Abstract

Crucial benefits provided by partially coherent light microscopy such as improved spatial resolution, optical sectioning and speckle-noise suppression are exploited here to achieve 3D quantitative imaging: reconstruction of the object refractive index (RI). We present a partially coherent optical diffraction tomography technique (PC-ODT) that can be easily implemented in commercially available bright-field microscopes. We show that the high numerical apertures of the objective and condenser lenses, together with optical refocusing, are main issues for achieving fast and successful 3D RI reconstruction of weak objects. In particular, the optical refocusing is performed by a high-speed focus tunable lens mounted in front of the digital camera enabling compatibility with commercial microscopes. The technique is experimentally demonstrated on different examples: diatom cells (biosilica shells), polystyrene micro-spheres and blood cells. The results confirm the straightforward 3D-RI reconstruction of the samples providing valuable quantitative information for their analysis. Thus, the PC-ODT can be considered as an efficient and affordable alternative to coherent ODT which requires specially designed holographic microscopes.

© 2017 Optical Society of America

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References

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2017 (2)

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberlé, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4, 460–463 (2017).
[Crossref]

2016 (2)

2015 (3)

2014 (3)

2013 (1)

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

2012 (1)

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

2010 (2)

D. S. C. Biggs, “3D deconvolution microscopy,” Curr. Protoc. Cytom. 52, 12 (2010).

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

2007 (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

2006 (1)

2004 (1)

1994 (1)

1985 (1)

Alieva, T.

Arganda-Carreras, I.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Badizadegan, K.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Bailleul, J.

Bao, Y.

Biggs, D. S. C.

D. S. C. Biggs, “3D deconvolution microscopy,” Curr. Protoc. Cytom. 52, 12 (2010).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
[Crossref]

Boss, D.

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

Cardona, A.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Charrière, F.

Chen, M.

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 9718, 971826 (2016).

Choi, C.

Choi, W.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Colomb, T.

Cotte, Y.

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

Cuche, E.

Dao, M.

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

Dasari, R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Dasari, R. R.

Debailleul, M.

Depeursinge, C.

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

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
[Crossref] [PubMed]

Dhal, B.

Diez-Silva, M.

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

Donati, L.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Ecoffet, C.

Eliceiri, K.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Fang-Yen, C.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Feld, M.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Feld, M. S.

Ferraro, P.

P. Ferraro, A. Wax, and Z. Zalevsky, Coherent Light Microscopy: Imaging and Quantitative Phase Analysis, Springer Series in Surface Sciences (Springer, 2011).

Fortun, D.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Frise, E.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Gaylord, T. K.

Goddard, L. L.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Gu, M.

Guiet, R.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Haeberlé, O.

Han, J.

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

Hartenstein, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Hayashida, N.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Hayes, J.

Houkal, M.

Jang, S.

Jenkins, M. H.

Jin, K. H.

Jourdain, P.

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

Kawata, S.

Kawata, Y.

Kaynig, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Kim, K.

Kim, T.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Kuehn, J.

Lambert, J.

Lee, K.

Lee, S.

Lim, C.-T.

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

Lim, J.

Liu, H.

Longair, M.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Magistretti, P.

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

Mancuso, A.

Marian, A.

Marquet, P.

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

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
[Crossref] [PubMed]

Mir, M.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Montfort, F.

Nugent, K.

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Ohguchi, M.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Park, H.

Park, Y.

Paterson, D.

Pavillon, N.

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

Peele, A.

Pietzsch, T.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Popescu, G.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Preibisch, S.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Rodrigo, J. A.

Rueden, C.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Saalfeld, S.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Sage, D.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Schindelin, J.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Schmid, B.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Schmit, G.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Scholten, R.

Seitz, A.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Sheppard, C. J. R.

Shin, S.

Simon, B.

Soppera, O.

Soulez, F.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Spangenberg, A.

Streibl, N.

Sung, Y.

Suresh, S.

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

Takeda, H.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Tian, L.

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 9718, 971826 (2016).

Tinevez, J.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Tomancak, P.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Toy, F.

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

Tran, C.

Turner, L.

Unser, M.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Usami, H.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Vonesch, C.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Waller, L.

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 9718, 971826 (2016).

Wax, A.

P. Ferraro, A. Wax, and Z. Zalevsky, Coherent Light Microscopy: Imaging and Quantitative Phase Analysis, Springer Series in Surface Sciences (Springer, 2011).

