Abstract

Annular folded imagers can be up to 10× thinner than corresponding full-aperture imagers, but have tight fabrication tolerances and relatively shallow depth of focus. Wavefront coding, the use of specialized optics with postdetection signal processing, has been used to improve the depth of focus in full-aperture imaging systems. Here we explore the application of wavefront coding to annular folded optics. We compare the design and experimental results for an imaging system with a 38  mm focal length and just 5  mm total track.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).
    [CrossRef]
  9. S. S. Sherif and W. T. Cathey, "Reduced depth of field in incoherent hybrid imaging systems," Appl. Opt. 41, 6062-6074 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. K. Kubala, E. Dowski, and W. T. Cathey, "Reducing complexity in computational imaging systems," Opt. Express 11, 2102-2108 (2003).
    [CrossRef] [PubMed]
  13. 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.
  14. H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice Hall, 1977), Chap. 8, pp. 147-152.

2007 (1)

2004 (1)

K. Kubala, E. Dowski, J. Kobus, and R. Brown, "Aberration and error invariant space telescope systems," in Novel Optical Systems Design and Optimization VII, J. M. Sasian, R. J. Koshel, P. K. Manhart, and R. C. Juergens, eds., Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

2003 (2)

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).
[CrossRef]

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

2002 (3)

V. Draganov and D. G. James, "Compact telescope for free-space communications," in Current Developments in Lens Design and Optical Engineering III, Robert E. Fischer, Warren J. Smith, R. Barry Johnson, eds., Proc. SPIE 4767, 151-158 (2002).
[CrossRef]

S. S. Sherif and W. T. Cathey, "Reduced depth of field in incoherent hybrid imaging systems," Appl. Opt. 41, 6062-6074 (2002).
[CrossRef] [PubMed]

W. T. Cathey and E. Dowski, "A new paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).
[CrossRef] [PubMed]

2001 (1)

1995 (1)

1974 (1)

S. N. Bezdidko, "The use of Zernike polynomials in optics," Sov. J. Opt. Technol. 41, 425-429 (1974).

1954 (1)

A. B. Bhatia and E. Wolf, "On the circle polynomials of Zernike and related orthogonal sets," Proc. Cambridge Philos. Soc. 50, 40-48 (1954).
[CrossRef]

Appl. Opt. (4)

Opt. Express (1)

Opt. Lett. (1)

Proc. Cambridge Philos. Soc. (1)

A. B. Bhatia and E. Wolf, "On the circle polynomials of Zernike and related orthogonal sets," Proc. Cambridge Philos. Soc. 50, 40-48 (1954).
[CrossRef]

Proc. SPIE (3)

V. Draganov and D. G. James, "Compact telescope for free-space communications," in Current Developments in Lens Design and Optical Engineering III, Robert E. Fischer, Warren J. Smith, R. Barry Johnson, eds., Proc. SPIE 4767, 151-158 (2002).
[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," in Visual Information Processing XII, Z. Rahman, R. Schowengerdt, and S. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).
[CrossRef]

K. Kubala, E. Dowski, J. Kobus, and R. Brown, "Aberration and error invariant space telescope systems," in Novel Optical Systems Design and Optimization VII, J. M. Sasian, R. J. Koshel, P. K. Manhart, and R. C. Juergens, eds., Proc. SPIE 5524, 54-65 (2004).
[CrossRef]

Sov. J. Opt. Technol. (1)

S. N. Bezdidko, "The use of Zernike polynomials in optics," Sov. J. Opt. Technol. 41, 425-429 (1974).

Other (3)

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

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.

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

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Figures (10)

Fig. 1
Fig. 1

Annular folded design. Zonal aspheric reflectors on the back side of the optical element focus light in an image sensor at the center of the element. (a) Cross section illustrating ray path. (b) Back (aspheric) side perspective view.

Fig. 2
Fig. 2

Three-dimensional surface measurement of a diamond turned asphere in calcium fluoride using a large-magnification white-light interferometer.

Fig. 3
Fig. 3

Ray trace comparison of aberrations in a 90% obscured imaging system (dark lines) versus those in a conventional imaging system (gray lines). (a) Spherical aberration translates into defocus. (b) Coma translates into tilt.

Fig. 4
Fig. 4

Thru-focus MTF plot for an on-axis field point at 156 cycles∕mm in image space, showing the expected extension of the depth of focus in the wavefront-coded design before filtering.

Fig. 5
Fig. 5

Thru-focus simulated digital PSFs for the nominal wavefront-coded and traditional imagers.

Fig. 6
Fig. 6

Digital filter used to process wavefront-coded images. The noise gain is 1.35, meaning that a small noise penalty is expected.

Fig. 7
Fig. 7

Best-focus PSF measured using wavefront-coded folded imaging system.

Fig. 8
Fig. 8

Filter designed using measured PSF. The filter noise gain is 3.64, indicating that noisy images should be expected.

Fig. 9
Fig. 9

U.S. Air Force (USAF) targets imaged through annular folded imagers at best-focus. (a) Non-wave-front-coded. (b) Wave-front-coded.

Fig. 10
Fig. 10

USAF targets imaged through annular folded imagers at 10 μm away from best focus. (a) Non-wave-front-coded. (b) Wave-front-coded.

Tables (1)

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Table 1 Calculated Fabrication Tolerances for the Annular Folded Design

Equations (4)

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z 9 , z 4 z 4 , z 4 = 0 2 π a 1 Z 9 Z 4 r d r d θ 0 2 π a 1 Z 4 Z 4 r d r d θ = 3 a 2 9 a 4 + 9 a 6 1 2 a 2 + 4 a 4 .
z 7 , z 2 z 2 , z 2 = 0 2 π a 1 Z 7 Z 2 r d r d θ 0 2 π a 1 Z 2 Z 2 r d r d θ = 2 a 4 1 + a 2 .
S a g WFC ( r , θ ) = i = 1 m a i r b i   cos ( w i θ + φ i ) ,
S a g WFC ( r , θ ) = i = 1 m a i ( 10 r 9 ) i   cos ( 3 θ ) for   { 0 .9 r 1.0 } .

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