Abstract

The ability to improve the limited resolving power of optical imaging systems while approaching the theoretical diffraction limit has been an attractive discipline with growing interest over the last years due to its benefits in many applied optics systems. This paper presents a new approach to achieve transverse superresolution in far-field imaging systems, with direct application in both digital microscopy and digital holographic microscopy. Theoretical analysis and computer simulations show the validity of the presented approach.

© 2008 Optical Society of America

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  1. E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung” Arch. Mikrosk. Anat. 9, 413-468 (1873).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  3. D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College Press, 2003).
  4. Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer, 2002).
  5. M. Bertero, C. De Mol, “Super-resolution by data inversion,” in E.Wolf. (ed.), Progress in Optics, Vol. XXXVI (Elsevier North-Holland, 1996), Chap. III, pp. 129-178.
    [CrossRef]
  6. P. Jacquinot, “Apodization,” Prog. Opt. 3, 29-186 (1964).
    [CrossRef]
  7. T. Wilson and C. J. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).
  8. G. Toraldo di Francia, “Resolving power and information,” J. Opt. Soc. Am. 45, 497-501 (1955).
    [CrossRef]
  9. G. Toraldo di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. 59, 799-804 (1969).
    [CrossRef] [PubMed]
  10. I. J. Cox and J. R. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A 3, 1152-1158 (1986).
    [CrossRef]
  11. A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547-557 (1997).
    [CrossRef]
  12. W. Lukosz, “Optical systems with resolving powers exceeding the classical limits,” J. Opt. Soc. Am. 56, 1463-1472 (1966).
    [CrossRef]
  13. W. Lukosz, “Optical systems with resolving powers exceeding the classical limits II,” J. Opt. Soc. Am. 57, 932-941 (1967).
    [CrossRef]
  14. M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).
  15. A. Shemer, D. Mendlovic, Z. Zalevsky, J. García, and P. García-Martínez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245-7251 (1999).
    [CrossRef]
  16. A. W. Lohmann and D. P. Paris, “Superresolution for nonbirefringent objects,” Appl. Opt. 3, 1037-1043 (1964).
    [CrossRef]
  17. A. I. Kartashev, “Optical system with enhanced resolving power,” Opt. Spectra 9, 204-206 (1960).
  18. M. A. Grimm and A. W. Lohmann, “Superresolution image for one-dimensional object,” J. Opt. Soc. Am. 56, 1151-1156 (1966).
    [CrossRef]
  19. Z. Zalevsky, P. García-Martínez, and J. García, “Superresolution using gray level coding,” Opt. Express 14, 5178-5182 (2006).
    [CrossRef] [PubMed]
  20. D. Mendlovic and A. W. Lohman, “Space-bandwidth product adaptation and its application to super resolution: fundamentals,” J. Opt. Soc. Am. A 14, 558-562 (1997).
    [CrossRef]
  21. D. Mendlovic, A. W. Lohman, and Z. Zalevsky, “Space-bandwidth product adaptation and its application for super resolution: examples,” J. Opt. Soc. Am. A 14, 563-567 (1997).
    [CrossRef]
  22. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Komforti, and I. Kiryushev, “Superresolution optical system with two fixed generalized Damman gratings,” Appl. Opt. 39, 5318-5325 (2000).
    [CrossRef]
  23. E. Sabo, Z. Zalevsky, D. Mendlovic, N. Komforti, and I. Kiryushev, “Superresolution optical system using three fixed generalized gratings: experimental results,” J. Opt. Soc. Am. A 18, 514-520 (2001).
    [CrossRef]
  24. A. Bachl and W. Lukosz, “Experiments on superresolution imaging of a reduced object field,” J. Opt. Soc. Am. 57, 163-169 (1967).
