Abstract

A method which is useful for obtaining superresolved imaging in a digital lensless Fourier holographic configuration is presented. By placing a diffraction grating between the input object and the CCD recording device, additional high-order spatial-frequency content of the object spectrum is directed towards the CCD. Unlike other similar methods, the recovery of the different band pass images is performed by inserting a reference beam in on-axis mode and using phase-shifting method. This strategy provides advantages concerning the usage of the whole frequency plane as imaging plane. Thus, the method is no longer limited by the zero order term and the twin image. Finally, the whole process results in a synthetic aperture generation that expands up the system cutoff frequency and yields a superresolution effect. Experimental results validate our concepts for a resolution improvement factor of 3.

© 2009 Optical Society of America

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  1. A. Bachl and A. W. Lukosz, "Experiments on superresolution imaging of a reduced object field," J. Opt. Soc. Am. 57, 163-169 (1967).
  2. E. Abbe, "Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,"Archiv. Microskopische Anat. 9, 413-468 (1873).
  3. W. Lukosz, "Optical systems with resolving powers exceeding the classical limit," J. Opt. Soc. Am. 56, 1463-1472 (1966).
  4. W. Lukosz, "Optical systems with resolving powers exceeding the classical limit II," J. Opt. Soc. Am. 57, 932-941 (1967).
  5. 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).
  6. A. I. Kartashev, "Optical systems with enhanced resolving power," Optics Spectrosc. 9, 204-206 (1960).
  7. J. D. Armitage, A. W. Lohmann, and D. P. Parish, "Superresolution image forming systems for objects with restricted lambda dependence," Jpn. J. Appl. Phys. 4, 273-275 (1965).
  8. M. A. Grim and A. W. Lohmann, "Superresolution image for 1-D objects," J. Opt. Soc. Am. 56, 1151-1156 (1966).
  9. H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).
  10. A. W. Lohmann and D. P. Paris, "Superresolution for nonbirrefringent objects," Appl. Opt. 3, 1037-1043 (1964).
  11. A. Zlotnik, Z. Zalevsky, and E. Marom, "Superresolution with nonorthogonal polarization coding," Appl. Opt. 44, 3705-3715 (2005).
    [PubMed]
  12. Z. Zalevsky, P. García-Martínez, and J. García, "Superresolution using gray level coding," Opt. Express 14, 5178-5182 (2006).
    [PubMed]
  13. Z. Zalevsky, D. Mendlovic and A. W. Lohmann, "Superresolution optical system for objects with finite size," Opt. Commun. 163, 79-85 (1999).
  14. 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).
  15. J. García, V. Micó, D. Cojoc, and Z. Zalevsky, "Full field of view super-resolution imaging based on two static gratings and white light illumination," Appl. Opt. 47, 3080-3087 (2008).
    [PubMed]
  16. Ch. J. Schwarz, Y. Kuznetsova and S. R. Brueck, "Imaging interferometric microscopy," Opt. Lett. 28, 1424-1426 (2003).
    [PubMed]
  17. V. Mico, Z. Zalevsky, and J. García, "Superresolution optical system by common-path interferometry," Opt. Express 14, 5168-5177 (2006).
    [PubMed]
  18. 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).
  19. G. Indebetouw, Y. Tada, J. Rosen, and G. Brooker, "Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms," Appl. Opt. 46, 993-1000 (2007).
    [PubMed]
  20. Y. Kuznetsova, A. Neumann, and S. R. J. Brueck "Imaging interferometric microscopy - approaching the linear system limits of optical resolution", Opt. Express 15, 6651-6663 (2007).
    [PubMed]
  21. V. Mico, Z. Zalevsky, and J. García, "Synthetic aperture microscopy using off-axis illumination and polarization coding," Opt. Commun. 276, 209-217 (2007).
  22. V. Mico, Z. Zalevsky, and J. García, "Common-path phase-shifting digital holographic microscopy: a way to quantitative imaging and superresolution," Opt. Commun. 281, 4273-4281 (2008).
  23. V. Mico, Z. Zalevsky, C. Ferreira, and J. García, "Superresolution digital holographic microscopy for three-dimensional samples," Opt. Express 16, 19260-19270 (2008).
  24. F. Le Clerc, M. Gross and L. Collot, "Synthetic aperture experiment in the visible with on-axis digital heterodyne holography," Opt. Lett. 26, 1550-1552 (2001).
  25. J. H. Massig, "Digital off-axis holography with a synthetic aperture," Opt. Lett. 27, 2179-2181 (2002).
  26. 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).
    [PubMed]
  27. J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, "High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning," Appl. Opt. 47, 5654-5658 (2008).
    [PubMed]
  28. Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).
  29. C. Yuan, H. Zhai, and H. Liu, "Angular multiplexing in pulsed digital holography for aperture synthesis," Opt. Lett. 33, 2356-2358 (2008).
    [PubMed]
  30. M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, "Super-resolution in digital holography by two-dimensional dynamic phase grating," Opt. Express 16, 17107-17118 (2008).
    [PubMed]
  31. I. Yamaguchi and T. Zhong, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
    [PubMed]
  32. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, "Image formation in phase-shifting digital holography and applications to microscopy," Appl. Opt. 40, 6177-6185 (2001).
  33. J. Goodman, Introduction to Fourier Optics 2nd ed., (McGraw-Hill, New York, 1996).
  34. T. Kreis, Handbook of Holographic Interferometry, (Wiley-VCH, 2005).

