Abstract

We present an iterative camera aperture design procedure, which determines an optimal mask pattern based on a sparse set of desired intensity distributions at different focal depths. This iterative method uses the ambiguity function as a tool to shape the camera’s response to defocus, and shares conceptual similarities with phase retrieval procedures. An analysis of algorithm convergence is presented, and experimental examples are shown to demonstrate the flexibility of the design process. This algorithm potentially ties together previous disjointed PSF design approaches under a common framework, and offers new insights for the creation of future application-specific imaging systems.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. A. W. Lohmann, “Three-dimensional properties of wave fields,” Optik (Stuttg.) 51, 105–117 (1978).

2010 (2)

2007 (2)

A. Ashok and M. Neifeld, “Pseudo-random phase masks for superresolution imaging from subpixel shifting,” Appl. Opt. 46(12), 2256 (2007).
[CrossRef]

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 70 (2007).
[CrossRef]

2006 (1)

2003 (2)

D. Elkind, Z. Zalevsky, U. Levy, and D. Mendlovic, “Optical transfer function shaping and depth of focus by using a phase only filter,” Appl. Opt. 42(11), 1925–1931 (2003).
[CrossRef] [PubMed]

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225(1-3), 19–30 (2003).
[CrossRef]

2002 (2)

2001 (2)

W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26(12), 875–877 (2001).
[CrossRef] [PubMed]

W. D. Furlan, D. Zalvidea, and G. Saavedra, “Synthesis of filters for specified axial irradiance by use of phase-space tomography,” Opt. Commun. 189(1-3), 15–19 (2001).
[CrossRef]

1997 (1)

J. Tu and S. Tamura, “Wave-field determination using tomography of the ambiguity function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(2), 1946–1949 (1997).
[CrossRef]

1995 (1)

1994 (1)

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef] [PubMed]

1988 (1)

1983 (2)

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73(11), 1434–1441 (1983).
[CrossRef]

K. H. Brenner, A. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

1982 (2)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).

1978 (1)

A. W. Lohmann, “Three-dimensional properties of wave fields,” Optik (Stuttg.) 51, 105–117 (1978).

1974 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane figures,” Optik (Stuttg.) 35, 237–246 (1972).

Ashok, A.

Barbastathis, G.

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef] [PubMed]

Berriel-Valdos, L. R.

Brenner, K. H.

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225(1-3), 19–30 (2003).
[CrossRef]

K. H. Brenner, A. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Cathey, W. T.

Chi, W.

Dowski, E. R.

Durand, F.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 70 (2007).
[CrossRef]

Elkind, D.

Fergus, R.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 70 (2007).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[CrossRef] [PubMed]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).

Freeman, W. T.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 70 (2007).
[CrossRef]

Furlan, W. D.

W. D. Furlan, D. Zalvidea, and G. Saavedra, “Synthesis of filters for specified axial irradiance by use of phase-space tomography,” Opt. Commun. 189(1-3), 15–19 (2001).
[CrossRef]

George, N.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane figures,” Optik (Stuttg.) 35, 237–246 (1972).

Greengard, A.

Kutay, M. A.

Levin, A.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 70 (2007).
[CrossRef]

Levy, U.

Li, Y.

Liu, X.

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225(1-3), 19–30 (2003).
[CrossRef]

Lohmann, A.

K. H. Brenner, A. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, “Three-dimensional properties of wave fields,” Optik (Stuttg.) 51, 105–117 (1978).

McAlister, D. F.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef] [PubMed]

Mendlovic, D.

Montes, E.

Neifeld, M.

Ojeda-Castaneda, J.

K. H. Brenner, A. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Ojeda-Castañeda, J.

Ozaktas, H. M.

Papoulis, A.

Piestun, R.

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31(2), 181–183 (2006).
[CrossRef] [PubMed]

R. Piestun and J. Shamir, “Synthesis of three-dimensional light fields and applications,” Proc. IEEE 90(2), 222–244 (2002).
[CrossRef]

Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef] [PubMed]

Saavedra, G.

W. D. Furlan, D. Zalvidea, and G. Saavedra, “Synthesis of filters for specified axial irradiance by use of phase-space tomography,” Opt. Commun. 189(1-3), 15–19 (2001).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane figures,” Optik (Stuttg.) 35, 237–246 (1972).

Schechner, Y. Y.

Shamir, J.

R. Piestun and J. Shamir, “Synthesis of three-dimensional light fields and applications,” Proc. IEEE 90(2), 222–244 (2002).
[CrossRef]

Tamura, S.

J. Tu and S. Tamura, “Wave-field determination using tomography of the ambiguity function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(2), 1946–1949 (1997).
[CrossRef]

Teague, M. R.

Tian, L.

Tu, J.

J. Tu and S. Tamura, “Wave-field determination using tomography of the ambiguity function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(2), 1946–1949 (1997).
[CrossRef]

Waller, L.

Wolf, E.

Yüksel, S.

Zalevsky, Z.

Zalvidea, D.

W. D. Furlan, D. Zalvidea, and G. Saavedra, “Synthesis of filters for specified axial irradiance by use of phase-space tomography,” Opt. Commun. 189(1-3), 15–19 (2001).
[CrossRef]

Zhao, H.

ACM Trans. Graph. (1)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 70 (2007).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. (3)

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

Opt. Commun. (3)

W. D. Furlan, D. Zalvidea, and G. Saavedra, “Synthesis of filters for specified axial irradiance by use of phase-space tomography,” Opt. Commun. 189(1-3), 15–19 (2001).
[CrossRef]

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225(1-3), 19–30 (2003).
[CrossRef]

K. H. Brenner, A. Lohmann, and J. Ojeda-Castaneda, “The ambiguity function as a polar display of the OTF,” Opt. Commun. 44(5), 323–326 (1983).
[CrossRef]

Opt. Eng. (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. 19, 297–305 (1980).

Opt. Express (1)

Opt. Lett. (3)

Optik (Stuttg.) (2)

A. W. Lohmann, “Three-dimensional properties of wave fields,” Optik (Stuttg.) 51, 105–117 (1978).

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane figures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

J. Tu and S. Tamura, “Wave-field determination using tomography of the ambiguity function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 55(2), 1946–1949 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72(8), 1137–1140 (1994).
[CrossRef] [PubMed]

Proc. IEEE (1)

R. Piestun and J. Shamir, “Synthesis of three-dimensional light fields and applications,” Proc. IEEE 90(2), 222–244 (2002).
[CrossRef]

Other (4)

M. D. Stenner, D. J. Townsend, and M. E. Gehm, “Static Architecture for Compressive Motion Detection in Persistent, Pervasive Surveillance Applications,” in Imaging Systems, OSA technical Digest (CD) (Optical Society of America, 2010), paper IMB2. http://www.opticsinfobase.org/abstract.cfm?URI=IS-2010-IMB2

M. Testorf, B. Hennelly, and J. Ojeda-Castaneda, Phase Space Optics: Fundamentals and Applications, (McGraw-Hill, (2010).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1982), Chap. 4.

L. Hogben, Handbook of Linear Algebra (Chapman & Hall, 2007) Chap. 5.

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