Abstract

In optical tomography, there exist certain spatial frequency components that cannot be measured due to the limited projection angles imposed by the numerical aperture of objective lenses. This limitation, often called as the missing cone problem, causes the under-estimation of refractive index (RI) values in tomograms and results in severe elongations of RI distributions along the optical axis. To address this missing cone problem, several iterative reconstruction algorithms have been introduced exploiting prior knowledge such as positivity in RI differences or edges of samples. In this paper, various existing iterative reconstruction algorithms are systematically compared for mitigating the missing cone problem in optical diffraction tomography. In particular, three representative regularization schemes, edge preserving, total variation regularization, and the Gerchberg-Papoulis algorithm, were numerically and experimentally evaluated using spherical beads as well as real biological samples; human red blood cells and hepatocyte cells. Our work will provide important guidelines for choosing the appropriate regularization in ODT.

© 2015 Optical Society of America

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References

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2015 (1)

2014 (8)

L. Ma, H. Wang, L. Su, Y. Li, and H. Jin, “Digital holographic microtomography with few angle data-sets,” J. Mod. Opt. 61, 1140–1146 (2014).
[Crossref]

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, 011005 (2014).
[Crossref]

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy [invited],” Appl. Opt. 53, G111–G122 (2014).
[Crossref] [PubMed]

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

Y.-C. Lin and C.-J. Cheng, “Sectional imaging of spatially refractive index distribution using coaxial rotation digital holographic microtomography,” J. Opt. 16, 065401 (2014).
[Crossref]

Y. Kim, H. Shim, K. Kim, H. Park, J. H. Heo, J. Yoon, C. Choi, S. Jang, and Y. Park, “Common-path diffraction optical tomography for investigation of three-dimensional structures and dynamics of biological cells,” Opt. Express 22, 10398–10407 (2014).
[Crossref] [PubMed]

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

K. Kim, Z. Yaqoob, K. Lee, J. W. Kang, Y. Choi, P. Hosseini, P. T. So, and Y. Park, “Diffraction optical tomography using a quantitative phase imaging unit,” Opt. Lett. 39, 6935–6938 (2014).
[Crossref] [PubMed]

2013 (5)

K. Kim, K. S. Kim, H. Park, J. C. Ye, and Y. Park, “Real-time visualization of 3-D dynamic microscopic objects using optical diffraction tomography,” Opt. Express 21, 32269–32278 (2013).
[Crossref]

S. Uttam, S. A. Alexandrov, R. K. Bista, and Y. Liu, “Tomographic imaging via spectral encoding of spatial frequency,” Opt. Express 21, 7488–7504 (2013).
[Crossref] [PubMed]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref] [PubMed]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
[Crossref] [PubMed]

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

2012 (4)

2011 (7)

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56, 4013 (2011).
[Crossref] [PubMed]

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref] [PubMed]

Z. Wang, D. L. Marks, P. S. Carney, L. J. Millet, M. U. Gillette, A. Mihi, P. V. Braun, Z. Shen, S. G. Prasanth, and G. Popescu, “Spatial light interference tomography (slit),” Opt. Express 19, 19907–19918 (2011).
[Crossref] [PubMed]

Y. Sung and R. R. Dasari, “Deterministic regularization of three-dimensional optical diffraction tomography,” J. Opt. Soc. Am. A 28, 1554–1561 (2011).
[Crossref]

Y. Park, C. A. Best, T. Kuriabova, M. L. Henle, M. S. Feld, A. J. Levine, and G. Popescu, “Measurement of the nonlinear elasticity of red blood cell membranes,” Phys. Rev. E 83, 051925 (2011).
[Crossref]

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref] [PubMed]

2010 (4)

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107, 1289–1294 (2010).
[Crossref] [PubMed]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

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

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[Crossref]

2009 (8)

R. Fiolka, K. Wicker, R. Heintzmann, and A. Stemmer, “Simplified approach to diffraction tomography in optical microscopy,” Opt. Express 17, 12407–12417 (2009).
[Crossref] [PubMed]

S. S. Kou and C. J. Sheppard, “Image formation in holographic tomography: high-aperture imaging conditions,” Appl. Opt. 48, H168–H175 (2009).
[Crossref] [PubMed]

J. Kühn, F. Montfort, T. Colomb, B. Rappaz, C. Moratal, N. Pavillon, P. Marquet, and C. Depeursinge, “Submicrometer tomography of cells by multiple-wavelength digital holographic microscopy in reflection,” Opt. Lett. 34, 653–655 (2009).
[Crossref] [PubMed]