    [CrossRef]
  25. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
    [CrossRef] [PubMed]
  26. R. Heintzmann and P. A. Benedetti, “High-resolution image reconstruction in fluorescence microscopy with patterned excitation,” Appl. Opt. 45, 5037-5045 (2006).
    [CrossRef] [PubMed]
  27. J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
    [CrossRef]
  28. J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232-7236 (2000).
    [CrossRef] [PubMed]
  29. R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy—a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19, 1599-1609 (2002).
    [CrossRef]
  30. M. G. L. Gustafsson, “Nonlinear structured illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081-13086 (2005).
    [CrossRef] [PubMed]
  31. J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13, 6073-6078 (2005).
    [CrossRef] [PubMed]
  32. E. Ben-Eliezer and E. Marom, “Aberration-free superresolution imaging via binary speckle pattern encoding and processing,” J. Opt. Soc. Am. A 24, 1003-1010 (2007).
    [CrossRef]
  33. B. J. Guo and S. L. Zhuang, “Image superresolution by using a source-encoding technique,” Appl. Opt. 30, 5159-5162 (1991).
    [CrossRef] [PubMed]
  34. Z. Zalevsky, J. García, P. García-Martínez, and C. Ferreira, “Spatial information transmission using orthogonal mutual coherence coding,” Opt. Lett. 30, 2837-2839 (2005).
    [CrossRef] [PubMed]
  35. E. N. Leith, D. Angell, and C.-P. Kuei, “Superresolution by incoherent-to-coherent conversion,” J. Opt. Soc. Am. A 4, 1050-1054 (1987).
    [CrossRef]
  36. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Single step superresolution by interferometric imaging,” Opt. Express 12, 2589-2596 (2004).
    [CrossRef] [PubMed]
  37. P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. 44, 1806-1812 (2005).
    [CrossRef] [PubMed]
  38. C. Iemmi, A. Moreno, and J. Campos, “Digital holography with a point-diffraction interferometer,” Opt. Express 13, 1885-1891 (2005).
    [CrossRef] [PubMed]
  39. X. Chen and S. R. J. Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt. Lett. 24, 124-126 (1999).
    [CrossRef]
  40. T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27-37 (2002).
    [CrossRef] [PubMed]
  41. H. Medecki, E. Tejnil, K. A. Goldberg, and J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526-1528 (1996).
    [CrossRef] [PubMed]
  42. T. Colomb, J. Kühn, F. Charrière, N. Aspert, P. Marquet, and C. Depeursinge, “Total aberration compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300-4306 (2006).
    [CrossRef] [PubMed]
  43. I. Tamaguchi and T. Zhong, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef]
  44. C. J. Schwarz, Y. Kuznetsova, and S. R. J. Brueck, “Imaging interferometric microscopy,” Opt. Lett. 28, 1424-1426 (2003).
    [CrossRef] [PubMed]
  45. 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]
  46. V. Mico, Z. Zalevsky, and J. García, “Superresolution optical system by common-path interferometry,” Opt. Express 14, 5168-5177 (2006).
    [CrossRef] [PubMed]
  47. V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution using multiple off-axis holograms,” J. Opt. Soc. Am. A 23, 3162-3170 (2006).
    [CrossRef]
  48. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
    [CrossRef]
  49. J. R. Price, P. R. Bingham, and C. E. Thomas, Jr., “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 826-833 (2007).
    [CrossRef]
  50. V. Mico, Z. Zalevsky, and J. García, “Synthetic aperture microscopy using off-axis illumination and polarization coding,” Opt. Commun. 276, 209-217 (2007).
    [CrossRef]
  51. 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]