2008 (6)

2007 (3)

2006 (3)

2005 (1)

2003 (1)

2002 (3)

2001 (3)

1999 (2)

Z. Zalevsky, D. Mendlovic and A. W. Lohmann, "Superresolution optical system for objects with finite size," Opt. Commun. 163, 79-85 (1999).

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).

1997 (1)

1982 (1)

H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).

1967 (2)

1966 (2)

1965 (1)

J. D. Armitage, A. W. Lohmann, and D. P. Parish, "Superresolution image forming systems for objects with restricted lambda dependence," Jpn. J. Appl. Phys. 4, 273-275 (1965).

1964 (1)

1960 (1)

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

1873 (1)

E. Abbe, "Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,"Archiv. Microskopische Anat. 9, 413-468 (1873).

Abbe, E.

E. Abbe, "Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,"Archiv. Microskopische Anat. 9, 413-468 (1873).

Armitage, J. D.

J. D. Armitage, A. W. Lohmann, and D. P. Parish, "Superresolution image forming systems for objects with restricted lambda dependence," Jpn. J. Appl. Phys. 4, 273-275 (1965).

Bachl, A.

Bartelt, H.

H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).

Binet, R.

Bo, F.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).

Brooker, G.

Brueck, S. R.

Brueck, S. R. J.

Cojoc, D.

Colineau, J.

Collot, L.

De Nicola, S.

Di, J.

Fan, Q.

Ferraro, P.

Ferreira, C.

Finizio, A.

García, J.

García-Martínez, P.

Grilli, S.

Grim, M. A.

Gross, M.

Indebetouw, G.

Jiang, H.

Kartashev, A. I.

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

Kato, J.

Kiryuschev, I.

Konforti, N.

Kuznetsova, Y.

Le Clerc, F.

Lehureau, J-C.

Liu, Ch.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).

Liu, H.

Liu, Z.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).

Lohmann, A. W.

Z. Zalevsky, D. Mendlovic and A. W. Lohmann, "Superresolution optical system for objects with finite size," Opt. Commun. 163, 79-85 (1999).

H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).

M. A. Grim and A. W. Lohmann, "Superresolution image for 1-D objects," J. Opt. Soc. Am. 56, 1151-1156 (1966).

J. D. Armitage, A. W. Lohmann, and D. P. Parish, "Superresolution image forming systems for objects with restricted lambda dependence," Jpn. J. Appl. Phys. 4, 273-275 (1965).

A. W. Lohmann and D. P. Paris, "Superresolution for nonbirrefringent objects," Appl. Opt. 3, 1037-1043 (1964).

Lukosz, A. W.

Lukosz, W.

Marom, E.

Massig, J. H.

Mendlovic, D.

Merola, F.

Mico, V.

