Abstract

We present an analysis of single-moving-element zoom lenses in the thin-lens limit and show how the length of these zoom lenses is determined by the zoom-factor, sensor-dimension and the depth-of-focus. By decreasing the sensor size and extending the depth-of-focus, the lengths of these zoom lenses can be reduced significantly. As an example we present a ray-traced design of a miniaturized single-moving-element zoom lens with a 2.3× zoom-factor and show how the exploitation of modern miniaturized detector array combined with wavefront coding enables a reduction in length of almost three orders-of-magnitude to 10mm.

© 2009 Optical Society of America

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References

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  1. K. Yamaji, "Design of zoom lenses," in Progress in Optics, E. Wolf, ed., (North Holland, Amsterdam, 1967), pp. 105-170.
  2. W. J. Smith, Modern Optical Engineering, Third edition, (McGraw-Hill, 2000).
  3. J. E. R. Dowski and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  4. S. Mezouari, G. Muyo, and A. R. Harvey, "Circularly symmetric phase filters for control of primary third-order aberrations: coma and astigmatism," J. Opt. Soc. Am. A 23, 1058-1062 (2006).
    [CrossRef]
  5. S. Mezouari and A. Harvey, "Phase pupil functions for reduction of defocus and spherical aberrations," Opt. Lett. 28, 771-773 (2003).
    [CrossRef] [PubMed]
  6. S. Mezouari, G. Muyo, and A. R. Harvey, "Amplitude and phase filters for mitigation of defocus and third-order aberrations," in Optical Design and Engineering, 238-248 (SPIE, St. Etienne, France, 2004).
  7. W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett. 26, 875-877 (2001).
    [CrossRef]
  8. D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998)
    [CrossRef]
  9. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "Radial mask for imaging systems that exhibit high resolution and extended depths of field," Appl. Opt. 45, 2001-2013 (2006).
    [CrossRef] [PubMed]
  10. Z. Zalevsky, A. Shemer, A. Zlotnik, E. B. Eliezer, and E. Marom, "All-optical axial super resolving imaging using a low-frequency binary-phase mask," Opt. Express 14, 2631-2643 (2006).
    [CrossRef] [PubMed]
  11. S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
    [CrossRef]
  12. J. Ares García, S. Bará, M. Gomez García, Z. Jaroszewicz, A. Kolodziejczyk, and K. Petelczyc, "Imaging with extended focal depth by means of the refractive light sword optical element," Opt. Express 16, 18371-18378 (2008).
    [CrossRef] [PubMed]
  13. I. A. Prischepa and J. E. R. Dowski, "Wavefront coded zoom lens system," in Zoom Lenses III 83-93, (SPIE, San Diego, CA, USA, 2001).
  14. K. Kubala, E. Dowski, and W. Cathey, "Reducing complexity in computational imaging systems," Opt. Express 11, 2102-2108 (2003).
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  15. G. Muyo, A. Singh, M. Andersson, D. Huckridge, and A. Harvey, "Optimized thermal imaging with a singlet and pupil plane encoding: experimental realization," in Electro-Optical and Infrared Systems: Technology and Applications III, 63950-63959 (SPIE, Stockholm, Sweden, 2006).
  16. G. Muyo and A. R. Harvey, "Decomposition of the optical transfer function: wavefront coding imaging systems," Opt. Lett. 30, 2715-2717 (2005).
    [CrossRef] [PubMed]

2008 (1)

2006 (3)

2005 (1)

2004 (1)

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

2003 (2)

2001 (1)

1998 (1)

1995 (1)

Ares García, J.

Bará, S.

Ben-Eliezer, E.

Cathey, W.

Cathey, W. T.

Chi, W.

Dowski, E.

Dowski, J. E. R.

Eliezer, E. B.

George, N.

Gomez García, M.

Harvey, A.

Harvey, A. R.

Jaroszewicz, Z.

Kolodziejczyk, A.

Konforti, N.

Kubala, K.

Marom, E.

Mezouari, S.

Muyo, G.

Pauca, V. P.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Petelczyc, K.

Plemmons, R. J.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Prasad, S.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Shemer, A.

Sicre, E. E.

Torgersen, T. C.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

van der Gracht, J.

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Zalevsky, Z.

Zalvidea, D.

Zlotnik, A.

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Express (3)

Opt. Lett. (3)

Proc. SPIE (1)

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization or extended focus, aberration corrected imaging systems," Proc. SPIE 5559, 335-345 (2004).
[CrossRef]

Other (5)

S. Mezouari, G. Muyo, and A. R. Harvey, "Amplitude and phase filters for mitigation of defocus and third-order aberrations," in Optical Design and Engineering, 238-248 (SPIE, St. Etienne, France, 2004).