2007 (4)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
[CrossRef]

J. R. Price, P. R. Bingham, and C. E. Thomas, Jr., “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 826-833 (2007).
[CrossRef]

V. Mico, Z. Zalevsky, and J. García, “Synthetic aperture microscopy using off-axis illumination and polarization coding,” Opt. Commun. 276, 209-217 (2007).
[CrossRef]

E. Ben-Eliezer and E. Marom, “Aberration-free superresolution imaging via binary speckle pattern encoding and processing,” J. Opt. Soc. Am. A 24, 1003-1010 (2007).
[CrossRef]

2006 (7)

2005 (5)

2004 (1)

2003 (1)

2002 (2)

2001 (1)

2000 (3)

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Komforti, and I. Kiryushev, “Superresolution optical system with two fixed generalized Damman gratings,” Appl. Opt. 39, 5318-5325 (2000).
[CrossRef]

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232-7236 (2000).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
[CrossRef] [PubMed]

1999 (2)

1997 (4)

1996 (2)

1991 (1)

1987 (1)

1986 (1)

1969 (1)

1967 (2)

1966 (2)

1964 (2)

1960 (1)

A. I. Kartashev, “Optical system with enhanced resolving power,” Opt. Spectra 9, 204-206 (1960).

1955 (1)

1952 (1)

M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).

Abbe, E.

E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung” Arch. Mikrosk. Anat. 9, 413-468 (1873).

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
[CrossRef]

Angell, D.

Aspert, N.

Bachl, A.

Beghuin, D.

Benedetti, P. A.

Ben-Eliezer, E.

Bertero, M.

M. Bertero, C. De Mol, “Super-resolution by data inversion,” in E.Wolf. (ed.), Progress in Optics, Vol. XXXVI (Elsevier North-Holland, 1996), Chap. III, pp. 129-178.
[CrossRef]

Bingham, P. R.

J. R. Price, P. R. Bingham, and C. E. Thomas, Jr., “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 826-833 (2007).
[CrossRef]

Bokor, J.

Brueck, S. R. J.

Campos, J.

Charrière, F.

Chen, X.

Colomb, T.

Courjon, D.

D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College Press, 2003).

Cox, I. J.

Cremer, C.

Cuche, E.

Dahlgren, P.

De Mol, C.

M. Bertero, C. De Mol, “Super-resolution by data inversion,” in E.Wolf. (ed.), Progress in Optics, Vol. XXXVI (Elsevier North-Holland, 1996), Chap. III, pp. 129-178.
[CrossRef]

den Dekker, A. J.

Depeursinge, C.

Dorsch, R. G.

Ferreira, C.

Fixler, D.

Francon, M.

M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).

Freeman, D. M.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Frohn, J. T.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232-7236 (2000).
[CrossRef] [PubMed]

García, J.

V. Mico, Z. Zalevsky, and J. García, “Synthetic aperture microscopy using off-axis illumination and polarization coding,” Opt. Commun. 276, 209-217 (2007).
[CrossRef]

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]

V. Mico, Z. Zalevsky, and J. García, “Superresolution optical system by common-path interferometry,” Opt. Express 14, 5168-5177 (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, P. García-Martínez, and J. García, “Synthetic aperture superresolution using multiple off-axis holograms,” J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

Z. Zalevsky, J. García, P. García-Martínez, and C. Ferreira, “Spatial information transmission using orthogonal mutual coherence coding,” Opt. Lett. 30, 2837-2839 (2005).
[CrossRef] [PubMed]

J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13, 6073-6078 (2005).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Single step superresolution by interferometric imaging,” Opt. Express 12, 2589-2596 (2004).
[CrossRef] [PubMed]

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

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]

García-Martínez, P.

Goldberg, K. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grimm, M. A.

Guo, B. J.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081-13086 (2005).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
[CrossRef] [PubMed]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
[CrossRef]

Heintzmann, R.

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
[CrossRef]

Hong, S. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Horn, B. K. P.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Iemmi, C.

Jacquinot, P.

P. Jacquinot, “Apodization,” Prog. Opt. 3, 29-186 (1964).
[CrossRef]

Jovin, T. M.

Kartashev, A. I.

A. I. Kartashev, “Optical system with enhanced resolving power,” Opt. Spectra 9, 204-206 (1960).

Kiryushev, I.

Knapp, H. F.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232-7236 (2000).
[CrossRef] [PubMed]

Komforti, N.

Kuei, C.-P.

Kühn, J.

Kuznetsova, Y.

