Abstract

An optical setup to achieve superresolution in microscopy using holographic recording is presented. The technique is based on off-axis illumination of the object and a simple optical image processing stage after the imaging system for the interferometric recording process. The superresolution effect can be obtained either in one step by combining a spatial multiplexing process and an incoherent addition of different holograms or it can be implemented sequentially. Each hologram holds the information of each different frequency bandpass of the object spectrum. We have optically implemented the approach for a low-numerical-aperture commercial microscope objective. The system is simple and robust because the holographic interferometric recording setup is done after the imaging lens.

© 2006 Optical Society of America

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2006 (1)

2005 (1)

2004 (2)

2003 (1)

2002 (1)

2001 (3)

2000 (3)

S. Lai and M. A. Neifeld, "Digital wavefront reconstruction and its application to image encryption," Opt. Commun. 178, 283-289 (2000).
[CrossRef]

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173, 155-160 (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 (2)

1998 (2)

1997 (1)

1994 (2)

1992 (2)

1990 (1)

1987 (1)

1986 (1)

1978 (1)

1969 (1)

1967 (1)

1964 (1)

1960 (1)

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

1955 (1)

1952 (1)

M. Françon, "Amélioration de la resolution d'optique," Nuovo Cimento, Suppl. 9, 283-290 (1952).
[CrossRef]

Angell, D.

Boyer, K.

Brueck, S. R. J.

Chen, X.

Claspy, P.

Collot, L.

Cox, I. J.

Cullen, D.

De Incola, S.

Decker, A.

Devaney, A. J.

Ferraro, P.

Finizio, A.

Françon, M.

M. Françon, "Amélioration de la resolution d'optique," Nuovo Cimento, Suppl. 9, 283-290 (1952).
[CrossRef]

Garcia, J.

García, J.

García-Martinez, P.

García-Martínez, P.

Grilli, S.

Gross, M.

Guo, P.

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]

Haddad, W. S.

Hegedus, Z.

J Brueck, S. R.

Jüpter, W. P. O.

Kartashev, A. I.

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

Kato, J.-I.

King, B.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Kuei, C.-P.

Kuznetsova, Y.

Lai, S.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173, 155-160 (2000).
[CrossRef]

S. Lai and M. A. Neifeld, "Digital wavefront reconstruction and its application to image encryption," Opt. Commun. 178, 283-289 (2000).
[CrossRef]

Le Clerc, F.

Leith, E. N.

Lohmann, A. W.

A. W. Lohmann and D. P. Parish, "Superresolution for nonbirefringent objects," Appl. Opt. 3, 1037-1043 (1964).
[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), Chap. 4.

Longworth, J. W.

Lukosz, W.

Marom, E.

Massig, J. H.

McPherson, A.

Mendlovic, D.

A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. García-Martínez, "Superresolving optical system with time multiplexing and computer decoding," Appl. Opt. 38, 7245-7251 (1999).
[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), Chap. 4.

Meucci, R.

Mico, V.

Mizuno, J.

Neifeld, M. A.

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173, 155-160 (2000).
[CrossRef]

S. Lai and M. A. Neifeld, "Digital wavefront reconstruction and its application to image encryption," Opt. Commun. 178, 283-289 (2000).
[CrossRef]

Otha, S.

Pao, Y.

Parish, D. P.

Pierattini, G.

Rhodes, C. K.

Schnars, U.

Schwarz, C. J.

Shemer, A.

Sheppard, C. J. R.

Sheppard, J. R.

Solem, J. C.

Sun, P. C.

Toraldo di Francia, G.

Yamaguchi, I.

Zalevsky, Z.

Zhang, T.

Zlotnik, A.

Appl. Opt. (9)

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, "Fourier-transform holographic microscope," Appl. Opt. 31, 4973-4978 (1992).
[CrossRef] [PubMed]

U. Schnars and W. P. O. Jüpter, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
[CrossRef] [PubMed]

A. Decker, Y. Pao, and P. Claspy, "Electronic heterodyne recording and processing of optical holograms using phase modulated reference waves (T)," Appl. Opt. 17, 917-921 (1978).
[CrossRef] [PubMed]

I. Yamaguchi, J.-I. Kato, S. Otha, and J. Mizuno, "Image formation in phase-shifting digital holography and applications to microscopy," Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

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

P. C. Sun and E. N. Leith, "Superresolution by spatial-temporal encoding methods," Appl. Opt. 31, 4857-4862 (1992).
[CrossRef] [PubMed]

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

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

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. (3)

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

Nuovo Cimento, Suppl. (1)

M. Françon, "Amélioration de la resolution d'optique," Nuovo Cimento, Suppl. 9, 283-290 (1952).
[CrossRef]

Opt. Commun. (2)

S. Lai and M. A. Neifeld, "Digital wavefront reconstruction and its application to image encryption," Opt. Commun. 178, 283-289 (2000).
[CrossRef]

S. Lai, B. King, and M. A. Neifeld, "Wave front reconstruction by means of phase-shifting digital in-line holography," Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

Opt. Spectrosc. (1)

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

Other (2)

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), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup. The reference and imaging arms are marked with dashed and dotted frames, respectively. The divergence distance d for the illumination in the imaging arm is depicted by broken segments ending in arrows.