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17, 12285–12292 (2009).
[Crossref] [PubMed]

Y. Park, T. Yamauchi, W. Choi, R. Dasari, and M. S. Feld, “Spectroscopic phase microscopy for quantifying hemoglobin concentrations in intact red blood cells,” Opt. Lett. 34, 3668–3670 (2009).
[Crossref] [PubMed]

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]

S. Bartolac, R. Clackdoyle, F. Noo, J. Siewerdsen, D. Moseley, and D. Jaffray, “A local shift-variant fourier model and experimental validation of circular cone-beam computed tomography artifacts,” Med. Phys. 36, 500–512 (2009).
[Crossref] [PubMed]

T. Goldstein and S. Osher, “The split Bregman method for l1-regularized problems,” SIAM. J. Imaging. Sci. 2, 323–343 (2009).
[Crossref]

2008 (5)

S. J. LaRoque, E. Y. Sidky, and X. Pan, “Accurate image reconstruction from few-view and limited-angle data in diffraction tomography,” J. Opt. Soc. Am. A 25, 1772–1782 (2008).
[Crossref]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref] [PubMed]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive mi-crotomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

M. Potcoava and M. Kim, “Optical tomography for biomedical applications by digital interference holography,” Meas. Sci. Technol. 19, 074010 (2008).
[Crossref]

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44, 29–35 (2008).
[Crossref]

2007 (1)

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[Crossref] [PubMed]

2006 (4)

2005 (4)

2002 (1)

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[Crossref] [PubMed]

1998 (1)

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Processing 7, 204–221 (1998).
[Crossref]

1997 (1)

P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. on Image Processing 6, 298–311 (1997).
[Crossref]

1994 (1)

1981 (1)

1975 (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits and Systems 22, 735–742 (1975).
[Crossref]

1974 (1)

R. Gerchberg, “Super-resolution through error energy reduction,” J. Mod. Opt. 21, 709–720 (1974).

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[Crossref]

1967 (1)

L. M. Bregman, “The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming,” USSR. Comp. Math. Math+. 7, 200–217 (1967).
[Crossref]

Abascal, J.-J.

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

Aguirre, J.

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

Alexandrov, S. A.

Arridge, S.

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

Aubert, G.

P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. on Image Processing 6, 298–311 (1997).
[Crossref]

Auth, T.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107, 1289–1294 (2010).
[Crossref] [PubMed]

Badizadegan, K.

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

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]

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17, 12285–12292 (2009).
[Crossref] [PubMed]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref] [PubMed]

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14, 8263–8268 (2006).
[Crossref] [PubMed]

Balduzzi, D.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
[Crossref] [PubMed]

Barlaud, M.

P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. on Image Processing 6, 298–311 (1997).
[Crossref]

Bartolac, S.

S. Bartolac, R. Clackdoyle, F. Noo, J. Siewerdsen, D. Moseley, and D. Jaffray, “A local shift-variant fourier model and experimental validation of circular cone-beam computed tomography artifacts,” Med. Phys. 36, 500–512 (2009).
[Crossref] [PubMed]

Bashir, R.

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref] [PubMed]

Bednarz, M.

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref] [PubMed]

Beghin, A.

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

Belkebir, K.

Best, C. A.

Y. Park, C. A. Best, T. Kuriabova, M. L. Henle, M. S. Feld, A. J. Levine, and G. Popescu, “Measurement of the nonlinear elasticity of red blood cell membranes,” Phys. Rev. E 83, 051925 (2011).
[Crossref]

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107, 1289–1294 (2010).
[Crossref] [PubMed]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

Best-Popescu, C.

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref] [PubMed]

Bishara, W.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref] [PubMed]

Bista, R. K.

Blanc-Féraud, L.

P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. on Image Processing 6, 298–311 (1997).
[Crossref]

Bon, P.

Boss, D.

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

Braun, P. V.

Bregman, L. M.

L. M. Bregman, “The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming,” USSR. Comp. Math. Math+. 7, 200–217 (1967).
[Crossref]

Bresler, Y.

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Processing 7, 204–221 (1998).
[Crossref]

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Information Theory 52, 489–509 (2006).
[Crossref]

Carney, P. S.

Chamorro-Servent, J.

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

Chang, G.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref] [PubMed]

Charbonnier, P.

P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. on Image Processing 6, 298–311 (1997).
[Crossref]

Charrière, F.

Chaumet, P.

