Abstract

We present the design and experimental demonstration of an ultrathin four-reflection imager. The F/1.15 prototype imager achieves a focal length of 18.6mm in a track length of just 5.5mm, providing a 17° field of view over 1.92 megapixels of a color image sensor with 3μm pixels. We also present the design and experimental results of pupil-phase encoding and postprocessing, which were applied to extend the depth of field and compensate a small amount of axial chromatic aberration present in the four-reflection imager prototype.

© 2009 Optical Society of America

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References

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    [CrossRef]
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2007 (2)

2006 (1)

2004 (2)

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

K. Kubala, E. Dowski, J. Kobus, and R. Brown, “Aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

2003 (2)

K. Kubala, E. Dowski, and W. T. Cathey, “Reducing complexity in computational imaging systems,” Opt. Express 11, 2102-2108 (2003).
[CrossRef] [PubMed]

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50, 4-11 (2003).
[CrossRef]

2002 (2)

2001 (1)

1999 (1)

G. Peterson, “Stray light calculation methods with optical ray trace software,” Proc. SPIE 3780, 132-137 (1999).
[CrossRef]

1998 (2)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

H. B. Wach, E. R. Dowski, Jr., and W. T. Cathey, “Control of chromatic focal shift through wavefront coding,” Appl. Opt. 37, 5359-5367 (1998).
[CrossRef]

1996 (1)

T. F. Coleman and Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

1995 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1977 (1)

1974 (1)

1968 (1)

1965 (1)

Agranov, G.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50, 4-11 (2003).
[CrossRef]

Andrews, H. C.

H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice-Hall, 1977), Chap. 8, pp. 147-152.

Ang, T.

T. Ang, Dictionary of Photography and Digital Imaging: the Essential Reference for the Modern Photographer (Watson-Guptill, 2002).
[PubMed]

Berezin, V.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50, 4-11 (2003).
[CrossRef]

Brown, R.

K. Kubala, E. Dowski, J. Kobus, and R. Brown, “Aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

Cathey, W. T.

Catrysse, P. B.

Chi, W.

Coleman, T. F.

T. F. Coleman and Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

Dirjish, M.

M. Dirjish, “BSI technology flips digital imaging upside down,” http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=19160.

Dowski, E.

Dowski, E. R.

Fainman, Y.

Ford, J. E.

Frieden, B. R.

B. R. Frieden, “Image enhancement and restoration,” in Topics in Applied Physics, Vol. 6 of Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, 1979), pp. 177-248.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

George, N.

Hall, J.

J. Hall, “F-number, numerical aperture, and depth of focus,” in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 556-559.

Haney, M. W.

Hunt, B. R.

H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice-Hall, 1977), Chap. 8, pp. 147-152.

Kelly, D. H.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Klüppelberg, D.

Kobus, J.

K. Kubala, E. Dowski, J. Kobus, and R. Brown, “Aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

Korsch, D.

D. Korsch, Reflective Optics (Academic, 1991).

Kubala, K.

K. Kubala, E. Dowski, J. Kobus, and R. Brown, “Aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

K. Kubala, E. Dowski, and W. T. Cathey, “Reducing complexity in computational imaging systems,” Opt. Express 11, 2102-2108 (2003).
[CrossRef] [PubMed]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Leinert, C.

Li, Y.

T. F. Coleman and Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

Mahajan, V. N.

Morrison, R. L.

Neifeld, M. A.

Pauca, V. P.

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

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1-12 (2003).

Peterson, G.

G. Peterson, “Stray light calculation methods with optical ray trace software,” Proc. SPIE 3780, 132-137 (1999).
[CrossRef]

Plemmons, R. J.

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

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1-12 (2003).

Prasad, S.

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

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1-12 (2003).

Prescott, R.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Rutkowski, J.

Silveira, P. E. X.

Smith, W. J.

W. J. Smith, Modern Lens Design (McGraw-Hill, 2005), Chap. 18.

Stack, R. A.

Tamayo, I.

Torgersen, T. C.

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

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1-12 (2003).

Tremblay, E. J.

Tsai, R. H.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50, 4-11 (2003).
[CrossRef]

van der Gracht, J.

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

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1-12 (2003).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Wach, H. B.

Wandell, B. A.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Appl. Opt. (9)

IEEE Trans. Electron Devices (1)

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron Devices 50, 4-11 (2003).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (3)

K. Kubala, E. Dowski, J. Kobus, and R. Brown, “Aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

G. Peterson, “Stray light calculation methods with optical ray trace software,” Proc. SPIE 3780, 132-137 (1999).
[CrossRef]

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

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

SIAM J. Optim. (2)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

T. F. Coleman and Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

Other (9)

H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice-Hall, 1977), Chap. 8, pp. 147-152.

