Abstract

We present an innovative approach that allows superresolved images to be obtained by axial moving of two gratings and time integrating in the detector plane. The two gratings do not have to be in contact with either the object or the detector, and both are positioned between the object and the image planes. One of the main applications for the proposed approach in contrast to previously discussed time multiplexing superresolving methods is that it may fit well to superresolved imaging of remote objects, since both gratings are not in contact with either the object or the detector planes.

© 2007 Optical Society of America

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  1. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," in Progress in Optics, Vol. XL, E.Wolf, ed. (Elsevier, 1999).
  2. Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).
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    [CrossRef]
  4. A. I. Kartashev, "Optical systems with enhanced resolving power," Opt. Spectrosc. 9, 204-206 (1960).
  5. W. Gartner and A. W. Lohmann, "Ein experiment zur uberschreitung der abbeschen auflosungsgrenze," Z. Physik 174, 18 (1963).
  6. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-428 (1952).
    [CrossRef]
  7. Z. Zalevsky, P. García-Martínez, and J. García, "Superresolution using gray level coding," Opt. Express 14, 5178-5182 (2006).
    [CrossRef] [PubMed]
  8. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, "About the space bandwidth product of optical signal and systems," J. Opt. Soc. Am. A 13, 470-473 (1996).
    [CrossRef]
  9. D. Mendlovic and A. W. Lohmann, "Space-bandwidth product adaptation and its application for superresolution: fundamentals," J. Opt. Soc. Am. A 14, 558-562 (1997).
    [CrossRef]
  10. D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application for superresolution: examples," J. Opt. Soc. Am. A 14, 563-567 (1997).
    [CrossRef]
  11. X. Chen and S. R. J. Brueck, "Imaging interferometric lithography: approaching the resolution limits of optics," Opt. Lett. 24, 124-126 (1999).
    [CrossRef]
  12. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
    [CrossRef] [PubMed]
  13. V. Mico, Z. Zalevsky, and J. García, "Superresolution optical system by common-path interferometry," Opt. Express 14, 5168-5177 (2006).
    [CrossRef] [PubMed]
  14. J. García, Z. Zalevsky, and C. Ferreira, "Superresolved imaging of remote moving targets," Opt. Lett. 31, 586-588 (2006).
    [CrossRef] [PubMed]
  15. R. Binet, J. Colineau, and J. C. Lehureau, "Short-range synthetic aperture imaging at 633 nm by digital holography," Appl. Opt. 41, 4775-4782 (2002).
    [CrossRef] [PubMed]
  16. J. H. Massig, "Digital off-axis holography with a synthetic aperture," Opt. Lett. 27, 2179-2181 (2002).
    [CrossRef]
  17. Ch. K. Hitzenberger, P. Trost, P. W. Lo, and Q. Zhou, "Three-dimensional imaging of the human retina by high-speed optical coherence tomography," Opt. Express 11, 2753-2761 (2003).
    [CrossRef] [PubMed]
  18. P. Massatsch, F. Charrère, E. Cuche, P. Marquet, and Ch. D. Depeursinge, "Time-domain optical coherence tomography with digital holographic microscopy," Appl. Opt. 44, 1806-1812 (2005).
    [CrossRef] [PubMed]
  19. D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, and Z. Zalevsky, "One-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 2353-2359 (1997).
    [CrossRef] [PubMed]
  20. D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, "Two-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 6687-6691 (1997).
    [CrossRef]
  21. A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, "Time multiplexing superresolution based on interference grating projection," Appl. Opt. 41, 7397-7404 (2002).
    [CrossRef] [PubMed]
  22. A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. G. Martínez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
    [CrossRef]
  23. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using two fixed generalized Dammann gratings," Appl. Opt. 39, 5318-5325 (2000).
    [CrossRef]
  24. Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Super resolution optical systems using fixed gratings," Opt. Commun. 163, 79-85 (1999).
    [CrossRef]
  25. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using three fixed generalized gratings: experimental results," J. Opt. Soc. Am. A 18, 514-520 (2001).
    [CrossRef]
  26. J. García, D. Mas, and R. G. Dorsch, "Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm," Appl. Opt. 35, 7013-7018 (1996).
    [CrossRef] [PubMed]
  27. A. Shemer, Z. Zalevsky, D. Mendlovic, E. Marom, J. Garcia, and P. G. Martinez, "Improved superresolution in coherent optical systems," Appl. Opt. 40, 4688-4696 (2001).
    [CrossRef]

2006

2005

2003

2002

2001

2000

1999

1997

1996

1966

1960

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

1952

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-428 (1952).
[CrossRef]

Binet, R.

Brueck, S. R. J.