V. Mico, Z. Zalevsky, and J. García, "Common-path phase-shifting digital holographic microscopy: a way to quantitative imaging and superresolution," Opt. Commun. 281, 4273-4281 (2008).

V. Mico, Z. Zalevsky, C. Ferreira, and J. García, "Superresolution digital holographic microscopy for three-dimensional samples," Opt. Express 16, 19260-19270 (2008).

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

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).

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

Micó, V.

Mizuno, J.

Neumann, A.

Ohta, S.

Paris, D. P.

Parish, D. P.

J. D. Armitage, A. W. Lohmann, and D. P. Parish, "Superresolution image forming systems for objects with restricted lambda dependence," Jpn. J. Appl. Phys. 4, 273-275 (1965).

Paturzo, M.

Rosen, J.

Sabo, E.

Schwarz, Ch. J.

Shemer, A.

Sun, W.

Tada, Y.

Wang, Y.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).

Yamaguchi, I.

Yuan, C.

Zalevsky, Z.

J. García, V. Micó, D. Cojoc, and Z. Zalevsky, "Full field of view super-resolution imaging based on two static gratings and white light illumination," Appl. Opt. 47, 3080-3087 (2008).
[PubMed]

V. Mico, Z. Zalevsky, C. Ferreira, and J. García, "Superresolution digital holographic microscopy for three-dimensional samples," Opt. Express 16, 19260-19270 (2008).

V. Mico, Z. Zalevsky, and J. García, "Common-path phase-shifting digital holographic microscopy: a way to quantitative imaging and superresolution," Opt. Commun. 281, 4273-4281 (2008).

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

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

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

A. Zlotnik, Z. Zalevsky, and E. Marom, "Superresolution with nonorthogonal polarization coding," Appl. Opt. 44, 3705-3715 (2005).
[PubMed]

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).

Z. Zalevsky, D. Mendlovic and A. W. Lohmann, "Superresolution optical system for objects with finite size," Opt. Commun. 163, 79-85 (1999).

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).

Zhai, H.

Zhang, P.

Zhao, J.

Zhong, T.

Zhu, J.

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).

Zlotnik, A.

Appl. Opt. (8)

Appl. Phys. Lett. (1)

Ch. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, "Super-resolution digital holographic imaging method," Appl. Phys. Lett. 81, 3143-3145 (2002).

Archiv. Microskopische Anat. (1)

E. Abbe, "Beitrage zür theorie des mikroskops und der mikroskopischen wahrnehmung,"Archiv. Microskopische Anat. 9, 413-468 (1873).

J. Opt. Soc. Am. (4)

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

Jpn. J. Appl. Phys. (1)

J. D. Armitage, A. W. Lohmann, and D. P. Parish, "Superresolution image forming systems for objects with restricted lambda dependence," Jpn. J. Appl. Phys. 4, 273-275 (1965).

Opt. Commun. (4)

H. Bartelt and A. W. Lohmann, "Optical processing of 1-D signals," Opt. Commun. 42, 87-91 (1982).

Z. Zalevsky, D. Mendlovic and A. W. Lohmann, "Superresolution optical system for objects with finite size," Opt. Commun. 163, 79-85 (1999).

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

V. Mico, Z. Zalevsky, and J. García, "Common-path phase-shifting digital holographic microscopy: a way to quantitative imaging and superresolution," Opt. Commun. 281, 4273-4281 (2008).

Opt. Express (5)

Opt. Lett. (5)

Optics Spectrosc. (1)

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

Other (2)

J. Goodman, Introduction to Fourier Optics 2nd ed., (McGraw-Hill, New York, 1996).

T. Kreis, Handbook of Holographic Interferometry, (Wiley-VCH, 2005).

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup used in the validation of the proposed approach.

Fig. 2.
Fig. 2.

Fig. 2. Schematic figure representative of the proposed approach for a 1D case.

Fig. 3.
Fig. 3.

(a) and (b) Fourier transformation of the recorded hologram without and with reference beam, respectively. The central spot has been blocked to enhance the contrast of the images.

Fig. 4.
Fig. 4.

Recovered band pass images when considering (a) off-axis holographic recording and (b) after applying the phase-shifting algorithm. The central spot has been blocked to enhance image contrast.