Cheng, C.-J.

Y.-C. Lin and C.-J. Cheng, “Sectional imaging of spatially refractive index distribution using coaxial rotation digital holographic microtomography,” J. Opt. 16, 065401 (2014).
[Crossref]

Cho, S.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref] [PubMed]

Choi, C.

Choi, W.

Choi, Y.

Choma, M. A.

Clackdoyle, R.

S. Bartolac, R. Clackdoyle, F. Noo, J. Siewerdsen, D. Moseley, and D. Jaffray, “A local shift-variant fourier model and experimental validation of circular cone-beam computed tomography artifacts,” Med. Phys. 36, 500–512 (2009).
[Crossref] [PubMed]

Colomb, T.

Coppola, G.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
[Crossref] [PubMed]

Correia, T.

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

Cotte, Y.

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

Creazzo, T. L.

Cuche, E.

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, 011005 (2014).
[Crossref]

Dasari, R.

Dasari, R. R.

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, 011005 (2014).
[Crossref]

Y. Sung, W. Choi, N. Lue, R. R. Dasari, and Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7, e49502 (2012).
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Y. Sung and R. R. Dasari, “Deterministic regularization of three-dimensional optical diffraction tomography,” J. Opt. Soc. Am. A 28, 1554–1561 (2011).
[Crossref]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

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]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref] [PubMed]

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14, 8263–8268 (2006).
[Crossref] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31, 775–777 (2006).
[Crossref] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005).
[Crossref] [PubMed]

Debailleul, M.

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

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive mi-crotomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44, 29–35 (2008).
[Crossref]

Deflores, L.

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref] [PubMed]

Delaney, A. H.

A. H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE Trans. Image Processing 7, 204–221 (1998).
[Crossref]

Depeursinge, C.

Desco, M.

J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
[Crossref] [PubMed]

Devaney, A.

Di Caprio, G.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
[Crossref] [PubMed]

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, 011005 (2014).
[Crossref]

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).
[Crossref] [PubMed]

Douplik, A.

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56, 4013 (2011).
[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, 046009 (2014).
[Crossref]

Ellerbee, A. K.

Fang-Yen, C.

Fauver, M.

Feld, M. S.

Y. Park, C. A. Best, T. Kuriabova, M. L. Henle, M. S. Feld, A. J. Levine, and G. Popescu, “Measurement of the nonlinear elasticity of red blood cell membranes,” Phys. Rev. E 83, 051925 (2011).
[Crossref]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107, 1289–1294 (2010).
[Crossref] [PubMed]

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]

Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17, 12285–12292 (2009).
[Crossref] [PubMed]

Y. Park, T. Yamauchi, W. Choi, R. Dasari, and M. S. Feld, “Spectroscopic phase microscopy for quantifying hemoglobin concentrations in intact red blood cells,” Opt. Lett. 34, 3668–3670 (2009).
[Crossref] [PubMed]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31, 775–777 (2006).
[Crossref] [PubMed]

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14, 8263–8268 (2006).
[Crossref] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005).
[Crossref] [PubMed]

Feng, S.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref] [PubMed]

Ferraro, P.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
[Crossref] [PubMed]

Fiolka, R.

Frank, W. Y.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref] [PubMed]

Fujimoto, J. G.

Galli, A.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
[Crossref] [PubMed]

Georges, V.

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44, 29–35 (2008).
[Crossref]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive mi-crotomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

Gerchberg, R.

R. Gerchberg, “Super-resolution through error energy reduction,” J. Mod. Opt. 21, 709–720 (1974).

Getreuer, P.

P. Getreuer, “Rudin-Osher-Fatemi total variation denoising using split Bregman,” Image Processing on Line 10, 74 (2012).

Gillette, M. U.

Giovaninni, H.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[Crossref]

Giovannini, H.

Golding, I.

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref] [PubMed]

Goldstein, T.

T. Goldstein and S. Osher, “The split Bregman method for l1-regularized problems,” SIAM. J. Imaging. Sci. 2, 323–343 (2009).
[Crossref]

Gov, N. S.

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107, 1289–1294 (2010).
[Crossref] [PubMed]

Haeberlé, O.

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

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[Crossref]

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, “Tomographic diffractive microscopy of transparent samples,” Eur. Phys. J. Appl. Phys. 44, 29–35 (2008).
[Crossref]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive mi-crotomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
[Crossref]

Hee, M. R.

Heintzmann, R.

Henle, M. L.