Charrère, F.

Chen, X.

Colineau, J.

Cuche, E.

Depeursinge, Ch. D.

Dorsch, R. G.

Farkas, D.

Ferreira, C.

Garcia, J.

García, J.

García-Martínez, P.

Gartner, W.

W. Gartner and A. W. Lohmann, "Ein experiment zur uberschreitung der abbeschen auflosungsgrenze," Z. Physik 174, 18 (1963).

Hitzenberger, Ch. K.

Kartashev, A. I.

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

Kiryuschev, I.

Konforti, N.

Lehureau, J. C.

Lo, P. W.

Lohmann, A. W.

Lukosz, W.

Marom, E.

Marquet, P.

Martinez, P. G.

Martínez, P. G.

Mas, D.

Massatsch, P.

Massig, J. H.

Mendlovic, D.

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, "Time multiplexing superresolution based on interference grating projection," Appl. Opt. 41, 7397-7404 (2002).
[CrossRef] [PubMed]

A. Shemer, Z. Zalevsky, D. Mendlovic, E. Marom, J. Garcia, and P. G. Martinez, "Improved superresolution in coherent optical systems," Appl. Opt. 40, 4688-4696 (2001).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using three fixed generalized gratings: experimental results," J. Opt. Soc. Am. A 18, 514-520 (2001).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using two fixed generalized Dammann gratings," Appl. Opt. 39, 5318-5325 (2000).
[CrossRef]

A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. G. Martínez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Super resolution optical systems using fixed gratings," Opt. Commun. 163, 79-85 (1999).
[CrossRef]

D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, "Two-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 6687-6691 (1997).
[CrossRef]

D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, and Z. Zalevsky, "One-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 2353-2359 (1997).
[CrossRef] [PubMed]

D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application for superresolution: examples," J. Opt. Soc. Am. A 14, 563-567 (1997).
[CrossRef]

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

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, "About the space bandwidth product of optical signal and systems," J. Opt. Soc. Am. A 13, 470-473 (1996).
[CrossRef]

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," in Progress in Optics, Vol. XL, E.Wolf, ed. (Elsevier, 1999).

Mico, V.

Sabo, E.

Shemer, A.

Toraldo di Francia, G.

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-428 (1952).
[CrossRef]

Trost, P.

Zalevsky, Z.

J. García, Z. Zalevsky, and C. Ferreira, "Superresolved imaging of remote moving targets," Opt. Lett. 31, 586-588 (2006).
[CrossRef] [PubMed]

Z. Zalevsky, P. García-Martínez, and J. García, "Superresolution using gray level coding," Opt. Express 14, 5178-5182 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, and J. García, "Superresolution optical system by common-path interferometry," Opt. Express 14, 5168-5177 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, "Time multiplexing superresolution based on interference grating projection," Appl. Opt. 41, 7397-7404 (2002).
[CrossRef] [PubMed]

A. Shemer, Z. Zalevsky, D. Mendlovic, E. Marom, J. Garcia, and P. G. Martinez, "Improved superresolution in coherent optical systems," Appl. Opt. 40, 4688-4696 (2001).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using three fixed generalized gratings: experimental results," J. Opt. Soc. Am. A 18, 514-520 (2001).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using two fixed generalized Dammann gratings," Appl. Opt. 39, 5318-5325 (2000).
[CrossRef]

A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. G. Martínez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Super resolution optical systems using fixed gratings," Opt. Commun. 163, 79-85 (1999).
[CrossRef]

D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, "Two-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 6687-6691 (1997).
[CrossRef]

D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, and Z. Zalevsky, "One-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 2353-2359 (1997).
[CrossRef] [PubMed]

D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application for superresolution: examples," J. Opt. Soc. Am. A 14, 563-567 (1997).
[CrossRef]

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, "About the space bandwidth product of optical signal and systems," J. Opt. Soc. Am. A 13, 470-473 (1996).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," in Progress in Optics, Vol. XL, E.Wolf, ed. (Elsevier, 1999).

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).

Zhou, Q.

Appl. Opt.

