Abstract

A new holographic data processing path for accurate quantitative tomographic reconstruction of 3D samples placed in a cylindrical capillary is proposed. The method considers strong unintentional focusing effects induced by the inner cylindrical boundary of the vessel: 1) introduction of cylindrical wave illumination of a sample, and 2) object wave deformation. The first issue is addressed by developing an arbitrary illumination tomographic reconstruction algorithm based on filtered backpropagation, while the second by a novel correction algorithm utilizing the optical rays analysis. Moreover, the processing path includes a novel holographic method for correction of spherical aberration related to refraction at a planar surface. Utility of the developed data processing path is proven with numerical simulations and experimental measurement of a specially prepared test sample.

© 2015 Optical Society of America

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References

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2014 (5)

2013 (2)

T. Kozacki, K. Liżewski, and J. Kostencka, “Holographic method for topography measurement of highly tilted and high numerical aperture micro structures,” Opt. Laser Technol. 49, 38–46 (2013).
[Crossref]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (1)

2007 (3)

2006 (4)

2005 (1)

2003 (1)

1998 (1)

1993 (1)

1982 (1)

A. J. Devaney, “A Filtered Backpropagation Algorithm for Diffraction Tomography,” Ultrason. Imaging 4(4), 336–350 (1982).
[Crossref] [PubMed]

Aspert, N.

Badizadegan, K.

Beghin, A.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Brenner, K.-H.

Charrière, F.

Choi, W.

Colomb, T.

Coppola, G.

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Cuche, E.

Dale, B.

Dale, R.

Dao, M.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref] [PubMed]

Dasari, R. R.

De Nicola, S.

Debailleul, M.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34(1), 79–81 (2009).
[Crossref] [PubMed]

Debeir, O.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Decaestecker, C.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Depeursinge, C.

Depeursinge, Ch.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Devaney, A. J.

A. J. Devaney, “A Filtered Backpropagation Algorithm for Diffraction Tomography,” Ultrason. Imaging 4(4), 336–350 (1982).
[Crossref] [PubMed]

Di Caprio, G.

Diez-Silva, M.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref] [PubMed]

Dubois, F.

G. Di Caprio, A. El Mallahi, P. Ferraro, R. Dale, G. Coppola, B. Dale, G. Coppola, and F. Dubois, “4D tracking of clinical seminal samples for quantitative characterization of motility parameters,” Biomed. Opt. Express 5(3), 690–700 (2014).
[Crossref] [PubMed]

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Dudek, M.

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref] [PubMed]

J. Kostencka, T. Kozacki, M. Dudek, and M. Kujawińska, “Noise suppressed optical diffraction tomography with autofocus correction,” Opt. Express 22(5), 5731–5745 (2014).
[Crossref] [PubMed]

El Mallahi, A.

Emery, Y.

Falaggis, K.

Fang-Yen, C.

Feld, M. S.

Ferraro, P.

Finizio, A.

Georges, V.

Górski, W.

Grilli, S.

Haeberlé, O.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34(1), 79–81 (2009).
[Crossref] [PubMed]

Heger, T. J.

Ikeda, T.

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Józwik, M.

Kemper, B.

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref] [PubMed]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008).
[Crossref] [PubMed]

Kim, K.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref] [PubMed]

Kiss, R.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Kostencka, J.

T. Kozacki, K. Liżewski, and J. Kostencka, “Absolute shape measurement of high NA focusing microobjects in digital holographic microscope with arbitrary spherical wave illumination,” Opt. Express 22(14), 16991–17005 (2014).
[Crossref] [PubMed]

J. Kostencka, T. Kozacki, M. Dudek, and M. Kujawińska, “Noise suppressed optical diffraction tomography with autofocus correction,” Opt. Express 22(5), 5731–5745 (2014).
[Crossref] [PubMed]

T. Kozacki, K. Liżewski, and J. Kostencka, “Holographic method for topography measurement of highly tilted and high numerical aperture micro structures,” Opt. Laser Technol. 49, 38–46 (2013).
[Crossref]

J. Kostencka and T. Kozacki, “Computational and experimental study on accuracy of off-axis reconstructions in optical diffraction tomography,” Opt. Eng. (to be published).

Kou, S. S.

Kozacki, T.

Kuehn, J.

Kühn, J.

Kujawinska, M.

Kus, A.

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref] [PubMed]

Legros, J. C.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Lizewski, K.

Lue, N.

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Magistretti, P. J.

Magro, C.

Marian, A.

Marque, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Marquet, P.

Mitchell, E. A. D.

Monnom, O.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Montfort, F.

Morin, R.

Osten, W.

Park, Y.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref] [PubMed]

Pavillon, N.

Pierattini, G.

Popescu, G.

Rappaz, B.

Rohrbach, A.

Sheppard, C. J.

Simon, B.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34(1), 79–81 (2009).
[Crossref] [PubMed]

Singer, W.

Sung, Y.

Tourneur, Y.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

Toy, F.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Van Ham, P.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Vollmer, A.

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref] [PubMed]

von Bally, G.

Yoon, H.

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref] [PubMed]

Yourassowsky, C.

