Abstract

We present a new four-dimensional phase unwrapping approach for time-lapse quantitative phase microscopy, which allows reconstruction of optically thick objects that are optically thin in a certain temporal point and angular view. We thus use all four dimensions of the dynamic quantitative phase profile acquired, including the angular dimension and the temporal dimension, in addition to the x-y dimensions. We first demonstrate the capabilities of this algorithm on simulative data, enabling the quantification of the reconstruction quality relative to both the ground truth and existing unwrapping approaches. Then, we demonstrate the applicability of the proposed four-dimensional phase unwrapping algorithm by experimentally capturing a dual-angular dynamic off-axis hologram with simultaneous recording of two angular views, using multiplexing of two off-axis holograms into a single multiplexed hologram.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
    [Crossref] [PubMed]
  2. 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(2), C538–C544 (2008).
    [Crossref] [PubMed]
  3. 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(9), 9673–9681 (2012).
    [Crossref] [PubMed]
  4. Y. Bishitz, H. Gabai, P. Girshovitz, and N. T. Shaked, “Optical-mechanical signatures of cancer cells based on fluctuation profiles measured by interferometry,” J. Biophotonics 7(8), 624–630 (2014).
    [Crossref] [PubMed]
  5. P. Girshovitz and N. T. Shaked, “Fast phase processing in off-axis holography using multiplexing with complex encoding and live-cell fluctuation map calculation in real-time,” Opt. Express 23(7), 8773–8787 (2015).
    [Crossref] [PubMed]
  6. P. Girshovitz and N. T. Shaked, “Real-time quantitative phase reconstruction in off-axis digital holography using multiplexing,” Opt. Lett. 39(8), 2262–2265 (2014).
    [Crossref] [PubMed]
  7. D. C. Ghihlia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  8. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21(14), 2470 (1982).
    [Crossref] [PubMed]
  9. J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
    [Crossref] [PubMed]
  10. M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
    [Crossref]
  11. G. Dardikman, S. Mirsky, M. Habaza, Y. Roichman, and N. T. Shaked, “Angular phase unwrapping of optically thick objects with a thin dimension,” Opt. Express 25(4), 3347–3357 (2017).
    [Crossref] [PubMed]
  12. E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
    [Crossref] [PubMed]
  13. B. J. Brewer, E. Chlebowicz-Sledziewska, and W. L. Fangman, “Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces Cerevisiae,” Mol. Cell. Biol. 4(11), 2529–2531 (1984).
    [Crossref] [PubMed]
  14. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41(35), 7437–7444 (2002).
    [Crossref] [PubMed]

2017 (1)

2015 (2)

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Fast phase processing in off-axis holography using multiplexing with complex encoding and live-cell fluctuation map calculation in real-time,” Opt. Express 23(7), 8773–8787 (2015).
[Crossref] [PubMed]

2014 (2)

P. Girshovitz and N. T. Shaked, “Real-time quantitative phase reconstruction in off-axis digital holography using multiplexing,” Opt. Lett. 39(8), 2262–2265 (2014).
[Crossref] [PubMed]

Y. Bishitz, H. Gabai, P. Girshovitz, and N. T. Shaked, “Optical-mechanical signatures of cancer cells based on fluctuation profiles measured by interferometry,” J. Biophotonics 7(8), 624–630 (2014).
[Crossref] [PubMed]

2012 (1)

2009 (1)

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

2008 (1)

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(2), C538–C544 (2008).
[Crossref] [PubMed]

2002 (1)

1993 (1)

1984 (1)

B. J. Brewer, E. Chlebowicz-Sledziewska, and W. L. Fangman, “Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces Cerevisiae,” Mol. Cell. Biol. 4(11), 2529–2531 (1984).
[Crossref] [PubMed]

1982 (1)

Badizadegan, K.

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(2), C538–C544 (2008).
[Crossref] [PubMed]

Barnhill, E.

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[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(2), C538–C544 (2008).
[Crossref] [PubMed]

Bishitz, Y.