Y. Park, C. A. Best, T. Kuriabova, M. L. Henle, M. S. Feld, A. J. Levine, and G. Popescu, “Measurement of the nonlinear elasticity of red blood cell membranes,” Phys. Rev. E 83, 051925 (2011).
[Crossref]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

Heo, J.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref] [PubMed]

Heo, J. H.

Hosseini, P.

Ikeda, T.

Isikman, S. O.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref] [PubMed]

Izatt, J. A.

Jaffray, D.

S. Bartolac, R. Clackdoyle, F. Noo, J. Siewerdsen, D. Moseley, and D. Jaffray, “A local shift-variant fourier model and experimental validation of circular cone-beam computed tomography artifacts,” Med. Phys. 36, 500–512 (2009).
[Crossref] [PubMed]

Jang, J.

Jang, S.

Jang, Y.

Jin, H.

L. Ma, H. Wang, L. Su, Y. Li, and H. Jin, “Digital holographic microtomography with few angle data-sets,” J. Mod. Opt. 61, 1140–1146 (2014).
[Crossref]

Jo, Y.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref] [PubMed]

Jourdain, P.

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

Jung, J.

J. Jung, K. Kim, H. Yu, K. Lee, S. Lee, S. Nahm, H. Park, and Y. Park, “Biomedical applications of holographic microspectroscopy [invited],” Appl. Opt. 53, G111–G122 (2014).
[Crossref] [PubMed]

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O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56, 4013 (2011).
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G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, “Three-dimensional limited-angle microtomography of blood cells: experimental results,” in “BiOS’98 International Biomedical Optics Symposium,” (International Society for Optics and Photonics, 1998), pp. 159–164.

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, 046009 (2014).
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M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
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Z. Wang, D. L. Marks, P. S. Carney, L. J. Millet, M. U. Gillette, A. Mihi, P. V. Braun, Z. Shen, S. G. Prasanth, and G. Popescu, “Spatial light interference tomography (slit),” Opt. Express 19, 19907–19918 (2011).
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O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56, 4013 (2011).
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Am. J. Physiol. Cell Physiol. (1)

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J. Biomed. Opt. (2)

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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, 462–467 (2010).
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Lab Chip (1)

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. Netti, and P. Ferraro, “Digital holography as a method for 3d imaging and estimating the biovolume of motile cells,” Lab Chip 13, 4512–4516 (2013).
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M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive mi-crotomography of transparent samples,” Meas. Sci. Technol. 19, 074009 (2008).
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Med. Phys. (2)

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J.-J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split Bregman method,” Med. Phys. 38, 6275–6284 (2011).
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Nature Photon. (1)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
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Opt. Commun. (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
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Opt. Express (10)

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).
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Y. Kim, H. Shim, K. Kim, H. Park, J. H. Heo, J. Yoon, C. Choi, S. Jang, and Y. Park, “Common-path diffraction optical tomography for investigation of three-dimensional structures and dynamics of biological cells,” Opt. Express 22, 10398–10407 (2014).
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K. Kim, K. S. Kim, H. Park, J. C. Ye, and Y. Park, “Real-time visualization of 3-D dynamic microscopic objects using optical diffraction tomography,” Opt. Express 21, 32269–32278 (2013).
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Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14, 8263–8268 (2006).
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Y. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17, 12285–12292 (2009).
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R. Fiolka, K. Wicker, R. Heintzmann, and A. Stemmer, “Simplified approach to diffraction tomography in optical microscopy,” Opt. Express 17, 12407–12417 (2009).
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Z. Wang, D. L. Marks, P. S. Carney, L. J. Millet, M. U. Gillette, A. Mihi, P. V. Braun, Z. Shen, S. G. Prasanth, and G. Popescu, “Spatial light interference tomography (slit),” Opt. Express 19, 19907–19918 (2011).
[Crossref] [PubMed]

S. Uttam, S. A. Alexandrov, R. K. Bista, and Y. Liu, “Tomographic imaging via spectral encoding of spatial frequency,” Opt. Express 21, 7488–7504 (2013).
[Crossref] [PubMed]

Y. Jang, J. Jang, and Y. Park, “Dynamic spectroscopic phase microscopy for quantifying hemoglobin concentration and dynamic membrane fluctuation in red blood cells,” Opt. Express 20, 9673–9681 (2012).
[Crossref] [PubMed]

M. Fauver, E. Seibel, J. R. Rahn, M. Meyer, F. Patten, T. Neumann, and A. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13, 4210–4223 (2005).
[Crossref] [PubMed]