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J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
[Crossref]

Yamanaka, S.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Yano, R.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Ye, J. C.

Yoon, J.

Yoshino, K.

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

Zalevsky, Z.

P. Ferraro, A. Wax, and Z. Zalevsky, Coherent Light Microscopy: Imaging and Quantitative Phase Analysis, Springer Series in Surface Sciences (Springer, 2011).

Zhou, R.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Appl. Opt. (1)

Biomed. Opt. Express (2)

Curr. Protoc. Cytom. (1)

D. S. C. Biggs, “3D deconvolution microscopy,” Curr. Protoc. Cytom. 52, 12 (2010).

J. Appl. Phys. (1)

S. Yamanaka, R. Yano, H. Usami, N. Hayashida, M. Ohguchi, H. Takeda, and K. Yoshino, “Optical properties of diatom silica frustule with special reference to blue light,” J. Appl. Phys. 103, 074701 (2008).
[Crossref]

J. Opt. Soc. Am. A (3)

Methods (1)

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

MRS bulletin (1)

M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, “Shape and biomechanical characteristics of human red blood cells in health and disease,” MRS bulletin 35, 382–388 (2010).
[Crossref] [PubMed]

Nat. Meth. (2)

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Meth. 9, 676–682 (2012).
[Crossref]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Meth. 4, 717–720 (2007).
[Crossref]

Nat. Phot. (2)

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

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Phot. 8, 256–263 (2014).

Opt. Express (4)

Opt. Lett. (2)

Optica (1)

Other (3)

S. Spaulding, D. Lubinski, and M. Potapova, “Diatoms of the United States,” “Available at: http://Westerndiatoms.colorado.edu , http://westerndiatoms.colorado.edu/taxa/species/cocconeis_placentula ” (2010).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
[Crossref]

P. Ferraro, A. Wax, and Z. Zalevsky, Coherent Light Microscopy: Imaging and Quantitative Phase Analysis, Springer Series in Surface Sciences (Springer, 2011).

Supplementary Material (5)

NameDescription
» Visualization 1: MP4 (1922 KB)      Intensity and refractive index stacks for S=0.34
» Visualization 2: MP4 (1333 KB)      Intensity and refractive index stacks for S=0.68
» Visualization 3: MP4 (1285 KB)      Intensity and refractive index stacks for S=0.68 (diatom Diploneis)
» Visualization 4: MP4 (1029 KB)      3D animation of the RI, diatom Cymbella
» Visualization 5: MP4 (1078 KB)      3D animation of the RI, diatom Diploneis

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Figures (7)

Fig. 1
Fig. 1

(a) Illumination configuration for a transmission wide-field microscope. (b) The C-ODT technique retrieves the scattering potential spectrum (ρ⃗) transmitted by the microscope. An illumination scanning approach (sequential object illumination) is used to collect all the cross sections of the object’s spectra with the Ewald sphere (semicircular arcs). As an example, only 3 scanning positions (thus 3 semicircular arcs) have been sketched. Note that the transmitted part of (ρ⃗) falls inside a 3D horn-torus in the reciprocal space, here only its section (ρx, 0, ρz) has been sketched (dashed curve). (c) The proposed PC-ODT technique retrieves the same horn-torus region because the illumination of the condenser aperture allows for coverage of all the illumination angles simultaneously.

Fig. 2
Fig. 2

Setup for the measurement of the stack of intensity images I (r⃗). The sample is imaged by the objective lens and tube lens. The obtained 3D image is then axially scanned by using the refocusing setup comprising the relay lens (RL) with focal length of 15 cm and the ETL lens with a varying focal length. The inset displays the measurement device: ETL (Optotune, EL-10-30-C) and a high-speed sCMOS camera (Hamamatsu, Orca Flash 4.0).

Fig. 3
Fig. 3

Bright-field intensity images (slices extracted from the measured intensity stack I (r⃗)) and the corresponding reconstruction of the refractive index (RI) for a Cocconeis placentula diatom obtained under two different illumination conditions: S = 0.34 for (a, b) and S = 0.68 for (c, d). The intensity and RI distributions (xy-slices) are displayed for two axial positions z in the first and second row. The measured intensity stack as well as the RI stack for both S values are provided in Visualization 1 and Visualization 2, respectively. (e) and (f) display a RI profile along region R3 for S = 0.34 and S = 0.68, correspondingly. (g) and (h) show a 2D section of the object intensity spectrum Î(ρx, 0, ρz) together with the POTF section Im{HP(ρx, 0, ρz)} corresponding to the case S = 0.34 and S = 0.68.

