Abstract

Tomographic phase microscopy (TPM) is an emerging optical microscopic technique for bioimaging. TPM uses digital holographic measurements of complex scattered fields to reconstruct three-dimensional refractive index (RI) maps of cells with diffraction-limited resolution by solving inverse scattering problems. In this paper, we review the developments of TPM from the fundamental physics to its applications in bioimaging. We first provide a comprehensive description of the tomographic reconstruction physical models used in TPM. The RI map reconstruction algorithms and various regularization methods are discussed. Selected TPM applications for cellular imaging, particularly in hematology, are reviewed. Finally, we examine the limitations of current TPM systems, propose future solutions, and envision promising directions in biomedical research.

© 2017 Optical Society of America

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2017 (2)

2016 (11)

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6, 36815 (2016).
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W. Krauze, P. Makowski, M. Kujawinska, and A. Kus, “Generalized total variation iterative constraint strategy in limited angle optical diffraction tomography,” Opt. Express 24, 4924–4936 (2016).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2, 59–70 (2016).
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G. Dardikman, M. Habaza, L. Waller, and N. T. Shaked, “Video-rate processing in tomographic phase microscopy of biological cells using CUDA,” Opt. Express 24, 11839–11854 (2016).
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T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser. Photon. Rev. 10, 13–39 (2016).
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K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photon. Eng. 2, 020201 (2016).

J. Jung, K. Kim, J. Yoon, and Y. Park, “Hyperspectral optical diffraction tomography,” Opt. Express 24, 2006–2012 (2016).
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M. Habaza, M. Kirschbaum, C. Guernth-Marschner, G. Dardikman, I. Barnea, R. Korenstein, C. Duschl, and N. T. Shaked, “Rapid 3D refractive-index imaging of live cells in suspension without labeling using dielectrophoretic cell rotation,” Adv. Sci. 4, 1600205 (2016).
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K. Kim, K. Choe, I. Park, P. Kim, and Y. Park, “Holographic intravital microscopy for 2-D and 3-D imaging intact circulating blood cells in microcapillaries of live mice,” Sci. Rep. 6, 33084 (2016).
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S. Lee, H. Park, S. Jang, and Y. Park, “Refractive index tomograms and dynamic membrane fluctuations of red blood cells from patients with diabetes mellitus,” Blood 128, 4813 (2016).

P. Hosseini, S. Z. Abidi, E. Du, D. P. Papageorgiou, Y. Choi, Y. Park, J. M. Higgins, G. J. Kato, S. Suresh, M. Dao, Z. Yaqoob, and P. T. So, “Cellular normoxic biophysical markers of hydroxyurea treatment in sickle cell disease,” Proc. Natl. Acad. Sci. USA 113, 9527–9532 (2016).
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2015 (16)

C. Zuo, J. Sun, J. Zhang, Y. Hu, and Q. Chen, “Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a LED matrix,” Opt. Express 23, 14314–14328 (2015).
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S. Y. Lee, H. J. Park, C. Best-Popescu, S. Jang, and Y. K. Park, “The effects of ethanol on the morphological and biochemical properties of individual human red blood cells,” PLoS One 10, e0145327 (2015).
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H. Park, T. Ahn, K. Kim, S. Lee, S. Y. Kook, D. Lee, I. B. Suh, S. Na, and Y. Park, “Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood,” J. Biomed. Opt. 20, 111208 (2015).
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K. Kim, J. Yoon, and Y. Park, “Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography,” Optica 2, 343–346 (2015).
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A. KuĹ and W. Krauze, “Active limited-angle tomographic phase microscope,” J. Biomed. Opt. 20, 111216 (2015).
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M. Habaza, B. Gilboa, Y. Roichman, and N. T. Shaked, “Tomographic phase microscopy with 180° rotation of live cells in suspension by holographic optical tweezers,” Opt. Lett. 40, 1881–1884 (2015).
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S. Shin, K. Kim, J. Yoon, and Y. Park, “Active illumination using a digital micromirror device for quantitative phase imaging,” Opt. Lett. 40, 5407–5410 (2015).
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P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, and P. T. C. So, “Scanning color optical tomography (SCOT),” Opt. Express 23, 19752–19762 (2015).
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J. Lim, K. Lee, K. H. Jin, S. Shin, S. Lee, Y. Park, and J. C. Ye, “Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography,” Opt. Express 23, 16933–16948 (2015).
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U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2, 517–522 (2015).
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L. Waller and L. Tian, “Computational imaging: machine learning for 3D microscopy,” Nature 523, 416–417 (2015).
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J. Yoon, K. Kim, H. Park, C. Choi, S. Jang, and Y. Park, “Label-free characterization of white blood cells by measuring 3D refractive index maps,” Biomed. Opt. Express 6, 3865–3875 (2015).
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H. Park, S. H. Hong, K. Kim, S. H. Cho, W. J. Lee, Y. Kim, S. E. Lee, and Y. Park, “Characterizations of individual mouse red blood cells parasitized by Babesia microti using 3-D holographic microscopy,” Sci. Rep. 5, 10827 (2015).
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V. Kollarova, J. Collakova, Z. Dostal, P. Vesely, and R. Chmelik, “Quantitative phase imaging through scattering media by means of coherence-controlled holographic microscope,” J. Biomed. Opt. 20, 111206 (2015).
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T. H. Nguyen, H. Majeed, and G. Popescu, “Plane-wave decomposition of spatially random fields,” Opt. Lett. 40, 1394–1397 (2015).
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L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2, 104–111 (2015).
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2014 (16)