Opt. Lett. (11)

L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005).
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G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31, 775–777 (2006).
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T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005).
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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).
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Y. Park, T. Yamauchi, W. Choi, R. Dasari, and M. S. Feld, “Spectroscopic phase microscopy for quantifying hemoglobin concentrations in intact red blood cells,” Opt. Lett. 34, 3668–3670 (2009).
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Phys. Med. Biol. (1)

O. Zhernovaya, O. Sydoruk, V. Tuchin, and A. Douplik, “The refractive index of human hemoglobin in the visible range,” Phys. Med. Biol. 56, 4013 (2011).
[Crossref] [PubMed]

Phys. Rev. E (1)

Y. Park, C. A. Best, T. Kuriabova, M. L. Henle, M. S. Feld, A. J. Levine, and G. Popescu, “Measurement of the nonlinear elasticity of red blood cell membranes,” Phys. Rev. E 83, 051925 (2011).
[Crossref]

PLoS ONE (1)

Y. Sung, W. Choi, N. Lue, R. R. Dasari, and Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7, e49502 (2012).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

Y. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A. 107, 1289–1294 (2010).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (3)

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. USA 107, 6731–6736 (2010).
[Crossref] [PubMed]

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref] [PubMed]

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
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Sci. Rep. (1)

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref] [PubMed]

Sensors (1)

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref] [PubMed]

SIAM. J. Imaging. Sci. (1)

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[Crossref]

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw Hill Professional, 2011).

G. G. Levin, G. N. Vishnyakov, C. S. Zakarian, A. V. Likhachov, V. V. Pickalov, G. I. Kozinets, J. K. Novoderzhkina, and E. A. Streletskaya, “Three-dimensional limited-angle microtomography of blood cells: experimental results,” in “BiOS’98 International Biomedical Optics Symposium,” (International Society for Optics and Photonics, 1998), pp. 159–164.

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Figures (7)

Fig. 1
Fig. 1

k-space sampling trajectories. (a) Spiral scanning trajectories in the k-space. Red and green dots show the low and high NAeff cases for 300 illumination angles, respectively. (b-c) Reconstructed 3-D k-space scattering potentials for (b) low (0.5) and (c) high (0.8) NAeff, respectively.

Fig. 2
Fig. 2

Numerical simulation results of a 5-μm-diameter fused silica bead phantom: 3-D RI tomograms numerically reconstructed by (a) FT, (b) GP, (c) EP, and (d) TV regularizations. (a-d); left column: z = 0 slice, right column: x = 0 slice, upper row: NAeff = 0.5, lower row: NAeff = 0.8, and the boundary of ROI is shown in white line. (e-f) Histograms of RI values in ROI divided by the total number of pixels in the ROI. (g-h) RI profiles along the z-axis. For figures (e-h), NAeff = 0.5 [(e) and (g)] and NAeff = 0.8 [(f) and (h)] were used. All scale bars are 2 μm.

Fig. 3
Fig. 3

Experimental results of a 5-μm-diameter fused silica bead: 3-D RI tomograms numerically reconstructed by (a) FT, (b) GP, (c) EP, and (d) TV regularizations. (a-d); left column: z = 0 slice, right column: x = 0 slice, upper row: NAeff = 0.5, lower row: NAeff = 0.8, and the boundary of ROI is shown in white line. (e-f) Histograms of RI values in ROI divided by the total number of pixels in the ROI. (g-h) RI profiles along the z-axis. For figures (e-h), NAeff = 0.5 [(e) and (g)] and NAeff = 0.8 [(f) and (h)] were used. All scale bars are 2 μm.

Fig. 4
Fig. 4

Experimental results of RBC RI tomograms obtained with (a) FT, (b) GP, (c) EP, and (d) TV regularization. The white dotted lines represent the slices of the complementary figures. All scale bars are 3 μm.

Fig. 5
Fig. 5

Experimental results of hepatocyte RI tomograms obtained with (a) FT, (b) GP, (c) EP, and (d) TV regularization. For figures (a-d), the white dotted lines represent the slices of the complementary figures. All scale bars are 5 μm.

Fig. 6
Fig. 6

Numerical simulation results of a 5-μm-diameter fused silica bead phantom with noise (SNR = 5dB): 3-D RI tomograms numerically reconstructed by (a) FT, (b) GP, (c) EP, and (d) TV regularizations. (a-d); left column: z = 0 slice, right column: x = 0 slice, upper row: NAeff = 0.5, lower row: NAeff = 0.8, and the boundary of ROI is shown in white line.

