Abstract

We present a proof of the conjecture reported in Stein and Barbastathis [“Axial imaging necessitates loss of lateral shift invariance,” Appl. Opt.41, 6055-6061 (2002)APOPAI0003-693510.1364/AO.41.006055] that axial imaging necessitates loss of lateral shift invariance. We apply the Wigner distribution function (WDF) to the axial imaging process and compare laterally shift variant and invariant imaging systems. Two conditions for axial imaging are established: (i) objects with spatially variant local spatial frequency content to create sufficient change in the WDF with defocus and (ii) properly designed shift variant imaging kernels to estimate the slope of the sheared WDF. The lateral shift variance is a necessary condition for axial imaging. We use two examples from Stein and Barbastathis to show how axial imaging is interpreted in Wigner space.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008 (1)

2005 (1)

2002 (1)

1992 (1)

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99-106 (1992).
[CrossRef]

1986 (1)

1984 (1)

K. H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta 31, 213-223(1984).

1973 (1)

1970 (1)

1965 (1)

1932 (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Adelson, E. H.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99-106 (1992).
[CrossRef]

Allen, J. B.

Barbastathis, G.

Bastiaans, M. J.

M. J. Bastiaans, “Application of the Wigner distribution function to partially coherent-light,” J. Opt. Soc. Am. A 3, 1227-1238 (1986).
[CrossRef]

M. J. Bastiaans, “Application of the Wigner distribution function in optics,” in “The Wigner Distribution--Theory and Applications in Signal Processing,” W.Mecklenbräuker and F.Hlawatsch, eds. (Elsevier Science, 1997), pp. 375-426.

Brenner, K. H.

K. H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta 31, 213-223(1984).

Durand, F.

A. Levin, W. T. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” Tech. Rep. MIT-CSAIL-TR-2008-049 (Massachusetts Institute of Technology, 2008).

Freeman, W. T.

A. Levin, W. T. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” Tech. Rep. MIT-CSAIL-TR-2008-049 (Massachusetts Institute of Technology, 2008).

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).

Johnson, W. O.

Levin, A.

A. Levin, W. T. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” Tech. Rep. MIT-CSAIL-TR-2008-049 (Massachusetts Institute of Technology, 2008).

Lohmann, A. W.

Meadows, D. M.

Ojeda-Castañeda, J.

K. H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta 31, 213-223(1984).

Pan, W.

Paris, D. P.

Sheppard, C. J. R.

C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (Springer, 1997).

Shotton, D. M.

C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (Springer, 1997).

Stein, A.

Sun, W.

Takasaki, H.

Wang, J. Y. A.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99-106 (1992).
[CrossRef]

Wigner, E.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99-106 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Acta (1)

K. H. Brenner and J. Ojeda-Castañeda, “Ambiguity function and Wigner distribution function applied to partially coherent imagery,” Opt. Acta 31, 213-223(1984).

Opt. Lett. (1)

Phys. Rev. (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Other (4)

M. J. Bastiaans, “Application of the Wigner distribution function in optics,” in “The Wigner Distribution--Theory and Applications in Signal Processing,” W.Mecklenbräuker and F.Hlawatsch, eds. (Elsevier Science, 1997), pp. 375-426.

A. Levin, W. T. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” Tech. Rep. MIT-CSAIL-TR-2008-049 (Massachusetts Institute of Technology, 2008).

C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (Springer, 1997).

K. J. Gåsvik, Optical Metrology, 3rd ed. (Wiley, 2002).

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