R. Zhou, T. Kim, L. L. Goddard, and G. Popescu, “Inverse scattering solutions using low-coherence light,” Opt. Lett. 39, 4494–4497 (2014).
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B. Redding, Y. Bromberg, M. A. Choma, and H. Cao, “Full-field interferometric confocal microscopy using a VCSEL array,” Opt. Lett. 39, 4446–4449 (2014).
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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. Photonics 8, 256–263 (2014).
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Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. T. C. So, “Three-dimensional holographic refractive-Index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1, 014002 (2014).
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B. Bhaduri, C. Edwards, H. Pham, R. J. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photon. 6, 57–119 (2014).
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Y. Choi, P. Hosseini, W. Choi, R. R. Dasari, P. T. C. So, and Z. Yaqoob, “Dynamic speckle illumination wide-field reflection phase microscopy,” Opt. Lett. 39, 6062–6065 (2014).
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S. Lee, K. Kim, A. Mubarok, A. Panduwirawan, K. Lee, S. Lee, H. Park, and Y. Park, “High-resolution 3-D refractive index tomography and 2-D synthetic aperture imaging of live phytoplankton,” J. Opt. Soc. Korea 18, 691–697 (2014).
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W. C. Hsu, J. W. Su, T. Y. Tseng, and K. B. Sung, “Tomographic diffractive microscopy of living cells based on a common-path configuration,” Opt. Lett. 39, 2210–2213 (2014).
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A. Kus, M. Dudek, B. Kemper, M. Kujawinska, and A. Vollmer, “Tomographic phase microscopy of living three-dimensional cell cultures,” J. Biomed. Opt. 19, 046009 (2014).
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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).
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J. Jin, F. Liu, and S. Crozier, “Image registration guided, sparsity constrained reconstructions for dynamic MRI,” Magn. Reson. Imaging 32, 1403–1417 (2014).
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S. R. Becker and P. L. Combettes, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” J. Nonlinear Convex Anal. 15, 137–159 (2014).

J. Gul-Mohammed, I. Arganda-Carreras, P. Andrey, V. Galy, and T. Boudier, “A generic classification-based method for segmentation of nuclei in 3D images of early embryos,” BMC Bioinf. 15, 9 (2014).
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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).
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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).
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W. C. Lee, H. Shi, Z. Poon, L. M. Nyan, T. Kaushik, G. V. Shivashankar, J. K. Chan, C. T. Lim, J. Han, and K. J. Van Vliet, “Multivariate biophysical markers predictive of mesenchymal stromal cell multipotency,” Proc. Natl. Acad. Sci. USA 111, E4409–E4418 (2014).
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2013 (6)

K. Lee, H. D. Kim, K. Kim, Y. Kim, T. R. Hillman, B. Min, and Y. Park, “Synthetic Fourier transform light scattering,” Opt. Express 21, 22453–22463 (2013).
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Y. Sung, A. Tzur, S. Oh, W. Choi, V. Li, R. R. Dasari, Z. Yaqoob, and M. W. Kirschner, “Size homeostasis in adherent cells studied by synthetic phase microscopy,” Proc. Natl. Acad. Sci. USA 110, 16687–16692 (2013).
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M. V. Oliva and H. H. Muhammed, “New approach for limited-angle problems in electron microscope based on compressed sensing,” Engineering 05, 575–578 (2013).
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J. W. Su, W. C. Hsu, C. Y. Chou, C. H. Chang, and K. B. Sung, “Digital holographic microtomography for high‐resolution refractive index mapping of live cells,” J. Biophoton. 6, 416–424 (2013).
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K. L. Cooper, S. Oh, Y. Sung, R. R. Dasari, M. W. Kirschner, and C. J. Tabin, “Multiple phases of chondrocyte enlargement underlie differences in skeletal proportions,” Nature 495, 375–378 (2013).
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Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
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2012 (4)