Fig. 7
Fig. 7

Numerical simulation results of a 5-μm-diameter fused silica bead phantom with noise (SNR = 10dB): 3-D RI tomograms numerically reconstructed by (a) FT, (b) GP, (c) EP, and (d) TV regularizations. (a-d); left column: z = 0 slice, right column: x = 0 slice, upper row: NAeff = 0.5, lower row: NAeff = 0.8, and the boundary of ROI is shown in white line.

Tables (1)

Tables Icon

Table 1 Description of data, used parameters, and the computation time

Equations (25)

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2 U ( r ) + k 2 U ( r ) = 4 π f ( r ) U ( r ) ,
f ( r ) = k 2 4 π ( n ( r ) 2 n 0 2 1 )
U s B ( r ) = V f ( r ) U 0 ( r ) G ( r r ) d r ,
U s R ( r ) = 1 U 0 ( r ) V f ( r ) U 0 ( r ) G ( r r ) d r .
g m = k s z ( m ) 2 π i + U 0 ( m ) ( r ) ln U ( r ) U 0 ( m ) ( r ) e i ( k s x ( m ) x + k s y ( m ) y ) d x d y ,
A m f = V f ( r ) e i ( k k m ) r d r .
A f g 2 2 = m = 1 M A m f g m 2 2 ,
J ( f ) = A f g 2 2 + α R ( f ) ,
J ( f ) = A f g 2 2 + α n ϕ ( D ( f ) n ) + β P f 2 2 ,
J ( f ) = inf b J * ( f , b ) = inf b A f g 2 2 + α n ( b n ) [ ( x f ) n 2 + ( y f ) n 2 + ( z f ) n 2 + ψ ( b n ) ] + β P f 2 2 .
( A H A + α x T B k + 1 x + α y T B k + 1 y + α z T B k + 1 z + β P k + 1 ) f k + 1 = A H g .
min f E ( f ) such that A f = g ,
f k + 1 = min f E ( f ) < p k , f f k > + μ 2 A f g 2 2 , p k + 1 = p k μ A H ( A f k + 1 g ) ,
f k + 1 = min f n D ( f ) + I ( f 0 ) + μ 2 A f g k 2 2 ,
g k + 1 = g k g A f k + 1 .
M S E ( x r e c o n ) = x t r u e x r e c o n 2 x t r u e 2 .
( f m + 1 , d m + 1 , v m + 1 ) = min f , d , v | d | + I ( v 0 ) + μ 2 A f g k 2 2 such that d = d ( f ) , v = f .
( f m + 1 , d m + 1 , v m + 1 ) = min f , d , v | d | + I ( v 0 ) + μ 2 A f g k 2 2 + α 2 d D ( f ) 2 2 + β 2 v f 2 2 .
( f m + 1 , d x m + 1 , d y m + 1 , d z m + 1 , v m + 1 ) = min f , d , v d x , d y , d z 2 + I ( v 0 ) + μ 2 A f g k 2 2 + α 2 d x x f b x m 2 2 + α 2 d y y f b y m 2 2 + α 2 d z z f b z m 2 2 + β 2 v f b v m 2 2 , b x m + 1 = b x m + ( x ( f m + 1 ) d x m + 1 ) , b y m + 1 = b y m + ( y ( f m + 1 ) d y m + 1 ) , b z m + 1 = b z m + ( z ( f m + 1 ) d z m + 1 ) , b v m + 1 = b v m + ( f m + 1 ) v m + 1 ) ,
min f μ 2 A f g k 2 2 + α 2 d x m x f b x m 2 2 + α 2 d y m y f b y m 2 2 + α 2 d z m z f b z m 2 2 + β 2 v m f b v m 2 2 .
( μ A H A α Δ + β I ) f m + 1 = r h s m ,
min d d x , d y , d z | 2 + α 2 d x x f m + 1 b x m 2 2 + α 2 d y y f m + 1 b y m 2 2 + α 2 d z z f m + 1 b z m 2 2 .
d x m + 1 = max ( s m 1 α , 0 ) x f m + 1 + b x m s m , d y m + 1 = max ( s m 1 α , 0 ) y f m + 1 + b y m s m , d z m + 1 = max ( s m 1 α , 0 ) z f m + 1 + b z m s m ,
min v I ( v 0 ) + β 2 v f m + 1 b v m 2 2 ,
v m + 1 = max ( f m + 1 + b v m , 0 ) .

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