P. A.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Schwiegerling, J.

Seger, E. M.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Su, G. D.

Suijver, J. F.

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

Tanaka, K.

Tao, C.

C. Tao, “The varifocal equation for a zoom system,” Kexue Tongbao22(Z1), 207–213 (1977).

Valley, P.

Wilson, C. R.

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Zhu, C.

Zhuang, S.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

Kexue Tongbao (1)

C. Tao, “The varifocal equation for a zoom system,” Kexue Tongbao22(Z1), 207–213 (1977).

Opt. Commun. (1)

A. Miks, J. Novak, and P. Novak, “Chromatic aberrations of thin refractive variable-focus lens,” Opt. Commun.285(10-11), 2506–2509 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (3)

E. Betensky, “Forty years of modern zoom lens design,” Proc. SPIE586506 (2005).
[CrossRef]

S. Kuiper, B. H. W. Hendriks, J. F. Suijver, S. Deladi, and I. Helwegen, “Zoom camera based on liquid lenses,” Proc. SPIE6466, 64660F, 64660F-7 (2007).
[CrossRef]

B. M. Kaylor, C. R. Wilson, N. J. Greenfield, P. A. Roos, E. M. Seger, M. J. Moghimi, and D. L. Dickensheets, “Miniature non-mechanical zoom camera using deformable MOEMS mirrors,” Proc. SPIE8252, 82520N, 82520N-7 (2012).
[CrossRef]

Other (3)

Q. Hao, X. Cheng, and Y. Song, “Zoom system of MOEMS elements,” PRC Patent 200810119431.4 (18 February 2008).

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

K. Tanaka, “Paraxial theory in optical design in terms of gaussian brackets,” in Progress in Optics, Vol. 23, E. Wolf, Ed. (North-Holland, Amsterdam, 1986), pp.63–111.

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Figures (7)

Fig. 1
Fig. 1

Optical layout of four-group stabilized zoom system.

Fig. 2
Fig. 2

The relationships of m 2 , m 3 and m 4 in 2:1 zoom systems: (a) for example 1 and (b) for example 2.

Fig. 3
Fig. 3

The layout of 2:1 zoom system: the tele-angle (a) and wide-angle (b) positions for example 1.

Fig. 4
Fig. 4

The layout of 2:1 zoom system: the tele-angle (a) and wide-angle (b) positions for example 2.

Fig. 5
Fig. 5

The relationships of m 2 , m 3 and m 4 in 5:1 zoom systems: (a) for example 3 and (b) for example 4.

Fig. 6
Fig. 6

The layout of 5:1 zoom system: the tele-angle (a) and wide-angle (b) positions for example 3.

Fig. 7
Fig. 7

The layout of 5:1 zoom system: the tele-angle (a) and wide-angle (b) positions for example 4.

Tables (4)

Tables Icon

Table 1 Gaussian parameters of 2:1 zoom system for example 1 a

Tables Icon

Table 2 Gaussian parameters of 2:1 zoom system for example 2 b

Tables Icon

Table 3 Gaussian parameters of 5:1 zoom system for example 3c

Tables Icon

Table 4 Gaussian parameters of 5:1 zoom system for example 4d

Equations (17)

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A i j =[ ϕ i , e i , ϕ i+1 , e i+1 ,, ϕ j1 , e j1 ], B i j =[ e i , ϕ i+1 , e i+1 ,, ϕ j1 , e j1 ], C i j =[ ϕ i , e i , ϕ i+1 , e i+1 ,, ϕ j1 , e j1 , ϕ j ], D i j =[ e i , ϕ i+1 , e i+1 ,, ϕ j1 , e j1 , ϕ j ],
Z= A 1 5 =[ ϕ 1 , e 1 , ϕ 2 , e 2 , ϕ 3 , e 3 , ϕ 4 , e 4 ]=0.
C 1 4 =[ ϕ 1 , e 1 , ϕ 2 , e 2 , ϕ 3 , e 3 , ϕ 4 ]=Φ,
Z= B 1' 5 =[ e 1' , ϕ 2 , e 2 , ϕ 3 , e 3 , ϕ 4 , e 4 ]=0.
{ m 2 =1/(1 e 1' ϕ 2 ), m 3 =1/(1( m 2 e 1' + e 2 ) ϕ 3 ), m 4 = e 4 /( m 3 ( m 2 e 1' + e 2 )+ e 3 ).
d m 3 /d m 2 = e 1' ϕ 3 / [1( m 2 e 1' + e 2 ) ϕ 3 ] 2 ,
d m 4 /d m 2 = e 1' e 4 / [ B 2 4 m 2 e 1' (1 e 3 ϕ 3 )] 2 ,
{ m 4 =1 e 4 ϕ 4 , m 3 =1 e 3 m 3 e 4 ϕ 3 / m 4 , m 2 =( e 3 m 4 + e 4 + e 2 m 3 m 4 )/( m 3 m 4 e 1' ).
d m 2 /d m 4 = e 3 /{ e 1' [ m 4 (1 e 3 ϕ 3 ) e 4 ϕ 3 ] 2 },
d m 3 /d m 4 = e 4 ϕ 3 / m 4 2 ,
{ Z ϕ 2 = A 1 2 B 2 5 , Z ϕ 4 = A 1 4 B 4 5 , 2 Z ϕ 2 2 =0, 2 Z ϕ 4 2 =0, 2 Z ϕ 2 ϕ 4 = A 1 2 B 2 4 B 4 5 .
{ d ϕ 2 d ϕ 4 = A 1 4 B 4 5 A 1 2 B 2 5 , d 2 ϕ 2 d ϕ 4 2 =0.
{ d ϕ 4 d ϕ 2 = A 1 2 B 2 5 A 1 4 B 4 5 , d 2 ϕ 4 d ϕ 2 2 =0.
ϕ 2 = e 4 Φ[ ϕ 1 ,( e 1 + e 2 ), ϕ 3 , e 3 ] (1 e 1 ϕ 1 ) B 2 4 ,
ϕ 4 = 1 e 1 ϕ 1 e 4 Φ B 2 4 + B 2 4 e 4 [ e 2 , ϕ 3 ] e 4 B 2 4 .
Δ ϕ 2 = e 4 (1 e 1 ϕ 1 ) B 2 4 ΔΦ,
Δ ϕ 4 = 1 e 1 ϕ 1 e 4 B 2 4 Δ( 1 Φ ),

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