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS One 7, e39816 (2012).
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S. Witte, A. Plauşka, M. C. Ridder, L. van Berge, H. D. Mansvelder, and M. L. Groot, “Short-coherence off-axis holographic phase microscopy of live cell dynamics,” Biomed. Opt. Express 3, 2184–2189 (2012).
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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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W. C. Hsu, J. W. Su, C. C. Chang, and K. B. Sung, “Investigating the backscattering characteristics of individual normal and cancerous cells based on experimentally determined three-dimensional refractive index distributions,” Proc. SPIE 8553, 85531O (2012).
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2011 (12)

H. Zhao, P. H. Brown, and P. Schuck, “On the distribution of protein refractive index increments,” Biophys. J. 100, 2309–2317 (2011).
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Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16, 116017 (2011).
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A. S. Greenberg, R. A. Coleman, F. B. Kraemer, J. L. McManaman, M. S. Obin, V. Puri, Q. W. Yan, H. Miyoshi, and D. G. Mashek, “The role of lipid droplets in metabolic disease in rodents and humans,” J. Clin. Invest. 121, 2102–2110 (2011).
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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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S. Vertu, J. Flügge, J.-J. Delaunay, and O. Haeberlé, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Open Phys. 9, 969–974 (2011).
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Y. Choi, T. D. Yang, K. J. Lee, and W. Choi, “Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination,” Opt. Lett. 36, 2465–2467 (2011).
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C. Fang-Yen, W. Choi, Y. J. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).
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L. Miccio, A. Finizio, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, “Dynamic DIC by digital holography microscopy for enhancing phase-contrast visualization,” Biomed. Opt. Express 2, 331–344 (2011).
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Z. Yaqoob, T. Yamauchi, W. Choi, D. Fu, R. R. Dasari, and M. S. Feld, “Single-shot full-field reflection phase microscopy,” Opt. Express 19, 7587–7595 (2011).
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T. Yamauchi, H. Iwai, and Y. Yamashita, “Label-free imaging of intracellular motility by low-coherent quantitative phase microscopy,” Opt. Express 19, 5536–5550 (2011).
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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).
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R. Chandramohanadas, Y. Park, L. Lui, A. Li, D. Quinn, K. Liew, M. Diez-Silva, Y. Sung, M. Dao, C. T. Lim, P. R. Preiser, and S. Suresh, “Biophysics of malarial parasite exit from infected erythrocytes,” PLoS One 6, e20869 (2011).
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2010 (3)

P. Kolman and R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express 18, 21990–22004 (2010).
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O. Haeberle, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
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N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010).
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2009 (7)

J. B. Moseley, A. Mayeux, A. Paoletti, and P. Nurse, “A spatial gradient coordinates cell size and mitotic entry in fission yeast,” Nature 459, 857–860 (2009).
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S. G. Martin and M. Berthelot-Grosjean, “Polar gradients of the DYRK-family kinase Pom1 couple cell length with the cell cycle,” Nature 459, 852–856 (2009).
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M. Kalashnikov, W. Choi, C. C. Yu, Y. Sung, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Assessing light scattering of intracellular organelles in single intact living cells,” Opt. Express 17, 19674–19681 (2009).
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S. S. Kou and C. J. Sheppard, “Image formation in holographic tomography: high-aperture imaging conditions,” Appl. Opt. 48, H168–H175 (2009).
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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).
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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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Y. J. 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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2008 (6)

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
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N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Opt. Express 16, 16240–16246 (2008).
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Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA 105, 13730–13735 (2008).
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M. G. L. Gustafsson, L. Shao, P. M. Carlton, C. J. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, and J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys. J. 94, 4957–4970 (2008).
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K. Keren, Z. Pincus, G. M. Allen, E. L. Barnhart, G. Marriott, A. Mogilner, and J. A. Theriot, “Mechanism of shape determination in motile cells,” Nature 453, 475–480 (2008).
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2007 (4)

L. Tilley, G. McFadden, A. Cowman, and N. Klonis, “Illuminating Plasmodium falciparum-infected red blood cells,” Trends Parasitol. 23, 268–277 (2007).
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T. Kozacki, M. Kujawińska, and P. Kniażewski, “Investigation of limitations of optical diffraction tomography,” Opto-Electron. Rev. 15, 102–109 (2007).
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W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
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2006 (4)

