Abstract

We present what we believe to be a new application of scanning holographic microscopy to superresolution. Spatial resolution exceeding the Rayleigh limit of the objective is obtained by digital coherent addition of the reconstructions of several off-axis Fresnel holograms. Superresolution by holographic superposition and synthetic aperture has a long history, which is briefly reviewed. The method is demonstrated experimentally by combining three off-axis holograms of fluorescent beads showing a transverse resolution gain of nearly a factor of 2.

© 2007 Optical Society of America

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2006

2005

2004

2003

2002

2001

2000

G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, "Imaging properties of scanning holographic microscopy," J. Opt. Soc. Am. A 17, 380-390 (2000).
[CrossRef]

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

1997

1994

M. Gu, T. Tannous, and C. R. J. Sheppard, "Improved axial resolution in focal fluorescence microscopy with annular pupils," Opt. Commun. 110, 533-539 (1994).
[CrossRef]

1992

1987

1986

1974

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

1973

T. Sato, M. Ueda, and G. Yamagishi, "Superresolution microscope using electrical superposition of holograms," Appl. Opt. 13, 406-408 (1973).
[CrossRef]

M. Ueda, T. Sato, and M. Kondo, "Superresolution by multiple superposition of images holograms having different carrier frequencies," Opt. Acta 20, 403-410 (1973).
[CrossRef]

1969

1967

J. W. Goodman and R. W. Lawrence, "Digital image information from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

W. Lukosz, "Optical systems with resolving power exceeding the classical limits, II," J. Opt. Soc. Am. 57, 932-941 (1967).
[CrossRef]

1966

1964

1955

1952

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento , Suppl. 9, 426-438 (1952).
[CrossRef]

Andres, P.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun 165, 267-278 (1999).
[CrossRef]

Angell, D.

Bertero, M.

M. Bertero and C. De Mol, "Superresolution by data inversion," in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 36, pp. 129-178.
[CrossRef]

Bevilacqua, F.

Brooker, G.

Brueck, S. R.

Brueck, S. R. J.

Caballero, M. T.

Chamberlin-Long, D.

Chen, X.

Colicchio, B.

B. Colicchio, O. Haeberle, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the LLS and MAP deconvolution algorithms by automatic determination of optimal regularization parameters and prefiltering of original data," Opt. Commun. 244, 37-49 (2005).
[CrossRef]

Collot, L.

Cox, I. J.

Cuche, E.

De Mol, C.

M. Bertero and C. De Mol, "Superresolution by data inversion," in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 36, pp. 129-178.
[CrossRef]

Depeursinge, C.

Dieterlen, A.

B. Colicchio, O. Haeberle, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the LLS and MAP deconvolution algorithms by automatic determination of optimal regularization parameters and prefiltering of original data," Opt. Commun. 244, 37-49 (2005).
[CrossRef]

El Maghnouji, A.

Fixler, D.

Foster, R.

Frohn, J. T.

Garcia, J.

Garcia-Martinez, P.

Gerchberg, R. W.

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image information from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1966).

Grimm, M. A.

Gross, M.

Gu, M.

M. Gu, T. Tannous, and C. R. J. Sheppard, "Improved axial resolution in focal fluorescence microscopy with annular pupils," Opt. Commun. 110, 533-539 (1994).
[CrossRef]

M. Gu, Advance in Optical Imaging Theory (Springer, 2000).

Gustafsson, M. G. L.

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]

Haeberle, O.

O. Haeberle and B. Simon, "Improving the lateral resolution in confocal fluorescence microscopy using laterally interfering excitation beams," Opt. Commun. 259, 400-408 (2006).
[CrossRef]

B. Colicchio, O. Haeberle, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the LLS and MAP deconvolution algorithms by automatic determination of optimal regularization parameters and prefiltering of original data," Opt. Commun. 244, 37-49 (2005).
[CrossRef]

Hassig, J. R.

Huysken, J.

Indebetouw, G.

Jung, G.

B. Colicchio, O. Haeberle, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the LLS and MAP deconvolution algorithms by automatic determination of optimal regularization parameters and prefiltering of original data," Opt. Commun. 244, 37-49 (2005).
[CrossRef]

Juskaitis, R.

Kato, J.-I.

Kim, T.

Kiryuschev, I.

Klysubun, P.

Knapp, H. F.

Kondo, M.

M. Ueda, T. Sato, and M. Kondo, "Superresolution by multiple superposition of images holograms having different carrier frequencies," Opt. Acta 20, 403-410 (1973).
[CrossRef]

Konforti, N.