Fig. 5.
Fig. 5.

(a) The conventional imaging system aperture, (b) the generated synthetic aperture, (c) the conventional image, and (d) the superresolved one.

Fig. 6.
Fig. 6.

(a) Magnified area marked with a white rectangle in Fig. 5(d), and (b) plot along the dashed white line of case (a).

Fig. 7.
Fig. 7.

Fourier transformation of the hologram recorded (a) without and (b) with reference beam. The central spot has been blocked to enhance image contrast.

Fig. 8.
Fig. 8.

(a) Whole Fourier domain image with the different band pass images resulting after applying the phase-shifting process and (b) to (e) are the magnified color rectangles of case (a) corresponding with the central region of the different band pass images.

Fig. 9.
Fig. 9.

(a)–(b) are the conventional imaging aperture and the generated synthetic aperture, respectively, and (c)–(d) are the conventional image and the superresolved one, respectively.

Equations (30)

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

U(x1)=exp {ik2z1x12} t (x)exp{ik2z1x2}exp{ik2z12x1x}dx
U(x1)=exp {ik2z1x12}t(x)exp{ik2z1x2}exp{ik2z12x1x}dxΣnBnexp{i2πnpx1}
p=λsinα0+sinα1
tanα0=Δxz0andtanα1=z1Δxz0(z0z1)
p=λ(z0z1)Δx
U(x)=C Σn Bn t (xnz1λp) exp {i2πnpx}
U1(x)=C' Σn exp {ik2z0x2}t(xnz1λp)exp{ik2z0x2}exp{i2π(xλz0np)x}dx
UR(x,t)=R0exp{ik2z0x2}exp{iϕ(t)}
U1(x)=exp {ik2z0x2}t(x+z1λp)exp{ik2z0x2}exp{i2π(xλz0+1p)x}dx
+exp {ik2z0x2}t(x)exp{ik2z0x2}exp{i2πxλz0x}dx
+exp {ik2z0x2}t(xz1λp)exp{ik2z0x2}exp{i2π(xλz01p)x}dx
=O1(x)+O0(x)+O+1(x)=Σn=11On(x)
ICCD(x)=O1(x)+O0(x)+O+1(x)+UR(x)2
=O1(x)2+O0(x)2+O+1(x)2+UR(x)2
+O1 (x)O0*(x)+O0(x)O1*(x)+O0(x)+O+0*(x)+O+1(x)O0*(x)
+O1(x)O+1*(x)+O+1(x)O1*(x)
+[O1(x)+O0(x)+O+1(x)]UR*(x)
+[O1*(x)+O0*(x)+O+1*(x)]UR(x)
ICCD(x,t)=Σn=11On(x)+UR(x)2
=Σn=11On(x)2+Σn,m=1nm1On(x)Om*(x)+Σn=11On(x)UR*(x)+Σm=11On*(x)UR(x)
=Σn=11On(x)2+Σn,m=1nm1On(x)Om*(x)
+Σn=11On(x)R0exp{ik2z0x2}exp{iϕ(t)}exp{iϕn(x)}
+Σn=11On*(x)R0exp{ik2z0x2}exp{iϕ(t)}exp{iϕn(x)}
ICCD(x,t)=Σn=11On(x)2+Σn,m=1nm1On(x)Om*(x)+R02
+2 R0 Re [Σn=11On(x)exp{ik2z0x2}]cos(pϕK+ϕn(x))
Σn=1+1ϕn(x)=arctan Σi=1mIi(x)sin[2πm(i1)]Σi=1mIi(x)cos[2πm(i1)]
ICCD(x)=[O1(x)+O0(x)+O+1(x)]UR*(x)
=[CΣn=11t(xnz1λp)exp{ik2z0x2}exp{i2π(xλz0np)x}dx]rect(xΔx)
=[CΣn=11FT{t(xnz1λp)}uFT{exp{ik2z0x2}}u]rect(xΔx)
FT{ICCD(x)}=[Dexp{ik2du2}Σn=11t(u+nz1pz0)exp{i2παu}]FT{rect(xΔx)}

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