F. Charriere, 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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V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
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S. Martin and R. G. Parton, “Lipid droplets: a unified view of a dynamic organelle,” Nat. Rev. Mol. Cell. Biol. 7, 373–378 (2006).
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2005 (1)

2004 (3)

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29, 2503–2505 (2004).
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K. E. Handwerger, J. A. Cordero, and J. G. Gall, “Cajal bodies, nucleoli, and speckles in the Xenopus oocyte nucleus have a low-density, sponge-like structure,” Mol. Biol. Cell 16, 202–211 (2004).
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2003 (1)

K. J. Van Vliet, G. Bao, and S. Suresh, “The biomechanics toolbox: experimental approaches for living cells and biomolecules,” Acta Mater. 51, 5881–5905 (2003).
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2002 (1)

L. H. Miller, D. I. Baruch, K. Marsh, and O. K. Doumbo, “The pathogenic basis of malaria,” Nature 415, 673–679 (2002).
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2000 (1)

M. G. Somekh, C. W. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174, 75–80 (2000).
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1998 (2)

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1997 (2)

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Figures (7)

Fig. 1.
Fig. 1.

Illustration of optical diffraction tomography. (Figure reprinted from Ref. [61] with permission.)

Fig. 2.
Fig. 2.

Illustration of angle scanning-based scattered field measurements and frequency domain mapping.

Fig. 3.
Fig. 3.

Temporally incoherent ODT reconstruction illustration. (a) Coherent transfer function. (b) The 3D PSF in xy (z=0) and xz (y=0) planes obtained from the CTF. (Figure reprinted from Ref. [41].)

Fig. 4.
Fig. 4.

Overall spatial correlation function for 800 nm speckle illumination with NA=1.0. (Figure reprinted from Ref. [39] with permission.)

Fig. 5.
Fig. 5.

Comparison of the 3D RI distribution of a hepatocyte cell reconstructed by (a) direct Fourier mapping, (b) NNC, (c) EP regularization, and (d) isotropic TV regularization. (Figure reprinted from Ref. [46] with permission.)

Fig. 6.
Fig. 6.

3D RI maps of Pf-RBCs during all intra-erythrocytic stages: (a) healthy RBCs, (b) ring stage, (c) trophozoite stage, (d) schizont stage. Images in rows show three different xy cross sections: 0.6 μm above the focused plane (top), on the focused plane (middle), and 0.6 μm below the focused plane (bottom). Two color maps show the RI (top right) and Hb concentration (bottom right) (scale bar, 1.5 μm). (Figure reprinted from Ref. [52] with permission. Copyright (2008) National Academy of Sciences, U.S.A.)

Fig. 7.
Fig. 7.

Representative 3D RI tomograms of (a) an RBC, (b) a macrophage, (c) a neuron, and (d) a hepatocyte. (Figures reprinted from Ref. [26] with permission.)

Equations (18)

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

2Us(r)+β2Us(r)=χ(r)U(r),
Us(kx,ky;z)=e±iqzqχ(kxkxi,kykyi,±qkzi),
χ(U,V,W)=qe±iqzUs(kx,ky;z),
Γ12(r,τ)=Us(r,t)Ur*(r,t+τ)t,
Γ12(r,τ)=0W12(r,ω)eiωτdω,
χ(U,V,W)=Γ12(U,V,W)Σ(U,V,W),
Σ(U,V,W)=[(W2+k2)2/W3]S[(W2+k2)/2W],
Γ12(zR;kxi,kyi)=P2(kxi,kyi)eikzi(2zR)kzi,
Re(Γ12)=sinc(2βzRπ)cosθmaxsinc(2βcosθmaxzRπ),
u(r)=a(r)eiβ0nmz,
βs(r)=β0n(r)=β0(nm+δn(r)).
a(x,y,z+δz)=eiβ0δn(r)δz×I2D1{I2D(a(x,y,z))×ei(kx2+ky2β0nm+β02nm2kx2ky2)δz},
J(f)=Afg22+αR(f),
Afg22=mA(m)fg(m)22,
A(m)f=1q(m)f(U,V,W)ei(Ux+Vy)dUdV,
RiTV(f)n[f]n2=n([xf]n)2+([yf]n)2+([zf]n)2,
RaTV(f)n[f]n1=n(|[xf]n|+|[yf]n|+|[zf]n|).
REP(f)nϕ([f]n2),

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