Abstract

We demonstrate experimentally that the method of scanning holographic microscopy is capable of producing images reconstructed numerically from holograms recorded digitally in the time domain by scanning, with transverse and axial resolutions comparable to those of wide-field or scanning microscopy with the same objective. Furthermore, we show that it is possible to synthesize the point-spread function of scanning holographic microscopy to obtain, with the same objective, holographic reconstructions with a transverse resolution exceeding the Rayleigh limit of the objective up to a factor of 2 in the limit of low numerical aperture. These holographic reconstructions also exhibit an extended depth of focus, the extent of which is adjustable without compromising the transverse resolution.

© 2005 Optical Society of America

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References

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  1. T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
    [CrossRef]
  2. A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1150 (1978).
    [CrossRef] [PubMed]
  3. G. Indebetouw, P. Klysubun, T. Kim, T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
    [CrossRef]
  4. G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth of focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
    [CrossRef]
  5. E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [CrossRef]
  6. H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
    [CrossRef]
  7. U. Schnars, W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  8. D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
    [CrossRef]
  9. B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. J. Swoger, M. Martinez-Corral, J. Huisken, E. H. K. Stelzer, “Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy,” J. Opt. Soc. Am. A 19, 1910–1918 (2002).
    [CrossRef]
  13. C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
    [CrossRef]
  14. M. Gu, “Imaging with a high numerical aperture objective,” in Advanced Optical Imaging Theory (Springer-Verlag, Berlin, 2000), Chap. 6.
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  16. W. Wang, A. T. Friberg, E. Wolf, “Structure of focus fields in systems with large Fresnel numbers,” J. Opt. Soc. Am. A 12, 1947–1953 (1995).
    [CrossRef]

2003 (1)

2002 (3)

J. Swoger, M. Martinez-Corral, J. Huisken, E. H. K. Stelzer, “Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy,” J. Opt. Soc. Am. A 19, 1910–1918 (2002).
[CrossRef]

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth of focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

U. Schnars, W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

2001 (1)

H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
[CrossRef]

2000 (1)

1999 (1)

1995 (2)

W. Wang, A. T. Friberg, E. Wolf, “Structure of focus fields in systems with large Fresnel numbers,” J. Opt. Soc. Am. A 12, 1947–1953 (1995).
[CrossRef]

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

1993 (1)

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

1989 (1)

1978 (1)

1959 (1)

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Cuche, E.

Depeursinge, C.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

Friberg, A. T.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gu, M.

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

M. Gu, “Imaging with a high numerical aperture objective,” in Advanced Optical Imaging Theory (Springer-Verlag, Berlin, 2000), Chap. 6.
[CrossRef]

Huisken, J.

Indebetouw, G.

Jerico, M. J.

H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
[CrossRef]

Juptner, W. P. O.

U. Schnars, W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kim, T.

Klysubun, P.

Kreuzer, H. J.

H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
[CrossRef]

Lohmann, A. W.

Mansuripur, M.

Marquet, P.

Martinez-Corral, M.

Meinertzhagen, I. A.

H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
[CrossRef]

Poon, T.-C.

Rhodes, W. T.

Richard, B.

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Schilling, B.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

Schnars, U.

U. Schnars, W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

Shinoda, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

Stelzer, E. H. K.

Suzuki, Y.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

Swoger, J.

Wang, W.

Wolf, E.

W. Wang, A. T. Friberg, E. Wolf, “Structure of focus fields in systems with large Fresnel numbers,” J. Opt. Soc. Am. A 12, 1947–1953 (1995).
[CrossRef]

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Wu, M.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

Xu, W.

H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (2)

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth of focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

C. J. R. Sheppard, M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
[CrossRef]

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

J. Phys. Condens. Matter (1)

H. J. Kreuzer, M. J. Jerico, I. A. Meinertzhagen, W. Xu, “Digital in-line holography with photons and electrons,” J. Phys. Condens. Matter 13, 10729–10741 (2001).
[CrossRef]

Meas. Sci. Technol. (1)

U. Schnars, W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Nature (London) (1)

D. Gabor, “A new microscopic principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Opt. Eng. (Bellingham) (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, Y. Suzuki, “Three dimensional microscopy by optical scanning holography,” Opt. Eng. (Bellingham) 34, 1338–1344 (1995).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

B. Richard, E. Wolf, “Electromagnetic diffraction in optical systems: structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Other (2)

M. Gu, “Imaging with a high numerical aperture objective,” in Advanced Optical Imaging Theory (Springer-Verlag, Berlin, 2000), Chap. 6.
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. EOPM, electro-optic phase modulator introducing a frequency difference between the two beams; Pat, encoding Fresnel pattern projected on the specimen through the objective; P’s, pupils; BS, beam splitter; BE, beam expander; M, mirror; AT, half-wave plate/polarizer attenuator; OBJ, objective; L’s, lenses; PM, photomultiplier tube detector; AS, aperture stop; C, collecting lens.