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

Appl. Opt. (6)

Biomed. Opt. Express (1)

J Biophotonics (1)

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

J. Biomed. Opt. (3)

A. Kuś, M. Dudek, B. Kemper, M. Kujawińska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19(4), 046009 (2014).
[Crossref] [PubMed]

F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006).
[Crossref] [PubMed]

K. Kim, H. Yoon, M. Diez-Silva, M. Dao, R. R. Dasari, and Y. Park, “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography,” J. Biomed. Opt. 19(1), 011005 (2014).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marque, and Ch. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (1)

T. Kozacki, K. Liżewski, and J. Kostencka, “Holographic method for topography measurement of highly tilted and high numerical aperture micro structures,” Opt. Laser Technol. 49, 38–46 (2013).
[Crossref]

Opt. Lett. (4)

Ultrason. Imaging (1)

A. J. Devaney, “A Filtered Backpropagation Algorithm for Diffraction Tomography,” Ultrason. Imaging 4(4), 336–350 (1982).
[Crossref] [PubMed]

Other (3)

J. Kostencka and T. Kozacki, “Computational and experimental study on accuracy of off-axis reconstructions in optical diffraction tomography,” Opt. Eng. (to be published).

D. Malacara and Z. Malacara, Handbook of optical design, Second edition, (Marcel Dekker Inc., 2004).

J. Kostencka, T. Kozacki, A. Kuś, M. Dudek, M. Kujawińska, and B. Kemper, “Holographic method for capillary induced aberration compensation for 3D tomographic measurements of living cells,” SPIE Proc., 8792, 8792–4 (2013).
[Crossref]

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Figures (17)

Fig. 1
Fig. 1

Scheme of the DHM tomographic system: SMF- single mode fiber, CO- collimating objective, P- polarizer, BS1, BS2- beam-splitting cube (50:50), M1, M2- mirror, ND- neutral density filter, L1, L2- beam expander, PD- Petri dish, FC- capillary, MO- microscope objective, TL- tube lens.

Fig. 2
Fig. 2

Schematic of the capillary holder.

Fig. 3
Fig. 3

Spherical aberration resulting from refraction at a planar surface.

Fig. 4
Fig. 4

Illustration of the cylindrical boundary correction algorithm.

Fig. 5
Fig. 5

Scheme of a tomographic data acquisition system.

Fig. 6
Fig. 6

Illustration of influence of cylindrical wave illumination: a) illumination conditions; b) backpropagation of a normalized object wave; c) backpropagation of an original object wave.

Fig. 7
Fig. 7

Reconstructed refractive index variation obtained with a standard tomographic approach.

Fig. 8
Fig. 8

Reconstructed refractive index variation obtained without correction of spherical aberration (results obtained with LRA and AI-FBPP).

Fig. 9
Fig. 9

Reconstructed refractive index variation (a) and its error (b) obtained with TEA correction (the results obtained with spherical aberration correction and AI-FBPP).

Fig. 10
Fig. 10

Reconstructed refractive index variation obtained with LRA correction and FBPP.

Fig. 11
Fig. 11

Reconstructed refractive index variations (a) and its error (b) obtained with the full data processing path proposed in the paper.

Fig. 12
Fig. 12

Reconstruction error as a function of distance from the center of the capillary.

Fig. 13
Fig. 13

Measurements of microspheres in the capillary: a) off-axis hologram; the reconstructed b) amplitude and c) phase.

Fig. 14
Fig. 14

Reconstructed refractive index distribution – 3D view.

Fig. 15
Fig. 15

The AI-FBPP reconstructions of refractive index distribution obtained with LRA (a) and TEA (b) correction; c – difference of the results in (a) and (b).

Fig. 16
Fig. 16

Tomographic reconstruction obtained with LRA correction and FBPP.

Fig. 17
Fig. 17

Tomographic reconstruction (LRA + AI-FBPP) without correction of spherical aberration.

Equations (16)

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

H eff ( f x , f y )=exp{ i k 0 L[ n' n n ' 2 λ 2 ( f x 2 + f y 2 ) n 2 λ 2 ( f x 2 + f y 2 ) ] },
u corr = FT 1 { FT[ u aberr ] H eff },
φ( x A )= φ aberr ( x C ) k 1 AB k 2 CB .
k 2 ( x C )=[ k 2x , k 2z ]=[ k 0 n 2 sin α 2 , k 0 n 2 cos α 2 ]=[Δ φ aberr ( x C ), ( k 0 2 n 2 2 φ aberr ( x C )) 1 2 ].
{ x B ( x C )=tan α 2 z B ( x C )+ x C z B ( x C )= R 2 x B 2 ( x C ) ,
α 1 = sin 1 ( x B /R)+ sin 1 [ n 2 n 1 sin( α 2 sin 1 ( x B /R) ) ].
φ corr = φ aberr k 1z z B k 1x ( x B x A )+ k 2x ( x B x C )+ k 2z z B ,
φ corr = φ aberr z B ( k 1z k 2z +tan α 1 k 1x tan α 2 k 2x ).
x A = x C +( x B x C )( x B x A )= x C + z B (tan α 2 tan α 1 )
Π θ (ξ,η)= 1 2π exp{i k 0 n 0 ( η 0 η)}F T 1 { FT[ U θ (ξ) ]exp{i k η (η η 0 )} },
Π N θ (ξ,η)= Π θ (ξ,η) / Π ill (ξ,η).
Φ θ (ξ,η)=iln[ Π N θ (ξ,η) ]/( k 0 n 0 ).
Φ HF θ = FT 1 { | k ξ |FT[ Φ θ ] }.
O(x,y)= 1 2π 0 2π Φ θ (xcosθysinθ, xsinθ+ycosθ)dθ ,
O(x,y)=[ 1 n (x,y) 2 n 0 2 ] 2 n 0 Δn(x,y).
E = R < 2 R s ( Δ n r e c Δ n m o d e l ) 2 / N ,

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