Kowalczyk, M.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun 165, 267-278 (1999).
[CrossRef]

Kuei, C. P.

Kuznetsova, Y.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image information from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Le Clerc, F.

Leacock, L.

G. Indebetouw, Y. Tada, and L. Leacock, "Quantitative phase imaging with scanning holographic microscopy:experimental assessment," Biomed. Eng. Online 5, doi: 10.1186/1475-925x-5-63 (2006).

Leith, E. N.

Leizerson, T.

Lipson, S. G.

Lohmann, A. W.

Lukosz, W.

Marquet, P.

Martinez-Corral, M.

McCutchen, C. W.

Mendlovic, D.

D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application to superresolution: examples," J. Opt. Soc. Am. A 4, 563-567 (1997).
[CrossRef]

D. Mendlovic and A. W. Lohmann, "Space-bandwidth product adaptation and its application to superresolution: fundamentals," J. Opt. Soc. Am. A 4, 558-562 (1997).
[CrossRef]

Mendlovics, D.

Mico, V.

Mizuno, J.

Neil, M. A. A.

Ohta, S.

Paris, D. P.

Poon, T.-C.

Rosen, J.

Sarafi, V.

Sato, T.

T. Sato, M. Ueda, and G. Yamagishi, "Superresolution microscope using electrical superposition of holograms," Appl. Opt. 13, 406-408 (1973).
[CrossRef]

M. Ueda, T. Sato, and M. Kondo, "Superresolution by multiple superposition of images holograms having different carrier frequencies," Opt. Acta 20, 403-410 (1973).
[CrossRef]

Schwarz, C. J.

Shemer, A.

Sheppard, C. R. J.

M. Gu, T. Tannous, and C. R. J. Sheppard, "Improved axial resolution in focal fluorescence microscopy with annular pupils," Opt. Commun. 110, 533-539 (1994).
[CrossRef]

Sheppard, J. R.

Simon, B.

O. Haeberle and B. Simon, "Improving the lateral resolution in confocal fluorescence microscopy using laterally interfering excitation beams," Opt. Commun. 259, 400-408 (2006).
[CrossRef]

Stelzer, E. H. K.

Stemmer, A.

Sun, P. C.

Swoger, J.

Tada, Y.

G. Indebetouw, Y. Tada, and L. Leacock, "Quantitative phase imaging with scanning holographic microscopy:experimental assessment," Biomed. Eng. Online 5, doi: 10.1186/1475-925x-5-63 (2006).

Tannous, T.

M. Gu, T. Tannous, and C. R. J. Sheppard, "Improved axial resolution in focal fluorescence microscopy with annular pupils," Opt. Commun. 110, 533-539 (1994).
[CrossRef]

Toraldo di Francia, G.

Ueda, M.

M. Ueda, T. Sato, and M. Kondo, "Superresolution by multiple superposition of images holograms having different carrier frequencies," Opt. Acta 20, 403-410 (1973).
[CrossRef]

T. Sato, M. Ueda, and G. Yamagishi, "Superresolution microscope using electrical superposition of holograms," Appl. Opt. 13, 406-408 (1973).
[CrossRef]

Wilson, T.

Xu, C.

B. Colicchio, O. Haeberle, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the LLS and MAP deconvolution algorithms by automatic determination of optimal regularization parameters and prefiltering of original data," Opt. Commun. 244, 37-49 (2005).
[CrossRef]

Yamagishi, G.

Yamaguchi, I.

Zalevsky, Z.

Zapata-Rodriguez, C. J.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun 165, 267-278 (1999).
[CrossRef]

Zhang, T.

Zhong, W.

Appl. Opt.

Appl. Phys. Lett.

J. W. Goodman and R. W. Lawrence, "Digital image information from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Microsc.

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.

J. Opt. Soc. Am. A

G. Indebetouw, A. El Maghnouji, and R. Foster, "Scanning holographic microscopy with transverse resolution exceeding the Rayleigh limit and extended depth of focus," J. Opt. Soc. Am. A 22, 892-898 (2005).
[CrossRef]

G. Indebetouw and W. Zhong, "Scanning holographic microscopy of three-dimensional fluorescent specimens," J. Opt. Soc. Am. A 23, 1699-1707 (2006).
[CrossRef]

G. Indebetouw, W. Zhong, and D. Chamberlin-Long, "Point-spread function synthesis in scanning holographic microscopy," J. Opt. Soc. Am. A 23, 1708-1717 (2006).
[CrossRef]