Fig. 4
Fig. 4

(a) Reconstructed RI for a Cymbella subturgidula diatom. The frustule made of biosilica exhibits distinct structures such as slits and striae comprising the valves. Two xy–RI slices are presented in the first column where two tiny stigmata are observed close to the valve center, at z = 2 μm. The following three columns are different points of view for 3D-RI (|Δn| = |nRenm|) where different structures of the diatom are observed. (b) Reconstructed RI for a Diploneis elliptica diatom. In the first column, the xy–RI slice reveals detailed structures such as the raphe slits and the pores comprising the diatom striae. The next two columns include different perspectives of the 3D-RI |Δn|, in which it is observed a rounded central area (nodule) located in the middle of a longitudinal canal (raphe). A 3D animated version of these diatoms (RI volume) is provided in Visualization 4 and Visualization 5, correspondingly.

Fig. 5
Fig. 5

(a) Refractive index slice of a blood smear where red blood cell (RBC), white blood cells (WBC) and platelets (P) are observed. (b) Close-up view of the refractive index slice of the RBC along xy–, yz–, and xz–planes. (c) 3D refractive index distribution (Δn) of the RBC exhibiting its characteristic biconcave disc-like shape.

Fig. 6
Fig. 6

(a) xy–slice of the RI reconstructed by using the effective OTF, HE (ρ⃗) = HP (ρ⃗) + εHA (ρ⃗), with ε = 0.05. (b) The reconstructed RI exhibits halo artifacts when only the POTF (ε = 0) is used.

Fig. 7
Fig. 7

(a) xy–slice of the bright-field intensity for a polystyrene sphere (bead diameter of 3.8 ± 0.1 μm, nRe = 1.59 ± 0.01, Spherotech Lot. AD01) immersed in oil (nm = 1.56, Cargille Labs Series A). (b) Reconstructed refractive index for the same xy–slice.

Equations (11)

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I ( r ) = B + P ( r ) h P ( r ) + A ( r ) h A ( r ) ,
I ^ ( ρ ) = B δ ( ρ ) + P ^ ( ρ ) H P ( ρ ) + A ^ ( ρ ) H A ( ρ ) ,
I ^ ( ρ ) = B δ ( ρ ) + P ( ρ ) × [ H P ( ρ ) + ε H A ( ρ ) ] .
P ( ρ ) = I ^ ( ρ ) H E * ( ρ ) | H E ( ρ ) | 2 + β ,
n Re ( r ) = | n 2 ( r ) | + Re { n 2 ( r ) } 2 ,
n Im ( r ) = | n 2 ( r ) | Re { n 2 ( r ) } 2 ,
H P ( ρ , ρ z ) = i λ 4 π [ F ( ρ , ρ z ) F ( ρ , ρ z ) ] ,
H A ( ρ , ρ z ) = λ 4 π [ F ( ρ , ρ z ) + F ( ρ , ρ z ) ] ,
F ( ρ , ρ z ) = ρ 2 σ ρ 2 ρ z λ 2 ρ 2 4 ρ 2 σ 2 ρ z 2 + ( λ 2 ρ 2 4 ρ z 2 2 ρ ) arccos ( ρ σ ρ z λ 2 ρ 2 / 4 ) .
σ = { ρ z ρ ( ρ z 2 λ 2 ρ S 2 ) If [ λ 2 ρ S 2 λ 2 ( ρ S ρ ) 2 ρ z λ 2 ρ S 2 λ 2 ( ρ S + ρ ) 2 ] ,
σ = { ρ z ρ ( ρ z 2 λ 2 ρ S 2 ) If [ λ 2 ρ S 2 λ 2 ( ρ S ρ ) 2 ρ z λ 2 ρ S 2 λ 2 ρ P 2 ] ρ z ρ ( ρ z 2 λ 2 ρ P 2 ) If [ λ 2 ρ S 2 λ 2 ρ P 2 ρ z λ 2 ( ρ P ρ ) 2 λ 2 ρ P 2 ] ,