Abstract

We present a new optical system capable of changing in real-time, anywhere in the field of view, the magnification of the image, while potentially keeping the total field of view constant. This is achieved by using an active optic element to change the direction of some selected rays, thus creating controlled distortion. A mathematical description of such a system is presented, along with the fundamental limits on the amplitude of the active surface and on the F/# to keep the image quality. Experimental results obtained with a simple prototype using a ferrofluidic deformable mirror as the active surface are also presented. The local magnifications obtained are in agreement with the developed mathematical model.

© 2011 OSA

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  1. J. J. Kumler and M. L. Bauer, “Fish-eye lenses designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
    [CrossRef]
  2. J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 7433D (2009).
  3. J. Parent and S. Thibault, “Spatial dependence of surface error slopes on tolerancing panoramic lenses,” Appl. Opt. 49(14), 2686–2693 (2010).
    [CrossRef]
  4. J. Parent and S. Thibault, “Active Imaging Lens with Real-Time Variable Resolution and Constant Field of View,” Proc. SPIE 7652, 76522F, 76522F-12 (2010).
    [CrossRef]
  5. D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43(1), 8 (2004).
    [CrossRef]
  6. V. Laude and C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163(1-3), 72–78 (1999).
    [CrossRef]
  7. G. Curatu and J. E. Harvey, “Lens design and system optimization for foveated imaging,” Proc. SPIE 7060, 70600P, 70600P-9 (2008).
    [CrossRef]
  8. S. Kuthirummal and S. K. Nayar, “Flexible Mirror Imaging,” Proc. IEEE Conf. Comput. Vision ICCV, 1–8 (2007).
  9. S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).
  10. www.zemax.com
  11. D. Malacara-Hernandez, “Some parameters and characteristics of an off-axis paraboloid,” Opt. Eng. 30(9), 1277–1280 (1991).
    [CrossRef]
  12. J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
    [CrossRef]
  13. W. J. Smith, Modern Optical Engineering 4th ed., (McGraw-Hill, 2007).
  14. D. Brousseau, E. F. Borra, M. Rochette, and D. B. Landry, “Linearization of the response of a 91-actuator magnetic liquid deformable mirror,” Opt. Express 18(8), 8239–8250 (2010).
    [CrossRef] [PubMed]
  15. L. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang, and A. K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Appl. Opt. 45(1), 90–94 (2006).
    [CrossRef] [PubMed]
  16. F. Pardo, et al., “Characterization of Piston-Tip-Tilt mirror pixels for scalable SLM arrays,” Proceedings of IEEE Conference on Optical MEMS and Their Applications, (2006), pp. 21–22.
  17. D. J. Reiley and R. A. Chipman, “Adjustable distortion corrector,” Proc. SPIE 1690, 11–19 (1992).
    [CrossRef]

2010 (4)

J. Parent and S. Thibault, “Active Imaging Lens with Real-Time Variable Resolution and Constant Field of View,” Proc. SPIE 7652, 76522F, 76522F-12 (2010).
[CrossRef]

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

D. Brousseau, E. F. Borra, M. Rochette, and D. B. Landry, “Linearization of the response of a 91-actuator magnetic liquid deformable mirror,” Opt. Express 18(8), 8239–8250 (2010).
[CrossRef] [PubMed]

J. Parent and S. Thibault, “Spatial dependence of surface error slopes on tolerancing panoramic lenses,” Appl. Opt. 49(14), 2686–2693 (2010).
[CrossRef]

2009 (1)

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 7433D (2009).

2008 (1)

G. Curatu and J. E. Harvey, “Lens design and system optimization for foveated imaging,” Proc. SPIE 7060, 70600P, 70600P-9 (2008).
[CrossRef]

2007 (1)

S. Kuthirummal and S. K. Nayar, “Flexible Mirror Imaging,” Proc. IEEE Conf. Comput. Vision ICCV, 1–8 (2007).

2006 (1)

2005 (1)

S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).