G. Indebetouw, "A posteriori quasi-sectioning of the three-dimensional reconstructions of scanning holographic microscopy," J. Opt. Soc. Am. A 23, 2657-2661 (2006).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, "Imaging properties of scanning holographic microscopy," J. Opt. Soc. Am. A 17, 380-390 (2000).
[CrossRef]

T. Leizerson, S. G. Lipson, and V. Sarafi, "Superresolution in far-field imaging," J. Opt. Soc. Am. A 19, 436-443 (2002).
[CrossRef]

J. Swoger, M. Martinez-Corral, J. Huysken, and 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]

D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application to superresolution: examples," J. Opt. Soc. Am. A 4, 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]

D. Mendlovic and A. W. Lohmann, "Space-bandwidth product adaptation and its application to superresolution: fundamentals," J. Opt. Soc. Am. A 4, 558-562 (1997).
[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]

Nuovo Cimento

G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento , Suppl. 9, 426-438 (1952).
[CrossRef]

Opt. Acta

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

M. Ueda, T. Sato, and M. Kondo, "Superresolution by multiple superposition of images holograms having different carrier frequencies," Opt. Acta 20, 403-410 (1973).
[CrossRef]

Opt. Commun

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun 165, 267-278 (1999).
[CrossRef]

Opt. Commun.

M. Gu, T. Tannous, and C. R. J. Sheppard, "Improved axial resolution in focal fluorescence microscopy with annular pupils," Opt. Commun. 110, 533-539 (1994).
[CrossRef]

B. Colicchio, O. Haeberle, C. Xu, A. Dieterlen, and G. Jung, "Improvement of the LLS and MAP deconvolution algorithms by automatic determination of optimal regularization parameters and prefiltering of original data," Opt. Commun. 244, 37-49 (2005).
[CrossRef]

O. Haeberle and B. Simon, "Improving the lateral resolution in confocal fluorescence microscopy using laterally interfering excitation beams," Opt. Commun. 259, 400-408 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Other

M. Bertero and C. De Mol, "Superresolution by data inversion," in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 36, pp. 129-178.
[CrossRef]

Z. Zalevsky, D. Mendlovics, and A. W. Lohmann, "Optical systems with improved resolving power," in Progress in Optics, E. Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 271-341.
[CrossRef]

G. Indebetouw, Y. Tada, and L. Leacock, "Quantitative phase imaging with scanning holographic microscopy:experimental assessment," Biomed. Eng. Online 5, doi: 10.1186/1475-925x-5-63 (2006).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1966).

M. Gu, Advance in Optical Imaging Theory (Springer, 2000).

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Figures (7)

Fig. 1
Fig. 1

Schematic of an off-axis scanning holographic microscope. M, mirrors; BS, beam splitters; DBS, dichroic beam splitter; EOM, electro-optic phase modulator. L 1 , 2 are achromat doublet lenses, 16   cm focal length, L 3 is a collecting lens, 1 cm focal length. The wedge on a rotating stage is used to create off-axis Fresnel patterns on the specimen.

Fig. 2
Fig. 2

(Color online) (a) Wrapped phase of the on-line hologram of a 0.5 μ m diameter pinhole. The scale bar is 10 μ m . The phase distribution has a radius 18 μ m , a Fresnel number 12 , and a radius of curvature 50 μ m . (b) Amplitude of the reconstruction of the 0.5 μ m pinhole using the on-line hologram. FWHM 1.0 μ m .

Fig. 3
Fig. 3

(Color online) (a) Wrapped phase of three off-axis holograms of the 0.5 μ m pinhole illustrating the idea of pupil synthesis. The scale bar is 10 μ m . (b) Amplitude of the reconstruction of the 0.5 μ m pinhole using the composite off-axis holograms. FWHM 0.7 μ m .

Fig. 4
Fig. 4

(Color online) (a) Reconstruction of the on-axis hologram of a collection of 1.0 μ m fluorescent beads (excitation∕emission wavelengths = 532 nm / 600   nm ) at the best focus distance of 47.5 μ m from the focal plane of the objective. The scale bar is 5 μ m . Bead clusters are just barely resolved. (b) Same reconstruction at a focus distance of 49 μ m . The two planes are within the Rayleigh range of the on-axis scanning FZP.

Fig. 5
Fig. 5

(Color online) Coherent sum of the complex amplitudes of the reconstructions of three off-axis holograms recorded with off sets 120° apart. The scale bar is 5 μ m . (a) Best focus at 47.5 μ m from the focal plane of the objective. (b) Same reconstruction at a focus distance of 49 μ m . The distance between the two planes is close to the Rayleigh range of the synthesized FZP, and different bead clusters are focused in different planes.