Leith, E. N.

Lohman, A. W.

Lohmann, A. W.

Lukosz, W.

Marom, E.

Marquet, P.

Mas, D.

Massatsch, P.

Medecki, H.

Mendlovic, D.

Mermelstein, M. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Mico, V.

Moreno, A.

Paris, D. P.

Price, J. R.

J. R. Price, P. R. Bingham, and C. E. Thomas, Jr., “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 826-833 (2007).
[CrossRef]

Ryu, J.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Sabo, E.

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
[CrossRef]

Schwarz, C. J.

Shemer, A.

Sheppard, C. J.

T. Wilson and C. J. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Sheppard, J. R.

Stemmer, A.

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232-7236 (2000).
[CrossRef] [PubMed]

Tamaguchi, I.

Tejnil, E.

Thomas, C. E.

J. R. Price, P. R. Bingham, and C. E. Thomas, Jr., “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 826-833 (2007).
[CrossRef]

Toraldo di Francia, G.

van den Bos, A.

Wilson, T.

T. Wilson and C. J. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Zalevsky, Z.

V. Mico, Z. Zalevsky, and J. García, “Synthetic aperture microscopy using off-axis illumination and polarization coding,” Opt. Commun. 276, 209-217 (2007).
[CrossRef]

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]

V. Mico, Z. Zalevsky, and J. García, “Superresolution optical system by common-path interferometry,” Opt. Express 14, 5168-5177 (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, P. García-Martínez, and J. García, “Synthetic aperture superresolution using multiple off-axis holograms,” J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

Z. Zalevsky, J. García, P. García-Martínez, and C. Ferreira, “Spatial information transmission using orthogonal mutual coherence coding,” Opt. Lett. 30, 2837-2839 (2005).
[CrossRef] [PubMed]

J. García, Z. Zalevsky, and D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13, 6073-6078 (2005).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Single step superresolution by interferometric imaging,” Opt. Express 12, 2589-2596 (2004).
[CrossRef] [PubMed]

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Komforti, and I. Kiryushev, “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. Komforti, and I. Kiryushev, “Superresolution optical system with two fixed generalized Damman gratings,” Appl. Opt. 39, 5318-5325 (2000).
[CrossRef]

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

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

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

Zhong, T.

Zhuang, S. L.

Appl. Opt. (10)

J. R. Price, P. R. Bingham, and C. E. Thomas, Jr., “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 826-833 (2007).
[CrossRef]

A. W. Lohmann and D. P. Paris, “Superresolution for nonbirefringent objects,” Appl. Opt. 3, 1037-1043 (1964).
[CrossRef]

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]

B. J. Guo and S. L. Zhuang, “Image superresolution by using a source-encoding technique,” Appl. Opt. 30, 5159-5162 (1991).
[CrossRef] [PubMed]

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

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Komforti, and I. Kiryushev, “Superresolution optical system with two fixed generalized Damman gratings,” Appl. Opt. 39, 5318-5325 (2000).
[CrossRef]

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41, 27-37 (2002).
[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]

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

R. Heintzmann and P. A. Benedetti, “High-resolution image reconstruction in fluorescence microscopy with patterned excitation,” Appl. Opt. 45, 5037-5045 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Il Nuovo Cimento Suppl. (1)

M. Francon, “Amélioration the résolution d'optique,” Il Nuovo Cimento Suppl. 9, 283-290 (1952).

J. Microsc. (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82-87 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (9)

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution using multiple off-axis holograms,” J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

E. Ben-Eliezer and E. Marom, “Aberration-free superresolution imaging via binary speckle pattern encoding and processing,” J. Opt. Soc. Am. A 24, 1003-1010 (2007).
[CrossRef]

A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547-557 (1997).
[CrossRef]

R. Heintzmann, T. M. Jovin, and C. Cremer, “Saturated patterned excitation microscopy—a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19, 1599-1609 (2002).
[CrossRef]

