Abstract

Tomographic diffractive microscopy exhibits intrinsic features making it a method of choice for 3D high-resolution label-free imaging. However, these results are achieved at the cost of a heavy data acquisition/reconstruction process. This drawback can be circumvented for certain classes of samples. For example, axisymmetric samples, like optical or textile fibers, present geometrical properties that can be advantageously used to speed-up the acquisition process. We propose to take benefit of these properties to allow for full reconstruction of axisymmetric samples’ complex refractive index distribution, using four approaches, adapted to 3D samples. We applied the proposed reconstruction scheme, based on a numerical rotation of data, to both simulated and experimental data sets.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (7)

Y. Bao and T. K. Gaylord, “Iterative optimization in tomographic deconvolution phase microscopy,” J. Opt. Soc. Am. A 35(4), 652–660 (2018).
[Crossref]

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

J. Bailleul, B. Simon, M. Debailleul, L. Foucault, N. Verrier, and O. Haeberlé, “Tomographic diffractive microscopy: Towards high-resolution 3-D real-time data acquisition, image reconstruction and display of unlabeled samples,” Opt. Commun. 422, 28–37 (2018).
[Crossref]

B. Vinoth, X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution,” Sci. Rep. 8(1), 5943 (2018).
[Crossref]

C. Wei, D. I. Pineda, C. S. Goldenstein, and R. M. Spearrin, “Tomographic laser absorption imaging of combustion species and temperature in the mid-wave infrared,” Opt. Express 26(16), 20944–20951 (2018).
[Crossref]

S. Ubaid, F. Liao, S. Linghu, J. Yu, and F. Gu, “Electrospun polymer bottle microresonators for stretchable single-mode lasing devices,” Opt. Lett. 43(13), 3128–3131 (2018).
[Crossref]

V. Contreras, R. Valencia, J. Peralta, H. Sobral, M. A. Meneses-Nava, and H. Martinez, “Chemical elemental analysis of single acoustic-levitated water droplets by laser-induced breakdown spectroscopy,” Opt. Lett. 43(10), 2260–2263 (2018).
[Crossref]

2017 (7)

C. Fournier, F. Jolivet, L. Denis, N. Verrier, E. Thiebaut, C. Allier, and T. Fournel, “Pixel super-resolution in digital holography by regularized reconstruction,” Appl. Opt. 56(1), 69–77 (2017).
[Crossref]

A. Berdeu, F. Momey, B. Laperrousaz, T. Bordy, X. Gidrol, J.-M. Dinten, N. Picollet-D’hahan, and C. Allier, “Comparative study of fully three-dimensional reconstruction algorithms for lens-free microscopy,” Appl. Opt. 56(13), 3939–3951 (2017).
[Crossref]

C. Macias-Romero, I. Nahalka, H. I. Okur, and S. Roke, “Optical imaging of surface chemistry and dynamics in confinement,” Science 357(6353), 784–788 (2017).
[Crossref]

H. Xia, S. Montresor, R. Guo, J. Li, F. Olchewsky, J.-M. Desse, and P. Picart, “Robust processing of phase dislocations based on combined unwrapping and inpainting approaches,” Opt. Lett. 42(2), 322–325 (2017).
[Crossref]

T. Fukuda, Y. Wang, P. Xia, Y. Awatsuji, T. Kakue, K. Nishio, and O. Matoba, “Three-dimensional imaging of distribution of refractive index by parallel phase-shifting digital holography using Abel inversion,” Opt. Express 25(15), 18066–18071 (2017).
[Crossref]

J. Li, Q. Chen, J. Zhang, Z. Zhang, Y. Zhang, and C. Zuo, “Optical diffraction tomography microscopy with transport of intensity equation using a light-emitting diode array,” Opt. Lasers Eng. 95, 26–34 (2017).
[Crossref]

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(4), 460–463 (2017).
[Crossref]

2016 (4)

2015 (4)

S. Hennig, S. van de Linde, M. Lummer, M. Simonis, T. Huser, and M. Sauer, “Instant Live-Cell Super-Resolution Imaging of Cellular Structures by Nanoinjection of Fluorescent Probes,” Nano Lett. 15(2), 1374–1381 (2015).
[Crossref]