Fig. 2
Fig. 2

Off-axis illumination case. The chief ray for each off-axis source (thick solid line) impinges on the CCD center. An approximate size and location of the virtual image of the pinhole mask are shown.

Fig. 3
Fig. 3

Lens selection process: (a) Synthetic aperture generated without the field lens (correct overlapping), (b) incorrect overlapping of the different frequency bands (reconstruction is not possible), (c) separated frequency bands obtained using a suitable lens that permits the separated processing of the frequency bands and correct relocation to obtain the desired synthetic aperture shown in (a).

Fig. 4
Fig. 4

Synthetic aperture generation by the off-axis illumination used in the present approach. The different gray levels represent the frequency bandpasses. The dashed area shows a full aperture of width 6 Δ ν .

Fig. 5
Fig. 5

(a) Image obtained with the 0.1 NA objective lens and coherent illumination. (b) High-resolution image obtained with a Spindler & Hoyer microscope objective with a 0.65 NA and coherent illumination. Note that the resolution limit corresponds to the rectangle shown in (a) and it implies a cutoff frequency of 203.0 line pairs/mm (group 7, element 5), which means a smallest resolved detail of 4.93 μ m .

Fig. 6
Fig. 6

Fourier transform of the addition of different recorded holograms. The dc has been blocked to improve contrast.

Fig. 7
Fig. 7

Resulting synthetic aperture.

Fig. 8
Fig. 8

(a) Image obtained with 0.1 NA lens and conventional illumination. (b) Superresolved image obtained with the synthetic aperture. The group 9, element 2 corresponding to the resolution limit using the proposed method is marked with an arrow.

Equations (14)

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U ( x , y ) = ( f ( x M , y M ) exp { j k 2 d [ x 2 + y 2 ] } ) disk ( Δ ν r ) ,
U m , n I ( x , y ) = ( f ( x M , y M ) exp { j k 2 d [ ( x M s x m ) 2 + ( y M s y n ) 2 ] } ) disk ( Δ ν r ) ,
d = a ( a d ) + F 2 F a .
M s = M s F F a .
U m , n R ( x , y ) = exp { j k 2 d [ ( x M s x m ) 2 + ( y M s y n ) 2 ] } .
I m , n ( x , y ) = U m , n I ( x , y ) + U m , n R ( x , y ) exp ( j 2 π Q x ) 2 .
I m , n ( x , y ) = 1 + U m , n I ( x , y ) 2 + U m , n I ( x , y ) [ U m , n R ( x , y ) ] * exp ( j 2 π Q x ) + [ U m , n I ( x , y ) ] * U m , n R ( x , y ) e j 2 π Q x = T 1 ( x , y ) + T 2 ( x , y ) + T 3 ( x , y ) + T 4 ( x , y ) .
T 3 ( x , y ) = [ ( f ( x M , y M ) exp { j k 2 d [ ( x M s x m ) 2 + ( y M s y n ) 2 ] } ) disk ( Δ ν r ) ] exp { j k 2 d [ ( x M s x m ) 2 + ( y M s y n ) 2 ] } exp ( j 2 π Q x ) .
T ̃ 3 ( u , ν ) = K [ ( f ̃ ( M u + M M s λ d x m , M ν + M M s λ d y n ) FT 1 { exp [ j k 2 d ( x 2 + y 2 ) ] } ) circ ( ρ Δ ν ) ] FT 1 { exp [ j k 2 d ( x 2 + y 2 ) ] } δ ( u + Q M s λ d x m , ν M s λ d y n ) ,
FT 1 { exp [ j k 2 d ( x 2 + y 2 ) ] } FT 1 { exp [ j k 2 d ( x 2 + y 2 ) ] } = FT 1 { exp [ j k 2 d ( 1 d 1 d ) ( x 2 + y 2 ) ] } .
T ̃ 3 ( u , ν ) = K { f ̃ ( M u + M M s λ d x m , M ν + M M s λ d y n ) circ ( ρ Δ ν ) } δ ( u + Q M s λ d x m , ν M s λ d y n ) .
T ̃ 3 sum ( u , ν ) = K m , n { [ f ̃ ( M ( u + M s λ d x m ) , M ( ν + M s λ d y n ) ) circ ( ρ Δ ν ) ] δ ( u M s λ d x m , ν M s λ d y n ) } δ ( u + Q , ν ) .
T ̃ 3 sum ( u , ν ) = K f ̃ ( M u , M ν ) SA ( u , ν ) δ ( u + Q , ν ) ,
SA ( u , ν ) = m , n circ ( u M s λ d x m Δ ν , ν M s λ d y m Δ ν ) .

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