Fig. 6
Fig. 6

(a) Absolute value and (b) wrapped phase of the reconstruction of a 0.5 μ m diameter pinhole from the on-axis hologram. The phase profile is typical of an Airy pattern with a central lobe diameter 1.5 μ m . The scale bar is 1 μ m .

Fig. 7
Fig. 7

(a) Absolute value and (b) wrapped phase of the coherent sum of the reconstructions of a 0.5 μ m diameter pinhole from the three off-axis holograms. The threefold symmetry of the destructive interference results in a narrower amplitude distribution (a), and a central lobe diameter 1.0 μ m . The scale bar is 1 μ m .

Equations (103)

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z 0
ρ M A X = N A O B J / λ
N A O B J
n ^
ρ 0 n ^
ρ M A X + ρ 0
n ^
P ˜ 1 ( ρ ) = exp ( i π λ z 0 ρ 2 ) Disk ( ρ / ρ M A X ) ,
P ˜ 2 j ( ρ ) = δ ( ρ ρ 0 n ^ j ) .
Disk ( x ) = 1
x < 1
= 0
x > 1
ρ
r P
ρ = r P / λ f O B J
f O B J
P 1 ( r )
z 0
P 2 j ( r )
ρ 0 n ^ j
S j ( r , z )
S ˜ j ( ρ , z ) = P ˜ 1 ( ρ , z ) P ˜ 2 j ( ρ , z ) = exp { i π λ [ z 0 ρ 0 2 + ( z 0 z ) ( ρ 2 2 ρ · ρ 0 n ^ j ) ] } × D i s k ( | ρ ρ 0 n ^ j | / ρ M A X ) ,
P ˜ 1 , 2 ( ρ , z )
P ˜ 1 , 2 ( ρ , z ) = P ˜ 1 , 2 ( ρ ) exp ( i 2 π z λ 2 ρ 2 ) ,
P ˜ 1 ( ρ , z ) = exp ( i 2 π z / λ ) exp [ i π λ ( z 0 z ) ρ 2 ] × D i s k ( ρ / ρ M A X ) ,
P ˜ 2 j ( ρ , z ) = exp ( i 2 π z / λ ) exp ( i π λ z ρ 0 2 ) δ ( ρ ρ 0 n ^ j ) .
H ˜ O j = d z I ˜ ( ρ , z ) S ˜ j ( ρ , z ) ,
I ˜ ( ρ , z )
I ( r , z )
z = z R
z 0 + z R
H R j ( r )
δ ( r , z )
P j ( r , z R )
H ˜ R j ( ρ ) = exp [ i π λ z 0 ( | ρ ρ 0 n ^ j | 2 ) ] × D i s k ( | ρ ρ 0 n ^ j | / ρ M A X ) ,
P ˜ j ( ρ , z R ) = exp [ i π λ z R ( ρ 2 2 ρ · ρ 0 n ^ j ) ] .
R ˜ j ( ρ , z R ) = H ˜ O j ( ρ ) [ H ˜ R j ( ρ ) P ˜ j ( ρ , z R ) ] * = d z I ˜ ( ρ , z ) exp [ i π λ ( z R z ) ( ρ 2 2 ρ · ρ 0 n ^ j ) ] × D i s k ( | ρ ρ 0 n ^ j | / ρ M A X ) ,
z = z R
ρ M A X
ρ 0 n ^ j
ρ 0 ρ M A X
2 / λ
1 μ m
0.5 μ m
1.22 λ E M / 2 N A 0.9 μ m
λ E M = 600   nm
0.5 μ m
F 12
a 18 μ m
F = a 2 / λ E X z 0
λ E X = 532   nm
z 0 50 μ m
a / z 0 0.35
0.9 μ m
1.0 μ m
0.5 μ m
0.9 μ m
ρ 0 ρ M A X 0.66 μ m - 1
0.7 μ m
0.6 μ m
0.6
0.5
λ / 2
0.9 μ m
0.9 μ m
z = 47.5 μ m
z = 49 μ m
1.5 μ m
3.5 μ m
1.5 μ m
1.8 μ m
0.5 μ m
π
+ π
L 1 , 2
16   cm
L 3
0.5 μ m
10 μ m
18 μ m
12
50 μ m
0.5 μ m
1.0 μ m
0.5 μ m
10 μ m
0.5 μ m
0.7 μ m
1.0 μ m
= 532 nm / 600   nm
47.5 μ m
5 μ m
49 μ m
5 μ m
47.5 μ m
49 μ m
0.5 μ m
1.5 μ m
1 μ m
0.5 μ m
1.0 μ m
1 μ m

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