T. Sokkar, K. El-Farahaty, W. Ramadan, H. Wahba, M. Raslan, and A. Hamza, “Nonray-tracing determination of the 3d refractive index profile of polymeric fibres using single-frame computed tomography and digital holographic interferometric technique,” J. Microsc. 257(3), 208–216 (2015).
[Crossref]

M. H. Jenkins and T. K. Gaylord, “Three-dimensional quantitative phase imaging via tomographic deconvolution phase microscopy,” Appl. Opt. 54(31), 9213–9227 (2015).
[Crossref]

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(8), 1881–1884 (2015).
[Crossref]

2014 (5)

2013 (5)

A. Eddi, K. G. Winkels, and J. H. Snoeijer, “Short time dynamics of viscous drop spreading,” Phys. Fluids 25(1), 013102 (2013).
[Crossref]

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(26), 32269–32278 (2013).
[Crossref]

Z. Pan, S. Li, and J. Zhong, “Digital holographic microtomography for geometric parameter measurement of optical fiber,” Opt. Eng. 52(3), 035801 (2013).
[Crossref]

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(4), 4170–4191 (2013).
[Crossref]

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

2011 (2)

N. Verrier and M. Atlan, “Off-axis digital hologram reconstruction: some practical considerations,” Appl. Opt. 50(34), H136–H146 (2011).
[Crossref]

S. Vertu, J. Flügge, J.-J. Delaunay, and O. Haeberlé, “Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation,” Cent. Eur. J. Phys. 9(4), 969–974 (2011).
[Crossref]

2010 (1)

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

2009 (4)

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22–31 (2009).
[Crossref]

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

R. Fiolka, K. Wicker, R. Heintzmann, and A. Stemmer, “Simplified approach to diffraction tomography in optical microscopy,” Opt. Express 17(15), 12407–12417 (2009).
[Crossref]

S. Jradi, O. Soppera, D. J. Lougnot, R. Bachelot, and P. Royer, “Tailoring the geometry of polymer tips on the end of optical fibers via control of physico-chemical parameters,” Opt. Mater. 31(4), 640–646 (2009).
[Crossref]

2008 (3)

J. G. Hardy, L. M. Römer, and T. R. Scheibel, “Polymeric materials based on silk proteins,” Polymer 49(20), 4309–4327 (2008).
[Crossref]

L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express 16(1), 161–169 (2008).
[Crossref]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
[Crossref]

2007 (4)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref]

M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. 32(11), 1456–1458 (2007).
[Crossref]

B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12(5), 054009 (2007).
[Crossref]

W. Gorski and W. Osten, “Tomographic imaging of photonic crystal fibers,” Opt. Lett. 32(14), 1977–1979 (2007).
[Crossref]

2005 (1)

2002 (3)

I. G. Loscertales, “Micro/Nano Encapsulation via Electrified Coaxial Liquid Jets,” Science 295(5560), 1695–1698 (2002).
[Crossref]

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205(2), 165–176 (2002).
[Crossref]

2001 (1)

2000 (1)

1998 (1)

1997 (2)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[Crossref]

M. Xiao, J. Nieto, J. Siqueiros, and R. Machorro, “Simple device for making optical fiber tips for scanning near field optical microscopes,” Rev. Sci. Instrum. 68(7), 2787–2789 (1997).
[Crossref]

1996 (1)

1995 (1)

T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross-sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsc. 177(1), 53–67 (1995).
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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(26), 32269–32278 (2013).
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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(4), 4170–4191 (2013).
[Crossref]

Park, Y.

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

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(4), 4170–4191 (2013).
[Crossref]

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(26), 32269–32278 (2013).
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Passy, R.

N. Gisin, R. Passy, and B. Perny, “Optical fiber characterization by simultaneous measurement of the transmitted and refracted near field,” J. Lightwave Technol. 11(11), 1875–1883 (1993).
[Crossref]

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Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).
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Perny, B.

N. Gisin, R. Passy, and B. Perny, “Optical fiber characterization by simultaneous measurement of the transmitted and refracted near field,” J. Lightwave Technol. 11(11), 1875–1883 (1993).
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Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
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T. Sokkar, K. El-Farahaty, W. Ramadan, H. Wahba, M. Raslan, and A. Hamza, “Nonray-tracing determination of the 3d refractive index profile of polymeric fibres using single-frame computed tomography and digital holographic interferometric technique,” J. Microsc. 257(3), 208–216 (2015).
[Crossref]

Raslan, M.