2004 (1)

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43(1), 8 (2004).
[CrossRef]

2000 (1)

J. J. Kumler and M. L. Bauer, “Fish-eye lenses designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

1999 (1)

V. Laude and C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163(1-3), 72–78 (1999).
[CrossRef]

1992 (1)

D. J. Reiley and R. A. Chipman, “Adjustable distortion corrector,” Proc. SPIE 1690, 11–19 (1992).
[CrossRef]

1991 (1)

D. Malacara-Hernandez, “Some parameters and characteristics of an off-axis paraboloid,” Opt. Eng. 30(9), 1277–1280 (1991).
[CrossRef]

Asundi, A. K.

Bai, N.

Bauer, M. L.

J. J. Kumler and M. L. Bauer, “Fish-eye lenses designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Borra, E. F.

Bouchez, A. H.

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

Brousseau, D.

Burruss, R. S.

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

Chipman, R. A.

D. J. Reiley and R. A. Chipman, “Adjustable distortion corrector,” Proc. SPIE 1690, 11–19 (1992).
[CrossRef]

Curatu, G.

G. Curatu and J. E. Harvey, “Lens design and system optimization for foveated imaging,” Proc. SPIE 7060, 70600P, 70600P-9 (2008).
[CrossRef]

Dekany, R. G.

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

Dirson, C.

V. Laude and C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163(1-3), 72–78 (1999).
[CrossRef]

Doucet, M.

S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).

Fang, Z. P.

Gauvin, J.

S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).

Guiwits, S. R.

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

Harvey, J. E.

G. Curatu and J. E. Harvey, “Lens design and system optimization for foveated imaging,” Proc. SPIE 7060, 70600P, 70600P-9 (2008).
[CrossRef]

Kumler, J. J.

J. J. Kumler and M. L. Bauer, “Fish-eye lenses designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Kuthirummal, S.

S. Kuthirummal and S. K. Nayar, “Flexible Mirror Imaging,” Proc. IEEE Conf. Comput. Vision ICCV, 1–8 (2007).

Landry, D. B.

Laude, V.

V. Laude and C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163(1-3), 72–78 (1999).
[CrossRef]

Li, X.

Malacara-Hernandez, D.

D. Malacara-Hernandez, “Some parameters and characteristics of an off-axis paraboloid,” Opt. Eng. 30(9), 1277–1280 (1991).
[CrossRef]

Martinez, T.

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43(1), 8 (2004).
[CrossRef]

Nayar, S. K.

S. Kuthirummal and S. K. Nayar, “Flexible Mirror Imaging,” Proc. IEEE Conf. Comput. Vision ICCV, 1–8 (2007).

Ong, L. S.

Parent, J.

J. Parent and S. Thibault, “Active Imaging Lens with Real-Time Variable Resolution and Constant Field of View,” Proc. SPIE 7652, 76522F, 76522F-12 (2010).
[CrossRef]

J. Parent and S. Thibault, “Spatial dependence of surface error slopes on tolerancing panoramic lenses,” Appl. Opt. 49(14), 2686–2693 (2010).
[CrossRef]

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 7433D (2009).

Reiley, D. J.

D. J. Reiley and R. A. Chipman, “Adjustable distortion corrector,” Proc. SPIE 1690, 11–19 (1992).
[CrossRef]

Roberts, J.

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

Rochette, M.

Thibault, S.

J. Parent and S. Thibault, “Spatial dependence of surface error slopes on tolerancing panoramic lenses,” Appl. Opt. 49(14), 2686–2693 (2010).
[CrossRef]

J. Parent and S. Thibault, “Active Imaging Lens with Real-Time Variable Resolution and Constant Field of View,” Proc. SPIE 7652, 76522F, 76522F-12 (2010).
[CrossRef]

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 7433D (2009).

S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).

Troy, M.

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

Wang, M.

S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).

Wick, D. V.

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43(1), 8 (2004).
[CrossRef]

Zhao, L.

