Abstract

Tomography has been applied to holographic imaging systems recently to improve the 3D imaging performance. However, there are two distinct ways to achieve this: either by rotation of the object or by rotation of the illumination beam. We provide a transfer function analysis to distinguish between these two techniques and to predict the 3D imaging performance in holographic tomography when diffraction effects are considered. The results show that the configuration of rotating the illumination beam in one direction while fixing the sample leads to different 3D imaging performance as compared to the configuration of rotating the sample. The spatial frequency cutoff is nonisotropic in the case of rotating the illumination, and a curved line of singularity is observed. Rotating of the sample, on the contrary, has more symmetry in spatial frequency coverage but has a single point of singularity. The 3D transfer function derived can be used for 3D image reconstruction.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2008

2007

S. S. Kou and C. J. R. Sheppard, Opt. Express 15, 13640 (2007).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

2006

2002

V. Lauer, J. Microsc. 205, 165 (2002).
[CrossRef] [PubMed]

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

1991

C. J. R. Sheppard and M. Gu, J. Microsc. 165, 377 (1991).
[CrossRef]

1986

C. J. R. Sheppard, Optik (Jena) 72, 131 (1986).

1982

A. Devaney, Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

1969

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Ahlgren, U.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Badizadegan, K.

W. S. Choi, C. Fang-Yen, K. Badizadegan, and M. S. Feld, Opt. Lett. 33, 171 (2008).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Baldock, R.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

Charriere, F.

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Choi, W. S.

Colomb, T.

Cuche, E.

Dasari, R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Davidson, D.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Delaunay, J.-J.

S. Vertu, J.-J. Delaunay, and O. Haeberlé, presented at Focus on Microscopy 2008, Awaji, Japan, 13-16 April 2008.

Depeursinge, C.

Devaney, A.

A. Devaney, Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

Fang-Yen, C.

W. S. Choi, C. Fang-Yen, K. Badizadegan, and M. S. Feld, Opt. Lett. 33, 171 (2008).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Feld, M.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Feld, M. S.

Gu, M.

C. J. R. Sheppard and M. Gu, J. Microsc. 165, 377 (1991).
[CrossRef]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Haeberlé, O.

S. Vertu, J.-J. Delaunay, and O. Haeberlé, presented at Focus on Microscopy 2008, Awaji, Japan, 13-16 April 2008.

Hecksher-Sørensen, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Hill, B.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Kou, S. S.

Kuehn, J.

Lauer, V.

V. Lauer, J. Microsc. 205, 165 (2002).
[CrossRef] [PubMed]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Marian, A.

Marquet, P.

Montfort, F.

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Perry, P.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Ross, A.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Sharpe, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Sheppard, C. J. R.

S. S. Kou and C. J. R. Sheppard, Opt. Express 15, 13640 (2007).
[CrossRef] [PubMed]

C. J. R. Sheppard and M. Gu, J. Microsc. 165, 377 (1991).
[CrossRef]

C. J. R. Sheppard, Optik (Jena) 72, 131 (1986).

Vertu, S.

S. Vertu, J.-J. Delaunay, and O. Haeberlé, presented at Focus on Microscopy 2008, Awaji, Japan, 13-16 April 2008.

Wolf, E.

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

J. Microsc.

V. Lauer, J. Microsc. 205, 165 (2002).
[CrossRef] [PubMed]

C. J. R. Sheppard and M. Gu, J. Microsc. 165, 377 (1991).
[CrossRef]

Nat. Methods

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, Nat. Methods 4, 717 (2007).
[CrossRef] [PubMed]

Opt. Commun.

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Jena)

C. J. R. Sheppard, Optik (Jena) 72, 131 (1986).

Phys. Rev. Lett.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Science

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, Science 296, 541 (2002)
[CrossRef] [PubMed]

Ultrason. Imaging

A. Devaney, Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

Other

S. Vertu, J.-J. Delaunay, and O. Haeberlé, presented at Focus on Microscopy 2008, Awaji, Japan, 13-16 April 2008.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

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Figures (3)

Fig. 1
Fig. 1

In-focus transfer function for holographic tomography with scanning illumination in one direction. Regions of different limits are represented by different colors.

Fig. 2
Fig. 2

Defocused transfer function for holographic tomography with scanning illumination in one direction. The left plots show the real part, and the right plots the imaginary part. The defocus distance is increased from top to bottom: top, u = 3 ; middle, u = 10 ; bottom, u = 20 .

Fig. 3
Fig. 3

3D transfer function cut-off with (a) top and (b) flipped bottom views.

Equations (10)

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c ( m , n ; u ) = 1 2 exp { i u 2 [ ( m 2 + n 2 ) ] } circ ( m , n ) × δ ( n n ) rect ( m m ) exp ( i u ( m m ) 2 2 ) d m d n .
c ( m , n ; u ) = 1 2 exp [ i u 2 ( n 2 m 2 ) ] A , B , C exp ( i u m m ) d m .
A m 1 1 n 2 , B 1 n 2 m + 1 , C 1 n 2 1 n 2 ,
c A , B ( m , n ; u ) = 1 2 i u m { exp [ i u ( n 2 m 2 2 + m 1 n 2 ) ] exp [ i u ( m 2 + n 2 2 m ) ] } ,
c C ( m , n ; u ) = 1 2 i u m { exp [ i u ( n 2 m 2 2 + m 1 n 2 ) ] exp [ i u ( n 2 m 2 2 m 1 n 2 ) ] } .
c ( m , n ) = 1 2 ( 1 m + 1 n 2 ) , 1 + 1 n 2 > m > 1 1 n 2 ,
= 1 n 2 , m < 1 1 n 2 ,
A and B : m 2 n 2 2 m 1 n 2 < s < m m 2 + n 2 2 , 1 n 2 > 1 m ,
C : m 2 n 2 2 m 1 n 2 < s < m 2 n 2 2 + m 1 n 2 ,
1 n 2 < 1 m ,

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