Abstract

The capability of the CLEAN algorithm, which is able to develop image information corresponding to spatial frequencies for which the imaging system’s optical transfer function (OTF) is equal to zero, is shown to be dependent on the limited size of the object being imaged. It is found that this capability is available without a severe signal-to-noise-ratio penalty only for the recovery of a spatial frequency that is sufficiently close to some other spatial frequency for which the OTF is not equal to zero. As used here the term “sufficiently close” means that the magnitude of the separation of the spatial frequencies is less than one half of the inverse of the size of the object being imaged. This represents a limitation of CLEAN’s capability deriving from object size. It is suggested that this capability can be thought of in terms of superresolution, with the same limitation in regard to object size.

© 1995 Optical Society of America

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References

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  2. J. A. Roberts, ed., Indirect Imaging, Proceedings of an International Symposium, Sydney Australia, 30 August to 2 September 1983 (Cambridge U. Press, London, 1984).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1993 (4)

J. P. Fillard, H. M’timet, J. M. Lussert, M. Castagne, “Computer simulation of super-resolution point source image detection,” Opt. Eng. 32, 2936 – 2944 (1993).
[CrossRef]

E. Noel, R. R. Khan, H. S. Dhadwal, “Optical implementation of a regularized Gerchberg iterative algorithm for super-resolution,” Opt. Eng. 32, 2866–2871 (1993).
[CrossRef]

J. G. Walker, E. R. Pike, R. E. Davies, M. R. Young, G. J. Brakenhoff, M. Bertero, “Superresolving scanning optical microscopy using holographic optical processing,” J. Opt. Soc. Am. A 10, 59–64 (1993).
[CrossRef]

E. Scales, G. A. Viano, “Resolving power and information theory in signal recovery,” J. Opt. Soc. Am. A 10, 991–996 (1993).
[CrossRef]

1992 (2)

1968 (1)

1967 (1)

1966 (2)

1964 (1)

Barnes, C. W.

Bertero, M.

Brakenhoff, G. J.

Castagne, M.

J. P. Fillard, H. M’timet, J. M. Lussert, M. Castagne, “Computer simulation of super-resolution point source image detection,” Opt. Eng. 32, 2936 – 2944 (1993).
[CrossRef]

Courjon, D.

Davies, R. E.

Dhadwal, H. S.

E. Noel, R. R. Khan, H. S. Dhadwal, “Optical implementation of a regularized Gerchberg iterative algorithm for super-resolution,” Opt. Eng. 32, 2866–2871 (1993).
[CrossRef]

Fillard, J. P.

J. P. Fillard, H. M’timet, J. M. Lussert, M. Castagne, “Computer simulation of super-resolution point source image detection,” Opt. Eng. 32, 2936 – 2944 (1993).
[CrossRef]

Frieden, B. R.

B. R. Frieden, “Band-unlimited reconstruction of optical objects and spectra,” J. Opt. Soc. Am. 57, 1013–1019 (1967).
[CrossRef]

B. R. Frieden, “Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1971), Vol. 19, pp. 311–407.
[CrossRef]

Harris, J. L.

Harris, R. W.

Khan, R. R.

E. Noel, R. R. Khan, H. S. Dhadwal, “Optical implementation of a regularized Gerchberg iterative algorithm for super-resolution,” Opt. Eng. 32, 2866–2871 (1993).
[CrossRef]

Leith, E. N.

Lukosz, W.

Lussert, J. M.

J. P. Fillard, H. M’timet, J. M. Lussert, M. Castagne, “Computer simulation of super-resolution point source image detection,” Opt. Eng. 32, 2936 – 2944 (1993).
[CrossRef]

M’timet, H.

J. P. Fillard, H. M’timet, J. M. Lussert, M. Castagne, “Computer simulation of super-resolution point source image detection,” Opt. Eng. 32, 2936 – 2944 (1993).
[CrossRef]

Moran, J. M.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986).

Noel, E.

E. Noel, R. R. Khan, H. S. Dhadwal, “Optical implementation of a regularized Gerchberg iterative algorithm for super-resolution,” Opt. Eng. 32, 2866–2871 (1993).
[CrossRef]

Pike, E. R.

Rushforth, C. K.

Scales, E.

Sun, P. C.

Swenson, G. W.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986).

Thompson, A. R.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986).

Viano, G. A.

Vigoureux, J. M.

Walker, J. G.

Young, M. R.

Appl. Opt. (2)

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

J. P. Fillard, H. M’timet, J. M. Lussert, M. Castagne, “Computer simulation of super-resolution point source image detection,” Opt. Eng. 32, 2936 – 2944 (1993).
[CrossRef]

E. Noel, R. R. Khan, H. S. Dhadwal, “Optical implementation of a regularized Gerchberg iterative algorithm for super-resolution,” Opt. Eng. 32, 2866–2871 (1993).
[CrossRef]

Other (3)

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, New York, 1986).

J. A. Roberts, ed., Indirect Imaging, Proceedings of an International Symposium, Sydney Australia, 30 August to 2 September 1983 (Cambridge U. Press, London, 1984).

B. R. Frieden, “Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1971), Vol. 19, pp. 311–407.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Array pattern for a six-element, one-dimensional, nonredundant array.

Fig. 2
Fig. 2

OTF for the six-element, one-dimensional, nonredundant array shown in Fig. 1.

Fig. 3
Fig. 3

Spatial-frequency-component estimation error.

Fig. 4
Fig. 4

Enhanced and filtered image signal-to-noise ratio as a function of spatial-frequency cutoff.

Fig. 5
Fig. 5

Enhanced image signal-to-noise ratio as a function of object size.

Equations (16)

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

f ( κ ) = d r exp ( 2 π i κ · r ) f ( r )
W ( r ) = { 1 if r ½ D 0 otherwise ,
f W ( r ) = f ( r ) W ( r ) .
f W ( κ ) = d r exp ( 2 π i κ · r ) f W ( r ) ,
f W ( κ ) f W * ( κ ) = d x Φ [ ½ ( κ + κ ) + x ] × W [ x ½ ( κ κ ) ] × W [ x + ½ ( κ κ ) ] ,
W ( κ ) = d r exp ( 2 π i κ · r ) W ( r ) = ( ¼ π D 2 ) 2 J 1 ( π κ D ) π κ D
Φ ( κ ) = d r exp ( 2 π i κ · r ) f ( r + ½ r ) f ( r ½ r ) .
| κ κ | < ½ D 1 ,
m = So + n ,
ô = Am ,
A = ( S T S ) 1 S T .
e ( κ ) = F inv C ( κ ) F A m F inv C ( κ ) F o .
e ( κ ) = F inv C ( κ ) F A n .
( κ ) = [ e ( κ ) ] T e ( κ ) ,
( κ ) = tr { [ F inv C ( κ ) F A ] [ F inv C ( κ ) F A ] T } σ 2 ,
E e ( κ ) = tr { [ D ( κ ) F A ] [ D ( κ ) F A ] T } σ 2 ,

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