Appl. Opt. (2)

Opt. Commun. (1)

V. Laude and C. Dirson, “Liquid-crystal active lens: application to image resolution enhancement,” Opt. Commun. 163(1-3), 72–78 (1999).
[CrossRef]

Opt. Eng. (2)

D. V. Wick and T. Martinez, “Adaptive optical zoom,” Opt. Eng. 43(1), 8 (2004).
[CrossRef]

D. Malacara-Hernandez, “Some parameters and characteristics of an off-axis paraboloid,” Opt. Eng. 30(9), 1277–1280 (1991).
[CrossRef]

Opt. Express (1)

Proc. IEEE Conf. Comput. Vision (1)

S. Kuthirummal and S. K. Nayar, “Flexible Mirror Imaging,” Proc. IEEE Conf. Comput. Vision ICCV, 1–8 (2007).

Proc. SPIE (7)

S. Thibault, J. Gauvin, M. Doucet, and M. Wang, “Enhanced optical design by distortion control,” Proc. SPIE 5962 (2005).

J. Roberts, A. H. Bouchez, R. S. Burruss, R. G. Dekany, S. R. Guiwits, and M. Troy, “Optical characterization of the PALM-3000 3388-actuator deformable mirror,” Proc. SPIE 7736, 77362E, 77362E-8 (2010).
[CrossRef]

J. Parent and S. Thibault, “Active Imaging Lens with Real-Time Variable Resolution and Constant Field of View,” Proc. SPIE 7652, 76522F, 76522F-12 (2010).
[CrossRef]

G. Curatu and J. E. Harvey, “Lens design and system optimization for foveated imaging,” Proc. SPIE 7060, 70600P, 70600P-9 (2008).
[CrossRef]

J. J. Kumler and M. L. Bauer, “Fish-eye lenses designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

J. Parent and S. Thibault, “Tolerancing panoramic lenses,” Proc. SPIE 7433, 7433D (2009).

D. J. Reiley and R. A. Chipman, “Adjustable distortion corrector,” Proc. SPIE 1690, 11–19 (1992).
[CrossRef]

Other (3)

F. Pardo, et al., “Characterization of Piston-Tip-Tilt mirror pixels for scalable SLM arrays,” Proceedings of IEEE Conference on Optical MEMS and Their Applications, (2006), pp. 21–22.

W. J. Smith, Modern Optical Engineering 4th ed., (McGraw-Hill, 2007).

www.zemax.com

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Figures (13)

Fig. 1
Fig. 1

Schematic representation of the concept behind a locally magnifying imager. Only a small fraction of the rays are affected by the active optical surface, the rays from the blue field in this case. By changing the object angle of these rays, a different magnification is produced at the image plane. For clarity, all the other optical surfaces except the stop are hidden.

Fig. 2
Fig. 2

Schematic of the problem with two chief-rays separated by an infinitesimal distance on the active surface. For this example, the active surface is chosen to be a mirror. The angle on the mirror with the horizontal at the two positions r and r + δr where the rays hit are different and given respectively by ψr and ψr + δr. L0 is the distance between the EP and the mirror.

Fig. 3
Fig. 3

Schematic showing the chief-rays for three fields. With a flat mirror, the original red rays are reflected toward the EP and reach the image plane. With the mirror in the correct shape, the green rays are now the rays reflected toward the EP. This creates 3 zones, one of higher magnification from r = 0 to r = a, one of lower magnification around it from r = a to r = b and one where the mirror stays flat, keeping the original magnification, from r = b to r = D/2. The ray hitting the extreme part of the mirror, at r = D/2, comes from an angle θmax and hits the image at a distance H from the center. Consequently, the FFOV is constant since this angle is the same before and after changing the shape of the mirror.

Fig. 4
Fig. 4

Graphical representation of Eq. (9), with RoM and H/f variable, and with values of D = 100 mm and α = 0.2. For realistic use, amplitudes of hundreds of µm are required.

Fig. 5
Fig. 5

Schematic of the experimental setup used. The camera + lens are pointed at the ferrofluidic deformable mirror to look by reflection at the object, a light diffuser on the ceiling. Not shown in the figure is an adaptive optics closed-loop used to set and measure the surface.

Fig. 6
Fig. 6

Reference image obtained with a flat deformable mirror. For the images to follow, only the cropped region is presented. In the central region, all the small targets are equally spaced. At the edge of the container, liquid meniscus effects produce some unimportant distortion.