B. R. Frieden, “Image enhancement and restoration,” in Topics in Applied Physics, Vol. 6 of Picture Processing and Digital Filtering, T. S. Huang, ed. (Springer-Verlag, 1979), pp. 177-248.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE 5108, 1-12 (2003).

J. Hall, “F-number, numerical aperture, and depth of focus,” in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 556-559.

W. J. Smith, Modern Lens Design (McGraw-Hill, 2005), Chap. 18.

D. Korsch, Reflective Optics (Academic, 1991).

M. Dirjish, “BSI technology flips digital imaging upside down,” http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=19160.

http://www.ispoptics.com/.

T. Ang, Dictionary of Photography and Digital Imaging: the Essential Reference for the Modern Photographer (Watson-Guptill, 2002).
[PubMed]

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Figures (12)

Fig. 1
Fig. 1

Design concept and geometry: (a) thin (paraxial) lens of focal length F and (b) four-reflection obscured version using a single thin (paraxial) reflector of focal length F.

Fig. 2
Fig. 2

Example curves of annular aperture width (w) versus FOV for various diameters using paraxial geometric calculations ( N = 4 , F = 20 mm , and n s = 1 in this example). As aperture size in increased, FOV decreases. As diameter is increased while maintaining fixed thickness, number of reflections, and focal length, both aperture and FOV increase.

Fig. 3
Fig. 3

(a) Layout drawing ( 3 / 4 section) of the four-reflection imager and (b) monochromatic MTF at the nominal design object distance of 10 m . OD, object distance; ID, image distance; OTF, optical transfer function.

Fig. 4
Fig. 4

Cross-section drawing of the mechanical lens package.

Fig. 5
Fig. 5

Simulated refocus performance of the four-reflection lens design. Monochromatic MTF curves at object distances of (a)  4 m and (b)  1 km . A 14 μm gap adjustment is required to focus from position (a) to position (b). OTF, optical transfer function.

Fig. 6
Fig. 6

Four-reflection imager assembly: (a) diamond turned and coated optical parts and (b) image of the assembled four-reflection imager with USB interface PCB.

Fig. 7
Fig. 7

Performance at 3.9 m : (a) full image, (b) enlarged and cropped 1951 USAF resolution chart, (c) measured CTF ( lens + sensor ) of the four-reflection imager compared to a conventional F / 1.4 lens of the same focal length and sensor, and (d) image space resolution versus object distance for the four-reflection imager and conventional F / 1.4 comparison imager.

Fig. 8
Fig. 8

Stray light in the four-reflection imager: (a) large angle oblique rays skip reflectors and arrive at the sensor as stray light, (b) axial light may enter through gaps in the front reflectors if a central block is not used, and (c) simulated and measured normalized intensity versus incidence angle.

Fig. 9
Fig. 9

Simulated PSFs at best focus and ± 10 μm defocus ( ± 3.5 waves defocus at 550 nm ). Unmodified PSFs (top row), PPE PSFs before filtering (middle row), and inverse-filtered PPE PSFs (bottom row).

Fig. 10
Fig. 10

Measured PSFs at 3.9 m (best focus) and ± 0.3 m ( ± 3.5 waves defocus at 550 nm ). Unmodified PSFs (top row), PPE PSFs before filtering (middle row), and inverse-filtered PPE PSFs (bottom row).

Fig. 11
Fig. 11

Experimental comparison images at 3.9 m (best focus): (a) unmodified imager and (b) processed PPE imager.

Fig. 12
Fig. 12

Experimental comparison images at 3.6 m ( 3.5 waves defocus at 550 nm ): (a) unmodified imager and (b) processed PPE imager.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

w = D 2 N tan ( FOV / 2 ) · F · ( 2 1 / N ) N ,
FOV = 2 tan 1 ( D N 2 F ( N 2 1 ) ) ,
w = D 2 N tan ( FOV / 2 ) · F · ( N 1 + 1 / N ) .
Sag ( r , θ ) = i = 1 m a i r b i cos ( w i θ + φ i ) ,
Sag ( r , θ ) = i = 1 8 a i ( r 0.81 ) i cos ( 3 θ ) for     { 0.81 r 1.0 } ,
merit value = offset α 1 A + α 2 B + α 3 C ,
A = mean c , f , λ ( mean u x , u y ( MTF c , f , λ ( u x , u y ) ) ) ,
B = mean u x , u y ( stdev c , f , λ ( MTF c , f , λ ( u x , u y ) ) ) .
C = mean c , f , λ ( β c , f , λ ) ,
β c , f , λ = { ( δ thresh MTF min ; c , f , λ ( δ thresh / 10 ) ) n if     ( δ thresh MTF min ; c , f , λ ( δ thresh / 10 ) ) > 0 0 otherwise .

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