T. Sokkar, K. El-Farahaty, W. Ramadan, H. Wahba, M. Raslan, and A. Hamza, “Nonray-tracing determination of the 3d refractive index profile of polymeric fibres using single-frame computed tomography and digital holographic interferometric technique,” J. Microsc. 257(3), 208–216 (2015).
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Richardson, D.

Roichman, Y.

Roke, S.

C. Macias-Romero, I. Nahalka, H. I. Okur, and S. Roke, “Optical imaging of surface chemistry and dynamics in confinement,” Science 357(6353), 784–788 (2017).
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Römer, L. M.

J. G. Hardy, L. M. Römer, and T. R. Scheibel, “Polymeric materials based on silk proteins,” Polymer 49(20), 4309–4327 (2008).
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Royer, P.

S. Jradi, O. Soppera, D. J. Lougnot, R. Bachelot, and P. Royer, “Tailoring the geometry of polymer tips on the end of optical fibers via control of physico-chemical parameters,” Opt. Mater. 31(4), 640–646 (2009).
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R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D.-J. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40(32), 5860–5871 (2001).
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Sandoghchi, S. R.

Sauer, M.

S. Hennig, S. van de Linde, M. Lummer, M. Simonis, T. Huser, and M. Sauer, “Instant Live-Cell Super-Resolution Imaging of Cellular Structures by Nanoinjection of Fluorescent Probes,” Nano Lett. 15(2), 1374–1381 (2015).
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J. G. Hardy, L. M. Römer, and T. R. Scheibel, “Polymeric materials based on silk proteins,” Polymer 49(20), 4309–4327 (2008).
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U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
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B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12(5), 054009 (2007).
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Sentenac, A.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
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Simic, A.

A. Simic, H. Freiheit, M. Agour, C. Falldorf, and R. B. Bergmann, “In-line quality control of micro parts using digital holography,” in Proceedings SPIE 10233 (SPIE, Prague, 2017).

Simon, B.

Simonis, M.

S. Hennig, S. van de Linde, M. Lummer, M. Simonis, T. Huser, and M. Sauer, “Instant Live-Cell Super-Resolution Imaging of Cellular Structures by Nanoinjection of Fluorescent Probes,” Nano Lett. 15(2), 1374–1381 (2015).
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M. Xiao, J. Nieto, J. Siqueiros, and R. Machorro, “Simple device for making optical fiber tips for scanning near field optical microscopes,” Rev. Sci. Instrum. 68(7), 2787–2789 (1997).
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A. Eddi, K. G. Winkels, and J. H. Snoeijer, “Short time dynamics of viscous drop spreading,” Phys. Fluids 25(1), 013102 (2013).
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Sobral, H.

Sokkar, T.

T. Sokkar, K. El-Farahaty, W. Ramadan, H. Wahba, M. Raslan, and A. Hamza, “Nonray-tracing determination of the 3d refractive index profile of polymeric fibres using single-frame computed tomography and digital holographic interferometric technique,” J. Microsc. 257(3), 208–216 (2015).
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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(2), 113–117 (2013).
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B. Vinoth, X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution,” Sci. Rep. 8(1), 5943 (2018).
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Valencia, R.

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S. Hennig, S. van de Linde, M. Lummer, M. Simonis, T. Huser, and M. Sauer, “Instant Live-Cell Super-Resolution Imaging of Cellular Structures by Nanoinjection of Fluorescent Probes,” Nano Lett. 15(2), 1374–1381 (2015).
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Verrier, N.

J. Bailleul, B. Simon, M. Debailleul, L. Foucault, N. Verrier, and O. Haeberlé, “Tomographic diffractive microscopy: Towards high-resolution 3-D real-time data acquisition, image reconstruction and display of unlabeled samples,” Opt. Commun. 422, 28–37 (2018).
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C. Fournier, F. Jolivet, L. Denis, N. Verrier, E. Thiebaut, C. Allier, and T. Fournel, “Pixel super-resolution in digital holography by regularized reconstruction,” Appl. Opt. 56(1), 69–77 (2017).
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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,” Cent. Eur. J. Phys. 9(4), 969–974 (2011).
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Vinoth, B.

