Abstract

We present an approach that provides superresolution beyond the classical limit as well as image restoration in the presence of aberrations; in particular, the ability to obtain superresolution while extending the depth of field (DOF) simultaneously is tested experimentally. It is based on an approach, recently proposed, shown to increase the resolution significantly for in-focus images by speckle encoding and decoding. In our approach, an object multiplied by a fine binary speckle pattern may be located anywhere along an extended DOF region. Since the exact magnification is not known in the presence of defocus aberration, the acquired low-resolution image is electronically processed via a parallel-branch decoding scheme, where in each branch the image is multiplied by the same high-resolution synchronized time-varying binary speckle but with different magnification. Finally, a hard-decision algorithm chooses the branch that provides the highest-resolution output image, thus achieving insensitivity to aberrations as well as DOF variations. Simulation as well as experimental results are presented, exhibiting significant resolution improvement factors.

© 2007 Optical Society of America

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References

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2006 (1)

2005 (2)

2004 (1)

Z. Zalevsky and D. Mendlovic, Optical Superresolution (Springer-Verlag, 2004).

2003 (1)

2001 (1)

1999 (2)

1997 (1)

1995 (1)

1991 (1)

1990 (1)

1989 (1)

1988 (1)

1985 (1)

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 371-372.

1984 (1)

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1984), pp. 9-75.

1974 (1)

1971 (1)

1969 (1)

1966 (1)

1963 (1)

W. Gartner and A. W. Lohmann, "An experiment going beyond Abbe's limit of diffraction," Z. Phys. 174, 18-23 (1963).

1960 (1)

A. I. Kartashev, "Optical systems with enhanced resolving power," Opt. Spectrosc. 9, 204-206 (1960).

1952 (1)

M. Francon, "Amelioration de resolution d'optique," Nuovo Cimento, Suppl. 9, 283-290 (1952).

Ben-Eliezer, E.

Bergstein, L.

Berriel-Valdos, L. R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Castaneda, J. O.

Cathey, W. T.

Chi, W.

Diaz, A.

Dowski, E. R.

Fixler, D.

Francon, M.

M. Francon, "Amelioration de resolution d'optique," Nuovo Cimento, Suppl. 9, 283-290 (1952).

Garcia, J.

García, J.

Garcia Martinez, P.

Gartner, W.

W. Gartner and A. W. Lohmann, "An experiment going beyond Abbe's limit of diffraction," Z. Phys. 174, 18-23 (1963).

George, N.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 371-372.

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1984), pp. 9-75.

Kartashev, A. I.

A. I. Kartashev, "Optical systems with enhanced resolving power," Opt. Spectrosc. 9, 204-206 (1960).

Konforti, N.

Kresic-Juric, S.

Lohmann, A. W.

D. Mendlovic and A. W. Lohmann, "Spacebandwidth product adaptation and its application to superresolution: fundamentals," J. Opt. Soc. Am. A 14, 558-562 (1997).
[CrossRef]

W. Gartner and A. W. Lohmann, "An experiment going beyond Abbe's limit of diffraction," Z. Phys. 174, 18-23 (1963).

Lukosz, W.

Marom, E.

Martial, G.

Mendlovic, D.

Mino, M.

Noyola-Isgleas, A.

Okano, Y.

Ramos, R.

Shemer, A.

Tatian, B.

Tepichin, E.

Toraldo Di Francia, G.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Zalevsky, Z.

Appl. Opt. (8)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (4)

Nuovo Cimento, Suppl. (1)

M. Francon, "Amelioration de resolution d'optique," Nuovo Cimento, Suppl. 9, 283-290 (1952).

Opt. Express (1)

Opt. Spectrosc. (1)

A. I. Kartashev, "Optical systems with enhanced resolving power," Opt. Spectrosc. 9, 204-206 (1960).

Z. Phys. (1)

W. Gartner and A. W. Lohmann, "An experiment going beyond Abbe's limit of diffraction," Z. Phys. 174, 18-23 (1963).

Other (4)

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1984), pp. 9-75.

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 371-372.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Z. Zalevsky and D. Mendlovic, Optical Superresolution (Springer-Verlag, 2004).

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Figures (10)

Fig. 1
Fig. 1

Imaging system block diagram.

Fig. 2
Fig. 2

(a) Typical binary speckle pattern. (b) Cross section of the correlation function for p = 10 % (solid curve), p = 20 % (dotted curve), and p = 50 % (dashed curve).

Fig. 3
Fig. 3

Acquired signal, I A , is processed in L parallel channels in an extended DOF decoding stage. In each channel the signal is multiplied by time-varying speckle S, summed ( ) , and thresholded (Thr.). The optimal channel is chosen by a hard-decision stage.

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

(a) Magnified object with reference squares. (b) A typical encoded object; reference squares are not encoded.

Fig. 6
Fig. 6

(a) Single frame of speckle-encoded object. (b) Image of (a) at out-of-focus position ( M t = 1.13 ) . (c) Restored noisy output if threshold is not applied. (d) Restored output with threshold.

Fig. 7
Fig. 7

Computer simulations, (a) Object’s smallest letter U. (b) Blurred image. (c) Same image at output—processed without threshold. (d) Output image—processed with threshold.

Fig. 8
Fig. 8

Experimental results for the in-focus position ( d o b j = 58.5 cm ) . (a) Typical captured blurred image. (b) Blurred image—averaged. (c) Superresolved signal restoration.

Fig. 9
Fig. 9

Experimental results for the severe out-of-focus position ( d o b j = 45 cm ) . (a) Typical captured blurred image, (b) Blurred image—averaged. (c) Superresolved signal restoration.

Fig. 10
Fig. 10

Computer simulation—spherical aberration restoration. (a) Output image with conventional imaging for two adjacent points. (b) Magnified cross section along the horizontal central line. (c) Output image with superresolving restoration for the same two adjacent points. (d) Magnified cross section along the horizontal central line.

Equations (9)

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I ( x , ξ ) = κ I o b j ( x M t ) S o b j ( ( x ξ ) M t ) h ( x x ) 2 d x ,
I ( x , t ) = κ I o b j ( x M t ) S o b j ( x M t ; t ) h ( x x ) 2 d x .
I ( x ) = κ n S o b j ( ( x ξ n ) M t ) I o b j ( x M t ) S o b j ( ( x ξ n ) M t ) h ( x x ) 2 d x ,
I ( x ) = κ n S o b j ( x M t ; t n ) I o b j ( x M t ) S o b j ( x M t ; t n ) h ( x x ) 2 d x .
lim N ξ n + 1 ξ n N n = 1 N S o b j ( ( x ξ n ) M t ) S o b j ( ( x ξ n ) M t ) = S o b j ( ( x ξ ) M t ) S o b j ( ( x ξ ) M t ) d ξ = I 2 ( 1 + μ ( x x ) 2 ) ,
lim N 1 N n = 1 N S o b j ( x M t ; t n ) S o b j ( x M t ; t n ) = p [ p + ( 1 p ) Λ ( x x M t L ) ] ,
I ( x ) = κ p I o b j ( x M t ) h ( x x ) 2 [ p + ( 1 p ) Λ ( x x M t L ) ] d x = κ p 2 I o b j ( x M t ) h ( x x ) 2 d x + κ ( p p 2 ) I o b j ( x M t ) h ( x x ) 2 Λ ( x x M t L ) d x .
I b l u r ( x ) = lim N κ N n = 1 N I o b j ( x M t ) S o b j ( x M t ; t n ) h ( x x ) 2 d x .
I b l u r ( x ) = κ p I o b j ( x M t ) h ( x x ) 2 d x .

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