Fig. 7
Fig. 7

Images of zones of increased and decreased magnification by using a parabola in the zone of interest. In all four images, the magnification is constant in the central zone and different from the original magnification of Fig. 6. The voltage in the actuators was scaled with the following factor: (a) −5 (b) −1 (c) + 1 (d) + 5

Fig. 8
Fig. 8

From the 7 images with a parabola, graph of: (a) the positions in pixels as a function of the target number for targets on a horizontal line and (b) the relative position showing the displacement in pixels of each target with respect to the reference of Fig. 6. In both graphs, the scale factors are −5, −3, −1, 0, 1, 3 and 5. The slopes in the central zone are linearly fitted and results are at Fig. 9.

Fig. 9
Fig. 9

From Fig. 8, a linear fit is done in the central region and from the slope of these fits, by dividing by the original magnification, RoMs are plotted as a function of the scale factor, along with their 95% confidence bound. As expected, it can be seen that the magnification in the zone of interest compliantly follows a fit having the shape of Eq. (6).

Fig. 10
Fig. 10

Images produced by Gaussian shaped deformations, creating a zone of increased magnification in the center and quickly dropping around it. In all four images, the magnification drops below the original magnification from Fig. 6 in an annular zone around the center. The voltage in the actuators was scaled with the following factor: (a) 0.5 (b) 1.0 (c) 1.3 (d) 1.5. With a scale factor of 1.5, the central region is a bit out of focus.

Fig. 11
Fig. 11

Graph of: (a) the position in pixels of each target on a horizontal line from the 8 images taken and (b) the relative position showing the displacement in pixels of each target with respect to the reference of Fig. 6. In both graphs the scale factors are 0, 0.5, 1.0, 1.1, 1.2, 1.3, 1.4 and 1.5. With increasing scale factor, the magnification in the center increases too and it is more visible by looking at the derivative in the center region as plotted in Fig. 12.

Fig. 12
Fig. 12

Resulting spatial RoM as a function of the target # for the 8 images taken with Gaussian shaped bumps on the deformable mirror. With increasing scale factor, the magnification in the center can become significant. The 8 curve scale factors, from the bottom to the top around their maximum are: 0, 0.5, 1.0, 1.1, 1.2, 1.3, 1.4 and 1.5.

Fig. 13
Fig. 13

Image with 2 zones of interest separated by a zone of lower magnification. Unlike all the previous examples having a single zone of interest, a real application of this kind of lens could have more than one zone of interest.

Equations (14)

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LFL(r) h φ = lim δ r 0 f [ tan ( θ ( r + δ r ) ) tan ( θ ( r ) ) ] ( θ ( r + δ r ) 2 ψ ( r + δ r ) ) ( θ ( r ) 2 ψ ( r ) ) ,
R o M ( r ) = lim δ r 0 ( θ ( r + δ r ) ) ( θ ( r ) ) ( θ ( r + δ r ) 2 ψ ( r + δ r ) ) ( θ ( r ) 2 ψ ( r ) )
= lim δ r 0 arctan ( r + δ r L 0 ) arctan ( r L 0 ) arctan ( r + δ r L 0 ) arctan ( r L 0 ) + 2 arctan ( Z ' ( r ) ) 2 arctan ( Z ' ( r + δ r ) ) ,
R o M ( r ) = lim δ r 0 1 1 2 Z ' ( r + δ r ) Z ' ( r ) arctan ( r + δ r L 0 ) arctan ( r L 0 )
R o M ( r ) = 1 1 2 L 0 Z ' ' ( r ) [ 1 + ( r L 0 ) 2 ] ,
RoM ( r ) = 1 1 2 L 0 Z ' ' ( r ) if r < < L 0
R o M ( r ) = 1 1 + ( n 1 ) L 0 Z ' ' ( r )
H f = tan ( θ max ) = D 2 L 0 ,
S a g = | 1 4 L 0 R o M 1 R o M ( α D 2 ) 2 | = | H 2 f D R o M 1 R o M ( α D 2 ) 2 |
S a g = A = | σ 2 2 L 0 1 R o M R o M | = | σ 2 H D f 1 R o M R o M |
PV OPD  Mirror = Z ' ' ( R o M × E P 2 ) 2
PV OPD  Exit pupil = Δ W 20 = Z ' ' R o M ( E P 2 ) 2 λ 4
F / # i m a g e r = f E P > H f D λ ( R o M 1 )
Δ R o M = 1 1 + ( 1 R o M ) Δ ( L 0 Ζ ' ' )   1

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