Fig. 2
Fig. 2

(a) Wrapped phase of the hologram of a 1 - μ m pinhole, representing the encoding pattern created by the interference of a plane wave and a spherical wave having the same numerical aperture as that of the objective ( sin α 0.2 ) . (b) Reconstruction of the 1 - μ m pinhole by autocorrelation of the hologram shown in (a). The FWHM 2.15 μ m compares well with the resolution limit of the objective ( 1.22 λ 2 sin α 2 μ m ) .

Fig. 3
Fig. 3

Reconstruction of the hologram of a 300 μ m × 300 μ m field of Micor zygotes obtained with the encoding pattern of Fig. 2a (interference of one plane wave and one spherical waves is limited by the numerical aperture of the objective). The theoretical resolution limit is equal to the Rayleigh limit of the objective ( 2 μ m ) , and the DOF is 16 μ m , with the larger zygotes in focus.

Fig. 4
Fig. 4

(a) Wrapped phase of the hologram of a 1 - μ m pinhole, representing the encoding pattern created by the interference of two spherical waves both having the same numerical aperture as that of the objective ( sin α 0.2 ) but opposite curvatures. (b) Reconstruction of the 1 - μ m pinhole by autocorrelation of the hologram shown in (a). The FWHM 1.1 μ m compares well with the theoretical expectation ( 1 μ m ) and represents an improvement of a factor 2 compared with the Rayleigh resolution limit of the objective ( 1.22 λ 2 sin α 2 μ m ) .

Fig. 5
Fig. 5

Reconstruction of the hologram of a 300 μ m × 300 μ m field of Micor zygotes obtained with the encoding pattern of Fig. 4a (interference of two spherical waves limited by the NA of the objective and having opposite curvatures). The theoretical resolution limit ( 1 μ m ) is half of the Rayleigh limit of the objective ( 2 μ m ) . The DOF is extended to 80 μ m , showing all the zygotes in focus.

Equations (21)

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Δ x = λ 2 sin α ,
Δ z = λ 2 ( 1 cos α ) = λ 4 sin 2 α 2 λ sin 2 α ,
A ( r , z ) = A 1 ( r , z ) + A 2 ( r , z ) exp ( i Ω t ) 2 ,
A j ( r , z ) = 0 ν max J 0 ( 2 π ν r ) P j ( ν ) exp ( i π λ z ν 2 ) 2 π ν d ν ,
S ( r , z ) = A 1 ( r , z ) A 2 * ( r , z ) ,
P 1 ( ν ) = δ ( ν ) ,
P 2 ( ν ) = exp ( i π λ z 0 ν 2 ) circ ( ν ν max ) ,
A 1 ( r , z ) circ ( r a ) ,
A 2 ( r , z ) exp [ i π r 2 λ ( z 0 + z ) ] circ [ r sin α ( z 0 + z ) ] .
S ( r , z ) exp [ i π r 2 λ ( z 0 + z ) ] circ [ r sin α ( z 0 + z ) ] .
h ( r , z ) = S ( r , z ) S ( r , 0 ) ,
H ( ν ; z ) exp ( i π λ ν 2 z ) circ ( λ ν sin α ) .
DOF = Δ z λ sin 2 α ,
P 1 ( ν ) = exp ( i π λ z 0 ν 2 ) circ ( ν ν max ) ,
P 2 ( ν ) = exp ( i π λ z 0 ν 2 ) circ ( ν ν max ) ,
A 1 ( r , z ) exp [ i π r 2 λ ( z 0 + z ) ] circ [ r sin α ( z 0 + z ) ] ,
A 2 ( r , z ) exp [ i π r 2 λ ( z 0 z ) ] circ [ r sin α ( z 0 z ) ] .
S ( r , z ) exp [ i π r 2 2 z ( z 0 2 z 2 ) ] circ ( r z 0 sin α ) .
H ( ν , z ) exp ( i π ν 2 z 2 2 z 0 ) circ ( λ ν 2 sin α ) .
ν cutoff = 2 sin α λ = 2 ν max .
DOF = Δ z λ F sin 2 α ,

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