G. Muyo, A. Singh, M. Andersson, D. Huckridge, and A. Harvey, "Optimized thermal imaging with a singlet and pupil plane encoding: experimental realization," in Electro-Optical and Infrared Systems: Technology and Applications III, 63950-63959 (SPIE, Stockholm, Sweden, 2006).

I. A. Prischepa and J. E. R. Dowski, "Wavefront coded zoom lens system," in Zoom Lenses III 83-93, (SPIE, San Diego, CA, USA, 2001).

K. Yamaji, "Design of zoom lenses," in Progress in Optics, E. Wolf, ed., (North Holland, Amsterdam, 1967), pp. 105-170.

W. J. Smith, Modern Optical Engineering, Third edition, (McGraw-Hill, 2000).

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Figures (5)

Fig. 1.
Fig. 1.

Two zoom lens configurations with one moving element and a total of 3 elements showing the defocus related to the movement of lens element B. The defocus is exaggerated to show the principle and the direction. Typically, the defocus for the two SME zoom lens configurations is not identical in magnitude as also indicated by the dashed curve.

Fig. 2.
Fig. 2.

Length as a function of (a) zoom factor and b) defocus constant in terms of waves for two SME zoom lens configurations. In a) defocus is given by Hopkins defocus criterion. In (b) a zoom factor of 2.5 is used. A horizontal sensor dimension of 3.58 mm is used in both cases. Solid line represents zoom lens configuration +-+ while dotted line represents zoom lens configuration -+-.

Fig. 3.
Fig. 3.

(a). Layout and ray-traces of the example zoom lens for lens displacement of 0.9mm and (b) the calculated defocus versus lens position with 5 defocus points obtained by ray-tracing.

Fig. 4.
Fig. 4.

PSFs without phase mask at lens position (a) 0.0 mm, (b) 0.9 mm and (c) 2.5 mm and PSFs with phase mask at lens position (d) 0.0 mm, (e) 0.9 mm and (f) 2.5 mm. Image size is 224 microns by 224 microns. MTFs with and without phase mask at lens position (g) 0.0 mm, (h) 0.9 mm and (i) 2.5 mm. Black line is the MTF in a SME zoom lens with phase mask, whilst gray line is the MTF in a SME zoom lens without phase mask. Dashed line is the in-focus MTF which could be obtained in a conventional mechanically-compensated zoom lens with two moving elements.

Fig. 5.
Fig. 5.

Images with lens position at 2.5mm acquired with (a) no implementation of phase mask, with (b) mechanically compensation, -with (c) implementation of phase mask before restoration and (d) with implementation of phase mask after restoration.

Tables (1)

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Table 1. Lens focal lengths for a 2.3× optical zoom lens with lens B travelling by 2.5 mm

Equations (11)

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BFL AB ( d ) = ( 1 ϕ A d ) / ϕ AB
ϕ A = ( R 1 ) / ( RS )
ϕ B = ( 1 R 2 ) / ( RS )
ϕ C = ϕ A + 1 / ( f min Z ) .
T ˭ = ( 1 BFL ABC 0 1 ) ( 1 3 ϕ C 1 ) ( 1 S d 0 1 ) ( 1 0 ϕ B 1 ) ( 1 d 0 1 ) ( 1 0 ϕ A 1 ) ,
BFL ABC ( d , S ) = 1 + φ B ( S + d ) φ A ( S φ B Sd + φ B d 2 ) φ B + φ C φ B φ C S + φ B φ C d φ A ( 1 + φ B d + φ C ( S φ B Sd + φ B d 2 ) )
BFL = f min Z
Δ z = f min 2 ( R 1 ) 3 Z 2 ( f min ( R 1 ) Z + ( 1 3 R ) RS ) ,
L x sensor Z ( 16 ( F / # ) 2 ( R 3 + 2 R 1 ) W 20 + 1 / 2 ( R 1 ) 3 x sensor Z · 1 / tan ( θ / 2 ) ) 32 ( F / # ) 2 R ( 3 R 1 ) W 20 tan ( θ / 2 ) ,
L ( R 1 ) 3 x sensor 2 Z 64 ( F / # ) 2 R ( 3 R 1 ) W 20 tan 2 ( θ / 2 ) .
γ = 1 mn u = 0 m 1 v = 0 n 1 F ( u , v ) 2 ,

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