Abstract

Digital Holographic Microscopy allows to numerically retrieve three dimensional information encoded in a single 2D snapshot of the coherent superposition of a reference and a scattered beam. Since no mechanical scans are involved, holographic techniques have a superior performance in terms of achievable frame rates. Unfortunately, numerical reconstructions of scattered field by back-propagation leads to a poor axial resolution. Here we show that overlapping the three numerical reconstructions obtained by tilted red, green and blue beams results in a great improvement over the axial resolution and sectioning capabilities of holographic microscopy. A strong reduction in the coherent background noise is also observed when combining the volumetric reconstructions of the light fields at the three different wavelengths. We discuss the performance of our technique with two test objects: an array of four glass beads that are stacked along the optical axis and a freely diffusing rod shaped E.coli bacterium.

© 2014 Optical Society of America

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2014

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

2013

2012

F. Saglimbeni, S. Bianchi, G. Bolognesi, G. Paradossi, R. Di Leonardo, “Optical characterization of an individual polymer-shelled microbubble structure via digital holography,” Soft Matter 8, 8822–8825 (2012).
[CrossRef]

2011

2010

R. Bowman, G. Gibson, M. Padgett, “Particle tracking in stereomicroscopy in optical tweezers: Control of trap shape,” Opt. Express 18, 11785–11790 (2010).
[CrossRef] [PubMed]

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

S. Bianchi, R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181, 1444–1448 (2010).
[CrossRef]

2009

S. J. Lee, S. Kim, “Advanced particle-based velocimetry techniques for microscale flows,” Microfluid. Nanofluid. 6, 577–588 (2009).

2008

2007

2006

2005

2004

2003

W. R. Zipfel, R. M. Williams, W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[CrossRef] [PubMed]

2002

1999

Adolf, J.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
[CrossRef] [PubMed]

Babacan, S. D.

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

Badizadegan, K.

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. 32, 811–813 (2007).
[CrossRef] [PubMed]

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

Belas, R.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
[CrossRef] [PubMed]

Bernet, S.

Bianchi, S.

F. Saglimbeni, S. Bianchi, G. Bolognesi, G. Paradossi, R. Di Leonardo, “Optical characterization of an individual polymer-shelled microbubble structure via digital holography,” Soft Matter 8, 8822–8825 (2012).
[CrossRef]

S. Bianchi, R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181, 1444–1448 (2010).
[CrossRef]

Bolognesi, G.

F. Saglimbeni, S. Bianchi, G. Bolognesi, G. Paradossi, R. Di Leonardo, “Optical characterization of an individual polymer-shelled microbubble structure via digital holography,” Soft Matter 8, 8822–8825 (2012).
[CrossRef]

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[CrossRef] [PubMed]

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M. Born, E. Wolf, Principles of Optics (Pergamon, 1993).

Boss, D.

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

Bowman, R.

Carney, P. S.

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

Cavallini, L.

Charrière, F.

Choi, W.

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

Colomb, T.

Cotte, Y.

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

Cuche, E.

Dam, J. S.

Dasari, R. R.

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

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. 32, 811–813 (2007).
[CrossRef] [PubMed]

Depeursinge, C.

Di Leonardo, R.

F. Saglimbeni, S. Bianchi, G. Bolognesi, G. Paradossi, R. Di Leonardo, “Optical characterization of an individual polymer-shelled microbubble structure via digital holography,” Soft Matter 8, 8822–8825 (2012).
[CrossRef]

L. Cavallini, G. Bolognesi, R. Di Leonardo, “Real-time digital holographic microscopy of multiple and arbitrarily oriented planes,” Opt. Lett. 36, 3491–3493 (2011).
[CrossRef] [PubMed]

S. Bianchi, R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181, 1444–1448 (2010).
[CrossRef]

Dubois, F.

Emery, Y.

Fang-Yen, C.

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

Feld, M. S.

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

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. 32, 811–813 (2007).
[CrossRef] [PubMed]

Ferraro, P.

Finizio, A.

Garcia-Sucerquia, J.

Gibson, G.

Gibson, G. M.

Glückstad, J.

Goddard, L. L.

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

Grier, D. G.

Han, S.

Heger, T. J.

Im, K. B.

