Abstract

For a severely defocused incoherent system, its optical transfer function (OTF) has isolated zeros; therefore, an exact inverse filtering cannot be performed. Isolated zeros in the OTF can be avoided by choosing an annular aperture with a proper radius ratio, as the aperture can extend the depth of focus of the system. However, in the process of increasing the depth of focus of the system, this method results in a loss of image contrast. A simple hybrid optical/digital image processing system in which a TV camera device is coupled with an annular aperture is considered. Annular-pass filtering to compensate for the loss of contrast is performed by a digital computer. Experimental results are presented.

© 1987 Optical Society of America

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References

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  1. M. Mino, Y. Okano, “Improvement in the OTF of a Defocused Optical System Through the use of Shaded Apertures,” Appl. Opt. 10, 2219 (1971).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. R. J. Pieper, A. Korpel, “Image Processing for Extended Depth of Field,” Appl. Opt. 22, 1449 (1983).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. G. Häusler, A. Lohmann, “Hybrid Image Processing,” Applications of Holography and Optical Data Processing, E. Maron, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, London, 1977), p. 9.
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. A. Korpel, “Comments on ‘Diffraction-Free Beams’,”submitted to Phys. Rev. Lett.
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1986 (1)

1985 (1)

1984 (1)

1983 (1)

1982 (1)

G. Häusler, E. Körner, “Expansion of Depth of Focus by Image De-Puzzling,” in Proceedings, Sixth International Conference on Pattern Recognition (1982), p. 1201.

1972 (1)

G. Hausler, “A Method to Increase the Depth of Focus by Two Step Image Processing,” Opt. Commun. 6, 38 (1972).
[CrossRef]

1971 (2)

1960 (1)

1956 (1)

1953 (1)

E. H. Linfoot, E. Wolf, “Diffraction Images in Systems with an Annular Aperture,” Proc. Phys. Soc. London Ser. B 66, 145 (1953).
[CrossRef]

Andres, P.

Bai, H.

Diaz, A.

Hausler, G.

G. Hausler, “A Method to Increase the Depth of Focus by Two Step Image Processing,” Opt. Commun. 6, 38 (1972).
[CrossRef]

Häusler, G.

G. Häusler, E. Körner, “Expansion of Depth of Focus by Image De-Puzzling,” in Proceedings, Sixth International Conference on Pattern Recognition (1982), p. 1201.

G. Häusler, A. Lohmann, “Hybrid Image Processing,” Applications of Holography and Optical Data Processing, E. Maron, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, London, 1977), p. 9.

Ichioka, Y.

Indebetouw, G.

Körner, E.

G. Häusler, E. Körner, “Expansion of Depth of Focus by Image De-Puzzling,” in Proceedings, Sixth International Conference on Pattern Recognition (1982), p. 1201.

Korpel, A.

R. J. Pieper, A. Korpel, “Image Processing for Extended Depth of Field,” Appl. Opt. 22, 1449 (1983).
[CrossRef] [PubMed]

A. Korpel, U. Iowa; private communication.

A. Korpel, “Comments on ‘Diffraction-Free Beams’,”submitted to Phys. Rev. Lett.

Linfoot, E. H.

E. H. Linfoot, E. Wolf, “Diffraction Images in Systems with an Annular Aperture,” Proc. Phys. Soc. London Ser. B 66, 145 (1953).
[CrossRef]

Lohmann, A.

G. Häusler, A. Lohmann, “Hybrid Image Processing,” Applications of Holography and Optical Data Processing, E. Maron, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, London, 1977), p. 9.

McCrickerd, J. T.

Mino, M.

Ojeda-Castaneda, J.

Okano, Y.

O'Neill, E. L.

Park, J.

R. J. Pieper, J. Park, T.-C. Poon, “Resolution-Dependent Depth of Focus for an Incoherent Imaging System,” submitted to Appl. Opt.
[PubMed]

Pieper, R. J.

R. J. Pieper, A. Korpel, “Image Processing for Extended Depth of Field,” Appl. Opt. 22, 1449 (1983).
[CrossRef] [PubMed]

R. J. Pieper, J. Park, T.-C. Poon, “Resolution-Dependent Depth of Focus for an Incoherent Imaging System,” submitted to Appl. Opt.
[PubMed]

Poon, T.-C.

R. J. Pieper, J. Park, T.-C. Poon, “Resolution-Dependent Depth of Focus for an Incoherent Imaging System,” submitted to Appl. Opt.
[PubMed]

Sugimoto, S. A.

Welford, W. T.

Wolf, E.

E. H. Linfoot, E. Wolf, “Diffraction Images in Systems with an Annular Aperture,” Proc. Phys. Soc. London Ser. B 66, 145 (1953).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

G. Hausler, “A Method to Increase the Depth of Focus by Two Step Image Processing,” Opt. Commun. 6, 38 (1972).
[CrossRef]

Opt. Lett. (1)

Proc. Phys. Soc. London Ser. B (1)

E. H. Linfoot, E. Wolf, “Diffraction Images in Systems with an Annular Aperture,” Proc. Phys. Soc. London Ser. B 66, 145 (1953).
[CrossRef]

Proceedings, Sixth International Conference on Pattern Recognition (1)

G. Häusler, E. Körner, “Expansion of Depth of Focus by Image De-Puzzling,” in Proceedings, Sixth International Conference on Pattern Recognition (1982), p. 1201.

Other (4)

A. Korpel, U. Iowa; private communication.

G. Häusler, A. Lohmann, “Hybrid Image Processing,” Applications of Holography and Optical Data Processing, E. Maron, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, London, 1977), p. 9.

A. Korpel, “Comments on ‘Diffraction-Free Beams’,”submitted to Phys. Rev. Lett.

R. J. Pieper, J. Park, T.-C. Poon, “Resolution-Dependent Depth of Focus for an Incoherent Imaging System,” submitted to Appl. Opt.
[PubMed]

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Figures (6)

Fig. 1
Fig. 1

Uncertainty principle used in finding depth of focus: (a) lens with no central obstruction; (b) lens with annular aperture.

Fig. 2
Fig. 2

Autocorrelation of annular pupil function.

Fig. 3
Fig. 3

(a) OTF of system with annular aperture; (b) normalized OTF.

Fig. 4
Fig. 4

Annular-pass filter.

Fig. 5
Fig. 5

Optical/digital image processing system.

Fig. 6
Fig. 6

(a) In-focus text; (b) severely out-of-focus text; (c) processing of (b) using annular aperture; (d) annular-pass filtered output of (c).

Equations (11)

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

δ z δ p z h ,
δ p z = p 0 p 0 cos ( β / 2 ) ,
δ z = λ / [ 1 cos ( β / 2 ) ] ,
δ z = λ / [ 1 1 sin 2 ( β / 2 ) ] 2 λ / sin 2 ( β / 2 ) ,
δ z 8 λ f # 2 ,
δ p z = δ p a δ p b ,
δ p z = p 0 [ cos ( α / 2 ) cos ( β / 2 ) ] ,
δ z = λ / [ cos ( α / 2 ) cos ( β / 2 ) ] ,
δ z = λ 1 1 + ( 2 f # ) 2 1 1 + ( 1 2 f # ) 2 ,
δ z 8 λ f # 2 / ( 1 2 ) .
OTF ( 0 ) = π ( a 2 b 2 ) = π a 2 ( 1 2 ) .

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