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

D. Mendlovic and A. W. Lohman, “Space-bandwidth product adaptation and its application to super resolution: fundamentals,” J. Opt. Soc. Am. A 14, 558-562 (1997).
[CrossRef]

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

I. J. Cox and J. R. Sheppard, “Information capacity and resolution in an optical system,” J. Opt. Soc. Am. A 3, 1152-1158 (1986).
[CrossRef]

E. N. Leith, D. Angell, and C.-P. Kuei, “Superresolution by incoherent-to-coherent conversion,” J. Opt. Soc. Am. A 4, 1050-1054 (1987).
[CrossRef]

Opt. Commun. (1)

V. Mico, Z. Zalevsky, and J. García, “Synthetic aperture microscopy using off-axis illumination and polarization coding,” Opt. Commun. 276, 209-217 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (5)

Opt. Spectra (1)

A. I. Kartashev, “Optical system with enhanced resolving power,” Opt. Spectra 9, 204-206 (1960).

Phys. Rev. Lett. (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (2)

J. T. Frohn, H. F. Knapp, and A. Stemmer, “True optical resolution beyond the Rayleigh limit achieved by standing wave illumination,” Proc. Natl. Acad. Sci. U.S.A. 97, 7232-7236 (2000).
[CrossRef] [PubMed]

M. G. L. Gustafsson, “Nonlinear structured illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U.S.A. 102, 13081-13086 (2005).
[CrossRef] [PubMed]

Prog. Opt. (1)

P. Jacquinot, “Apodization,” Prog. Opt. 3, 29-186 (1964).
[CrossRef]

Other (6)

T. Wilson and C. J. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung” Arch. Mikrosk. Anat. 9, 413-468 (1873).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

D. Courjon, Near-Field Microscopy and Near-Field Optics (Imperial College Press, 2003).

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

M. Bertero, C. De Mol, “Super-resolution by data inversion,” in E.Wolf. (ed.), Progress in Optics, Vol. XXXVI (Elsevier North-Holland, 1996), Chap. III, pp. 129-178.
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Optical setup for the DIA. The 1-D grating is mounted on a rotatable platform to accomplish the 2-D SR process.

Fig. 2
Fig. 2

SA generated using DHIA. The smaller circles represent the region of the frequency space that is observable through the conventional system aperture in comparison with the right-hand figure, which shows the SA (external black circle) achieved using the DHIA approach.

Fig. 3
Fig. 3

Distortion generated in DHIA. The object’s spectral DC term is represented by a black point at the center of the laterally positioned gray circles and was generated by dragging the enhanced black circle represented in the SA after performance of the DHIA approach.

Fig. 4
Fig. 4

(a) Overall object spectrum and selection of the right frequency band corresponding to the combination ( n = 1 , θ = 0 ° ), and (b) its relocation during the decoding process at the left and central position given by k 1 .

Fig. 5
Fig. 5

(a) Low-resolution image of the input object provided by the system without the approach present, (b) its FT, and (c) the desired high-resolution image (that obtained with an aperture that triples the original one).

Fig. 6
Fig. 6

(a) Total spectrum when digital decoding is produced, (b) FT of the image shown in (a), and (c) FT of the whole intensity distribution recorded at the CCD.

Fig. 7
Fig. 7

(a) Dragged DC term of the diffraction orders of the digital decoding grating, (b) final synthesized spectrum, and (c) FT of the image shown in (b) that shows the final superresolved image.

Fig. 8
Fig. 8

(a) PSF intensity without the present approach, (b) PSF intensity with the present approach, and (c) cross section of the PSF depicted in (a) and (b) that shows the improvement in resolution.

Fig. 9
Fig. 9

(a), (d) show the input objects: USAF resolution test and Barbara images, respectively; (b), (e) Fourier transformations of (a) and (d), where the white circle represents the limited system aperture; and (c), (f) the low-resolution images obtained taking into account an imaging system with the previous limited aperture.