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

P. Massatsch, F. Charrère, E. Cuche, P. Marquet, and Ch. D. Depeursinge, "Time-domain optical coherence tomography with digital holographic microscopy," Appl. Opt. 44, 1806-1812 (2005).
[CrossRef] [PubMed]

D. Mendlovic, A. W. Lohmann, N. Konforti, I. Kiryuschev, and Z. Zalevsky, "One-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 2353-2359 (1997).
[CrossRef] [PubMed]

D. Mendlovic, I. Kiryuschev, Z. Zalevsky, A. W. Lohmann, and D. Farkas, "Two-dimensional superresolution optical system for temporally restricted objects," Appl. Opt. 36, 6687-6691 (1997).
[CrossRef]

A. Shemer, Z. Zalevsky, D. Mendlovic, N. Konforti, and E. Marom, "Time multiplexing superresolution based on interference grating projection," Appl. Opt. 41, 7397-7404 (2002).
[CrossRef] [PubMed]

A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. G. Martínez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
[CrossRef]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, "Superresolution optical system using two fixed generalized Dammann gratings," Appl. Opt. 39, 5318-5325 (2000).
[CrossRef]

R. Binet, J. Colineau, and J. C. Lehureau, "Short-range synthetic aperture imaging at 633 nm by digital holography," Appl. Opt. 41, 4775-4782 (2002).
[CrossRef] [PubMed]

J. García, D. Mas, and R. G. Dorsch, "Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm," Appl. Opt. 35, 7013-7018 (1996).
[CrossRef] [PubMed]

A. Shemer, Z. Zalevsky, D. Mendlovic, E. Marom, J. Garcia, and P. G. Martinez, "Improved superresolution in coherent optical systems," Appl. Opt. 40, 4688-4696 (2001).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nuovo Cimento, Suppl.

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento, Suppl. 9, 426-428 (1952).
[CrossRef]

Opt. Commun.

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Super resolution optical systems using fixed gratings," Opt. Commun. 163, 79-85 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

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

Other

W. Gartner and A. W. Lohmann, "Ein experiment zur uberschreitung der abbeschen auflosungsgrenze," Z. Physik 174, 18 (1963).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Optical systems with improved resolving power," in Progress in Optics, Vol. XL, E.Wolf, ed. (Elsevier, 1999).

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).

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Figures (3)

Fig. 1
Fig. 1

Schematic sketch of the setup. The gray arrows (red online) show the axial movement of both the encoding and the decoding gratings.

Fig. 2
Fig. 2

Numerical simulations. (a) Point-spread function for intensity for the regular system. (b) Point-spread function for the superresolved system designed for a superresolution factor of 5 with gray-level (phase and amplitude) grating (left) and with binary phase grating (right). (c) Cross section of the optical transfer function (OTF) for superresolution factor of 5. Left, with the gray-level grating; right, the binary phase grating.

Fig. 3
Fig. 3

Performance analysis. (a) USAF resolution target, (b) Low-resolution image, (c) reconstructed high-resolution image.

Equations (13)

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U z 1 ( x ) = G ( ν ) exp ( j π λ z 1 ν 2 ) exp ( j 2 π x ν ) d ν ,
n A n exp ( j 2 π ν 0 n x ) .
U ̂ 0 ( x ) = n A n exp ( j π λ z 1 n 2 ν 0 2 ) exp ( j 2 π n ν 0 x ) g ( x + λ z 1 n ν 0 ) .
U ̂ 4 F ( x ) = n A n exp ( π i λ z 1 n 2 ν 0 2 ) rect ( λ F ν Δ ) G ( ν + n ν 0 ) exp [ j 2 π n λ z 1 ν 0 ν ] exp ( j 2 π ν x ) d ν ,
m B m exp ( j 2 π ν 0 m x ) .
U 4 F ( x ) = n , m A n B m exp ( j π λ ν 0 2 ( z 1 n 2 z 2 m 2 2 z 1 n m ) ) rect ( ν + m ν 0 Δ λ F ) G ( ν + ( n m ) ν 0 ) exp ( j 2 π λ ν ν 0 ( z 1 n + z 2 m ) ) exp ( j 2 π ν x ) d ν .
z 1 = z 2 = z ( t ) .
U 4 F ( x , t ) = n , m A n B m exp [ j π λ ν 0 2 z ( t ) ( n m ) 2 ] rect ( ν + m ν 0 Δ λ F ) G ( ν + ( n m ) ν 0 ) exp [ j 2 π λ ν ν 0 z ( t ) ( n m ) ] exp ( j 2 π ν x ) d ν .
1 T 0 T exp { j π λ ν 0 z ( t ) [ ν 0 ( n m ) 2 2 ν ( n m ) ] } d t = δ n , m .
U 4 F ( x , t ) = [ n A n B n rect ( ν + n ν 0 Δ λ F ) ] G ( ν ) exp ( j 2 π ν x ) d ν .
T > 1 λ V ν 0 2 ,
OTF ( ν ) = n , n A n B n A n * B n * rect ( μ + ν 2 + n ν 0 Δ λ F ) rect ( μ ν 2 + n ν 0 Δ λ F ) d μ .
Z c = δ x 2 N λ = L x δ x λ ,

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