Isikman, S. O.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Jericho, M. H.

Jericho, S. K.

Joannes, L.

Jourdain, P.

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

Katz, J.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
[CrossRef] [PubMed]

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Kim, B. M.

Kim, D.

Kim, K.

Kim, K. S.

Kim, M. K.

M. K. Kim, Digital Holography and Microscopy: Principles, Techniques, and Applications (Springer, 2011).
[CrossRef]

Kim, S.

Kim, T.

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

Klages, P.

Kreuzer, H. J.

Kuehn, J.

Lee, M. P.

Lee, S.

Lee, S. J.

S. J. Lee, S. Kim, “Advanced particle-based velocimetry techniques for microscale flows,” Microfluid. Nanofluid. 6, 577–588 (2009).

Legros, J.

Lue, N.

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

Magistretti, P.

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

Magistretti, P. J.

Malkiel, E.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
[CrossRef] [PubMed]

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Marian, A.

Marquet, P.

Meinertzhagen, I. A.

Memmolo, P.

Miccio, L.

Mir, M.

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

Mitchell, E. A. D.

Montfort, F.

Mudanyali, O.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Oh, S.

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

Ozcan, A.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Oztoprak, C.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Padgett, M.

Padgett, M. J.

Palima, D.

Paradossi, G.

F. Saglimbeni, S. Bianchi, G. Bolognesi, G. Paradossi, R. Di Leonardo, “Optical characterization of an individual polymer-shelled microbubble structure via digital holography,” Soft Matter 8, 8822–8825 (2012).
[CrossRef]

Park, H.

Park, Y.

Paturzo, M.

Pavillon, N.

Pawley, J. B.

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3 (Springer, 2006).
[CrossRef]

Perch-Nielsen, I. R.

Phillips, D. B.

Piano, E.

Place, A. R.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
[CrossRef] [PubMed]

Pontiggia, C.

Popescu, G.

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

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. 32, 811–813 (2007).
[CrossRef] [PubMed]

Rappaz, B.

Repetto, L.

Ritsch-Marte, M.

Roichman, Y.

Saglimbeni, F.

F. Saglimbeni, S. Bianchi, G. Bolognesi, G. Paradossi, R. Di Leonardo, “Optical characterization of an individual polymer-shelled microbubble structure via digital holography,” Soft Matter 8, 8822–8825 (2012).
[CrossRef]

Santi, P.

P. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem. 59, 129–138 (2011).
[CrossRef] [PubMed]

Sencan, I.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Shen, F.

Sheng, J.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
[CrossRef] [PubMed]

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Toy, F.

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

Tseng, D.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

van Blaaderen, A.

van Oostrum, P.

Wang, A.

Webb, W. W.

W. R. Zipfel, R. M. Williams, W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[CrossRef] [PubMed]

Williams, R. M.

W. R. Zipfel, R. M. Williams, W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1993).

Xu, W.

Yagliderea, O.

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Yang, S.

Ye, J. C.

Yi, G.

Zhou, R.

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

Zipfel, W. R.

W. R. Zipfel, R. M. Williams, W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[CrossRef] [PubMed]

Appl. Opt.

Comput. Phys. Commun.

S. Bianchi, R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181, 1444–1448 (2010).
[CrossRef]

J. Histochem. Cytochem.

P. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem. 59, 129–138 (2011).
[CrossRef] [PubMed]

Lab Chip

D. Tseng, O. Mudanyali, C. Oztoprak, S. O. Isikman, I. Sencan, O. Yagliderea, A. Ozcan, “Lensfree microscopy on a cellphone,” Lab Chip 10, 1787–1792 (2010).
[CrossRef] [PubMed]

Microfluid. Nanofluid.

S. J. Lee, S. Kim, “Advanced particle-based velocimetry techniques for microscale flows,” Microfluid. Nanofluid. 6, 577–588 (2009).

Nat. Biotechnol.