Fig. 10
Fig. 10

(a), (c) Simulated holograms for USAF and Barbara objects, and (b), (d) their Fourier transformations, respectively. The central pixel has been blocked to enhance the visibility of the overall image.

Fig. 11
Fig. 11

(a), (d) Raw result of the present approach, and (b), (e) equalized central part of the object spectrum. (c), (f) show the distorted final image.

Fig. 12
Fig. 12

(a), (d) Digital procedure to avoid distortion; (b), (e) generated SA in comparison with the real one (white circle); and (c), (f) final superresolved images obtained with the present approach.

Fig. 13
Fig. 13

(a) Object image and (b) its FT that can be separated in diffrerent contiguous circles.

Equations (29)

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U 0 ( x 0 , y 0 ) = n C n exp { j 2 π n ν 0 [ x 0 cos θ ( t ) + y 0 sin θ ( t ) ] } ,
U z ( x , y ) = n C n exp { j 2 π n ν 0 ( x cos θ + y sin θ ) } ,
U IP ( x , y ) = t ( x , y ) n C n exp { j 2 π n ν 0 ( x cos θ + y sin θ ) } ,
U FP ( u , v ) = [ t ̃ ( u , v ) n C n δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] circ ( ρ Δ ν ) ,
U Out ( x , y ) = n C n [ t ( x , y ) exp { j 2 π n ν 0 ( x cos θ + y sin θ ) } ] disk ( Δ ν r ) ,
I Out ( x , y ) = n , m C n C m * { [ t ( x , y ) exp { j 2 π n ν 0 ( x cos θ + y sin θ ) } ] disk ( Δ ν r ) } { [ t ( x , y ) exp { j 2 π m ν 0 ( x cos θ + y sin θ ) } ] * disk ( Δ ν r ) } ,
I Out ( x , y ) = I Out ( x , y ) k B k exp { j 2 π k ν 0 ( x cos φ + y sin φ ) } .
I ˜ ( u , v ) = n , m , k ( λ z ) 2 C n C m * B k exp { j π λ z ( n 2 m 2 ) ν 0 2 } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } δ { u [ ( n m ) cos θ k cos φ ] ν 0 , v [ ( n m ) sin θ k sin φ ] ν 0 } ,
I ˜ ( u , v ; θ ) = θ n , m k = n m ( λ z ) 2 C n C m * B k exp { j π λ z ( n 2 m 2 ) ν 0 2 } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } + θ n = m k n m ( λ z ) 2 C n 2 B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } δ ( u + k ν 0 cos θ , v + k ν 0 sin θ ) + θ n m k n m ( λ z ) 2 C n C m * B k exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } δ [ u ( n m k ) ν 0 cos θ , v ( n m k ) ν 0 sin θ ] = I ˜ 1 ( u , v ; θ ) + I ˜ 2 ( u , v ; θ ) + I ˜ 3 ( u , v ; θ ) .
I ˜ 1 ( u , v ; θ ) = ( λ z ) 2 n , m k = n m C n C m * B k exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] [ t ̃ ( u , v ) S A n ( u , v ) ] [ t ̃ ( u , v ) S A m ( u , v ) ] ,
S A n ( u , v ) = θ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) .
( λ z ) 2 C n C m * B n m exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] = A n A m *
I ˜ 2 ( u , v ; θ ) = θ n = m = 0 k n m ( λ z ) 2 C 0 2 B k [ t ̃ ( u , v ) circ ( ρ Δ ν ) ] [ t ̃ ( u , v ) circ ( ρ Δ ν ) ] δ ( u + k ν 0 cos θ , v + k ν 0 sin θ ) + θ n = m 0 k n m ( λ z ) 2 C n 2 B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } δ ( u + k ν 0 cos θ , v + k ν 0 sin θ ) .
I ˜ 3 ( u , v ; θ ) = θ n m k n m ( λ z ) 2 C n C m * B k exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } δ [ u ( n m k ) ν 0 cos θ , v ( n m k ) ν 0 sin θ ] .