B. Vinoth, X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution,” Sci. Rep. 8(1), 5943 (2018).
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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(4), 046009 (2014).
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B. Kemper, S. Kosmeier, P. Langehanenberg, G. von Bally, I. Bredebusch, W. Domschke, and J. Schnekenburger, “Integral refractive index determination of living suspension cells by multifocus digital holographic phase contrast microscopy,” J. Biomed. Opt. 12(5), 054009 (2007).
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Wahba, H.

T. Sokkar, K. El-Farahaty, W. Ramadan, H. Wahba, M. Raslan, and A. Hamza, “Nonray-tracing determination of the 3d refractive index profile of polymeric fibres using single-frame computed tomography and digital holographic interferometric technique,” J. Microsc. 257(3), 208–216 (2015).
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A. Eddi, K. G. Winkels, and J. H. Snoeijer, “Short time dynamics of viscous drop spreading,” Phys. Fluids 25(1), 013102 (2013).
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E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
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S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Cent. Eur. J. Phys. 7(1), 22–31 (2009).
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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,” Cent. Eur. J. Phys. 9(4), 969–974 (2011).
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U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
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M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19(7), 074009 (2008).
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S. Hennig, S. van de Linde, M. Lummer, M. Simonis, T. Huser, and M. Sauer, “Instant Live-Cell Super-Resolution Imaging of Cellular Structures by Nanoinjection of Fluorescent Probes,” Nano Lett. 15(2), 1374–1381 (2015).
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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(2), 113–117 (2013).
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Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
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Opt. Commun. (2)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
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J. Bailleul, B. Simon, M. Debailleul, L. Foucault, N. Verrier, and O. Haeberlé, “Tomographic diffractive microscopy: Towards high-resolution 3-D real-time data acquisition, image reconstruction and display of unlabeled samples,” Opt. Commun. 422, 28–37 (2018).
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Opt. Eng. (1)

Z. Pan, S. Li, and J. Zhong, “Digital holographic microtomography for geometric parameter measurement of optical fiber,” Opt. Eng. 52(3), 035801 (2013).
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Opt. Express (7)

Opt. Lasers Eng. (1)

J. Li, Q. Chen, J. Zhang, Z. Zhang, Y. Zhang, and C. Zuo, “Optical diffraction tomography microscopy with transport of intensity equation using a light-emitting diode array,” Opt. Lasers Eng. 95, 26–34 (2017).
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Opt. Mater. (1)

S. Jradi, O. Soppera, D. J. Lougnot, R. Bachelot, and P. Royer, “Tailoring the geometry of polymer tips on the end of optical fibers via control of physico-chemical parameters,” Opt. Mater. 31(4), 640–646 (2009).
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Optica (1)

Phys. Fluids (1)

A. Eddi, K. G. Winkels, and J. H. Snoeijer, “Short time dynamics of viscous drop spreading,” Phys. Fluids 25(1), 013102 (2013).
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Polymer (1)

J. G. Hardy, L. M. Römer, and T. R. Scheibel, “Polymeric materials based on silk proteins,” Polymer 49(20), 4309–4327 (2008).
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Rev. Sci. Instrum. (1)

M. Xiao, J. Nieto, J. Siqueiros, and R. Machorro, “Simple device for making optical fiber tips for scanning near field optical microscopes,” Rev. Sci. Instrum. 68(7), 2787–2789 (1997).
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Sci. Rep. (1)

B. Vinoth, X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution,” Sci. Rep. 8(1), 5943 (2018).
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C. Macias-Romero, I. Nahalka, H. I. Okur, and S. Roke, “Optical imaging of surface chemistry and dynamics in confinement,” Science 357(6353), 784–788 (2017).
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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(4), 4170–4191 (2013).
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A. Simic, H. Freiheit, M. Agour, C. Falldorf, and R. B. Bergmann, “In-line quality control of micro parts using digital holography,” in Proceedings SPIE 10233 (SPIE, Prague, 2017).

M. Born and E. Wolf, Principles of optics - Electromagnetic theory of propagation, interference and diffraction of light (Cambridge University Press, 1999), 7th ed.