W. R. Zipfel, R. M. Williams, W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003).
[CrossRef] [PubMed]

Nat. Methods

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

Nat. Photon.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photon. 7, 113–117 (2013).
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T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, G. Popescu, “White-light diffraction tomography of unlabeled live cells,” Nat. Photon. 8, 256–263 (2014).
[CrossRef]

Opt. Express

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

K. B. Im, S. Han, H. Park, D. Kim, B. M. Kim, “Simple high-speed confocal line-scanning microscope,” Opt. Express 13, 5151–5156 (2005).
[CrossRef] [PubMed]

J. S. Dam, I. R. Perch-Nielsen, D. Palima, J. Glückstad, “Three-dimensional imaging in three-dimensional optical multi-beam micromanipulation,” Opt. Express 16, 7244–7250 (2008).
[CrossRef] [PubMed]

R. Bowman, G. Gibson, M. Padgett, “Particle tracking in stereomicroscopy in optical tweezers: Control of trap shape,” Opt. Express 18, 11785–11790 (2010).
[CrossRef] [PubMed]

M. P. Lee, G. M. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. B. Phillips, M. J. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21, 16541–16551 (2013).
[CrossRef] [PubMed]

P. Memmolo, A. Finizio, M. Paturzo, L. Miccio, P. Ferraro, “Twin-beams digital holography for 3D tracking and quantitative phase-contrast microscopy in microfluidics,” Opt. Express 19, 25833–25842 (2011).
[CrossRef]

F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express 14, 7005–7013 (2006).
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S. Lee, D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007).
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Opt. Lett.

Proc. Natl. Acad. Sci. U. S. A.

J. Sheng, E. Malkiel, J. Katz, J. Adolf, R. Belas, A. R. Place, “Digital holographic microscopy reveals prey-induced changes in swimming behavior of predatory dinoflagellates,” Proc. Natl. Acad. Sci. U. S. A. 104, 17512–17517 (2007).
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Other

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[CrossRef]

Supplementary Material (1)

» Media 1: MP4 (3192 KB)     

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Figures (5)

Fig. 1
Fig. 1

Optical setup. Three LED sources are used for illumination. Light from each LED is collected by a lens (L) and filtered through a diaphragm (D) to enhance the spatial coherence. The trapping IR laser (shown in pink) is expanded, phase modulated by a SLM, reflected by a dichroic mirror (DC) and sent to the back pupil of a 100X oil immersion objective.

Fig. 2
Fig. 2

3-axis DHM on a 2 μm silica bead: recorded RGB hologram (a), volumetric reconstruction (b). The three color channels are numerically reconstructed by free-space back-propagation. The elongated refocusing regions intersect at the scatterer location, which appear as a mildly elongated blob, depicted in white. (c) Profiles of the reconstructed intensity of a single color channel along parallel and transverse directions with respect to the illumination axis (solid red and dashed red lines). (d) Axial and transverse profiles (solid and dashed black lines) of the volumetric image V obtained overlapping the three color channels. Gray shaded area in (c–d) indicates the size of the 2 μm silica bead. Scale bar in (a) is 5 μm.

Fig. 3
Fig. 3

Four silica beads are trapped along a vertical line. (a) RGB hologram of the four beads. (b) The volumetric reconstruction V (x, y, z) of the RGB hologram computed as in Eq. (4). (c) A plot of V along the vertical axis that passes through all the four beads. (d) In-line monochrome hologram of the same four particles. Volumetric reconstruction of the field intensity of the in-line hologram (e) and the corresponding intensity profile along the vertical axis (f). Scale bars in (a) and (d) are 10 μm.

Fig. 4
Fig. 4

Sample frames from a video (see Media 1) showing the RGB holograms of a nonmotile freely diffusing bacterium (right panels) together with their volumetric reconstructions observed from the x, y, and z axes directions.

Fig. 5
Fig. 5

Histograms of measured values of a single E. coli cell length (blue) and thickness (green). The values are obtained analyzing individual frames collected during free diffusion.

Equations (4)

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I ( x , y , 0 ) | E i | 2 + 2 { | E i | e j ( k x x + k y y ) E s ( x , y , 0 ) }
E ( x , y , 0 ) = ( I ( x , y , 0 ) | E i | 2 ) | E i | 1 e j ( k x x + k y y )
G ( x , y , z ) = e j k r 2 π z r 2 ( 1 r j k )
V ( x , y , z ) = [ I R ( x , y , z ) I G ( x , y , z ) I B ( x , y , z ) ] 1 / 3

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