I ˜ ( u , v ; θ ) = θ n , m k 0 ( λ z ) 2 C n C m * B k exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } δ [ u ( n m k ) ν 0 cos θ , v ( n m k ) ν 0 sin θ ] .
I ˜ ( u , v ; θ ) = θ n = m k 0 ( λ z ) 2 C n 2 B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } δ ( u k ν 0 cos θ , v k ν 0 sin θ ) + θ n m k 0 ( λ z ) 2 C n C m * B k exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } δ ( u k ν 0 cos θ , v k ν 0 sin θ ) .
I ˜ RE ( u , v ; θ ) = θ n m ( λ z ) 2 C n C m * B 0 exp [ j π λ z ( n 2 m 2 ) ν 0 2 ] { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] } { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + m ν 0 cos θ , v + m ν 0 sin θ ) ] } ,
U Out ( x , y ) = n C n { t ( x , y ) exp [ j 2 π n ν 0 ( x cos θ + y sin θ ) ] } disk ( Δ ν r ) + R exp [ j 2 π μ 0 x ] ,
I ̃ 2 ( u , v ) = R * n , θ k , φ C n B k { [ t ̃ ( u , v ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] circ ( ρ Δ ν ) } δ ( u + k ν 0 cos φ , v + k ν 0 sin φ ) = R * θ , φ n , k C n B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u n ν 0 cos θ , v n ν 0 sin θ ) ] } δ [ u + ( n cos θ + k cos φ ) ν 0 , v + ( n sin θ + k sin φ ) ν 0 ] .
I ̃ 2 ( u , v ) = R * θ n k = n C n B n { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u n ν 0 cos θ , v n ν 0 sin θ ) ] } + R * θ n = 0 k n C 0 B k { t ̃ ( u , v ) circ ( ρ Δ ν ) } δ ( u + k ν 0 cos θ , v + k ν 0 sin θ ) + R * θ n 0 k n C n B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u n ν 0 cos θ , v n ν 0 sin θ ) ] } δ ( u + ( n + k ) ν 0 cos θ , v + ( n + k ) ν 0 sin θ ) = T ̃ 1 ( u , v ) + T ̃ 2 ( u , v ) + T ̃ 3 ( u , v ) .
T ̃ 1 ( u , v ) = t ̃ ( u , v ) R * n C n B n S A n ( u , v ) ,
S A n ( u , v ) = θ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ )
j λ z exp ( j k z ) R * C n B n exp [ j π λ z n 2 ν 0 2 ] = A n .
T ̃ 2 ( u , v ) = R * θ n = 0 k n C 0 B k [ t ̃ ( u , v ) c i r c ( ρ Δ ν ) ] δ ( u + k ν 0 cos θ , v + k ν 0 sin θ ) .
T ̃ 3 ( u , v ) = R * θ n 0 k n C n B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u n ν 0 cos θ , v n ν 0 sin θ ) ] } δ ( u + ( n + k ) ν 0 cos θ , v + ( n + k ) ν 0 sin θ ) .
T ̃ 3 ( u , v ) = R * θ n 0 k n k = n C n B k { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u n ν 0 cos θ , v n ν 0 sin θ ) ] } δ ( u + ( n + k ) ν 0 cos θ , v + ( n + k ) ν 0 sin θ ) + R * θ n 0 k n k = 0 C n B 0 { t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u n ν 0 cos θ , v n ν 0 sin θ ) ] } δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) .
t ̃ F ( u , v ) = θ n A n t ̃ ( u , v ) [ circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ ) ] .
H n ( u , v ) = θ n A n circ ( ρ Δ ν ) δ ( u + n ν 0 cos θ , v + n ν 0 sin θ )
FT [ I f ( u , v ) ] = F T [ t ̃ F ( u , v ) 2 ] = θ n , m A n A m * [ t ̃ ( u , v ) H n ( u , v ) ] [ t ̃ ( u , v ) H m ( u , v ) ] ,

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