J. W. Goodman, Introduction to Fourier optics (W.H. Freeman, Macmillan Learning, 2017), 4th ed.

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Figures (12)

Fig. 1.
Fig. 1. Schematic representation of the TDM set-up. BS: beam splitter; CD$_1$, CD$_2$ and CD$_3$: collimating doublets; FD: field diaphragm; L$_1$: scanning lens; L$_\mathrm {T}$: tube lens; AD: aperture diaphragm; RC: recombination cube; M$_2$ and M$_3$: mirrors. L$_2$ and CD$_3$ are used for sampling purposes.
Fig. 2.
Fig. 2. (a) Optical Transfert Function (OTF) in a simple holographic transmission setup. (b) OTF in TDM with illumination otation (note the “missing cone” along the optical axis). (c) OTF in TDM with sample rotation (note the “missing apple core” along $k_x$). (d) OTF for a combination of illumination and sample rotation approaches (0°, 60° and 120°).
Fig. 3.
Fig. 3. Synoptics of the simulated data acquisition/reconstruction procedures of (a) FINER/DINER methods (applied to infinite samples) and (b) TINER/F-TINER method (applied to finite samples).
Fig. 4.
Fig. 4. (a) Accessible information in 2D Fourier space for DHM. (b) Digital rotation of the holographic circular arc. (c) Final frequency support merging nine digital rotations.
Fig. 5.
Fig. 5. Reconstruction of the simulated fiber in holography. (a) and (b) show the Fourier spectra corresponding to the images in the lower row. (c),(g) Simulated cylinder. (d),(h) Reconstruction in the DHM case. (e),(i) Reconstruction using FINER and (f),(j) DINER approach with 360 rotation angles. (k),(l) Profiles of (y–z) and (x–z) cross sections respectively. Color bar: real part of the refractive index. Scale bar: 2.5 µm.
Fig. 6.
Fig. 6. Reconstrution of the simulated fiber in tomography. (a)–(d) show the Fourier spectra corresponding to the images in the lower row. (e),(j) Simulated cylinder. (f),(k) Reconstruction in DHM. (g),(i) Reconstruction using FINER method. (h),(m) Reconstruction in TDM with illumination rotation (600 angles). (i),(n) Reconstruction using F-TINER approach with two rotation angles (0° and 90°). (o),(p) Profiles of (x–y) and (x–z) cross sections respectively. Color bar: real part of the refractive index. Scale bar: 2.5 µm.
Fig. 7.
Fig. 7. Reconstruction of a simulated bead attached to an optical fiber. (a) Simulated object. (b) FINER method. (c) TDM with illumination rotation. (d) F-TINER method. Scale bar: 2.5 µm.
Fig. 8.
Fig. 8. Top row: Fourier space. Bottom row: sagittal cut. (a),(c) D300-T2: 300 illuminations angles donut-shaped spectrum numerically rotated twice using F-TINER method. (b),(d) D100-T6. (e) Plotted profiles. Scale bar: 2.5 µm.
Fig. 9.
Fig. 9. Noise effect on reconstructions. (a) Cylinder with white Gaussian noise of $\sigma = {10}\%$ of the global value range. Reconstructions using (b) FINER and (c) DINER methods for 360 angles of rotation. (d) Respective profiles. Scale bar: 5 µm.
Fig. 10.
Fig. 10. Logarithmic representation of SNR in dB as a function of the number of rotation angles for different values of standard deviation.
Fig. 11.
Fig. 11. Reconstruction of the sample presenting a defect of refractive index 1.51. (a)–(c) Simulated object. (d)–(f) Reconstruction with FINER approach. (g)–(i) Reconstruction with DINER approach. Color bar: refractive index. Scale bar: 2.5 µm.
Fig. 12.
Fig. 12. Lateral (left), axial (center) and sagittal (right) views of a stretched optical fiber reconstructed in the Rytov approximation using TDM. (a)–(c) Reconstruction in TDM with illumination rotation without sample rotation. (d)–(f) 4-angles physical rotation (0°, 54°, 90° and 126°). (g)–(i) 4-angles numerical rotation with the same 4 angles using TINER method. (j)–(l) 20-angles numerical rotation. (m) Plotted profiles. Scale bar: 3 µm.

Equations (5)

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ko=kdki
φ(x,y)=z0/2z0/22πλΔn(r,y)dz ,
n(r,y)=nim+λ2π2rR[φ(x,y)x]dxx2r2 ,
FT{g(x,y,z)}=G(fx,fycosθ+fzsinθ,fysinθ+fzcosθ) ,
G(fx,fy,fz)=FT{g(x,ycosθ+zsinθ,ysinθ+zcosθ)} ,

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