Y. Bishitz, H. Gabai, P. Girshovitz, and N. T. Shaked, “Optical-mechanical signatures of cancer cells based on fluctuation profiles measured by interferometry,” J. Biophotonics 7(8), 624–630 (2014).
[Crossref] [PubMed]

Brewer, B. J.

B. J. Brewer, E. Chlebowicz-Sledziewska, and W. L. Fangman, “Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces Cerevisiae,” Mol. Cell. Biol. 4(11), 2529–2531 (1984).
[Crossref] [PubMed]

Burton, D. R.

Cano, E.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Chlebowicz-Sledziewska, E.

B. J. Brewer, E. Chlebowicz-Sledziewska, and W. L. Fangman, “Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces Cerevisiae,” Mol. Cell. Biol. 4(11), 2529–2531 (1984).
[Crossref] [PubMed]

Colomb, T.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Costantini, M.

M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
[Crossref]

Dardikman, G.

Dasari, R. R.

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(2), C538–C544 (2008).
[Crossref] [PubMed]

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(2), C538–C544 (2008).
[Crossref] [PubMed]

Depeursinge, C.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Fangman, W. L.

B. J. Brewer, E. Chlebowicz-Sledziewska, and W. L. Fangman, “Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces Cerevisiae,” Mol. Cell. Biol. 4(11), 2529–2531 (1984).
[Crossref] [PubMed]

Feld, M. S.

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(2), C538–C544 (2008).
[Crossref] [PubMed]

Gabai, H.

Y. Bishitz, H. Gabai, P. Girshovitz, and N. T. Shaked, “Optical-mechanical signatures of cancer cells based on fluctuation profiles measured by interferometry,” J. Biophotonics 7(8), 624–630 (2014).
[Crossref] [PubMed]

Gdeisat, M. A.

Girshovitz, P.

Habaza, M.

Herráez, M. A.

Huntley, J. M.

Itoh, K.

Jang, J.

Jang, Y.

Johnson, C. L.

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[Crossref] [PubMed]

Kennedy, P.

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[Crossref] [PubMed]

Kühn, J.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Lalor, M. J.

Lue, N.

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(2), C538–C544 (2008).
[Crossref] [PubMed]

Mada, M.

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[Crossref] [PubMed]

Magistretti, P. J.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Malvarosa, F.

M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
[Crossref]

Marquet, P.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Milillo, G.

M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
[Crossref]

Minati, F.

M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
[Crossref]

Mirsky, S.

Park, Y.

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(9), 9673–9681 (2012).
[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(2), C538–C544 (2008).
[Crossref] [PubMed]

Pietranera, L.

M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
[Crossref]

Popescu, G.

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(2), C538–C544 (2008).
[Crossref] [PubMed]

Rappaz, B.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Roberts, N.

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[Crossref] [PubMed]

Roichman, Y.

Saldner, H.

Shaked, N. T.

Simanis, V.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

Am. J. Physiol. Cell Physiol. (1)

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(2), C538–C544 (2008).
[Crossref] [PubMed]

Appl. Opt. (3)

J. Biomed. Opt. (1)

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009).
[Crossref] [PubMed]

J. Biophotonics (1)

Y. Bishitz, H. Gabai, P. Girshovitz, and N. T. Shaked, “Optical-mechanical signatures of cancer cells based on fluctuation profiles measured by interferometry,” J. Biophotonics 7(8), 624–630 (2014).
[Crossref] [PubMed]

Magn. Reson. Med. (1)

E. Barnhill, P. Kennedy, C. L. Johnson, M. Mada, and N. Roberts, “Real-time 4D phase unwrapping applied to magnetic resonance elastography,” Magn. Reson. Med. 73(6), 2321–2331 (2015).
[Crossref] [PubMed]

Mol. Cell. Biol. (1)

B. J. Brewer, E. Chlebowicz-Sledziewska, and W. L. Fangman, “Cell cycle phases in the unequal mother/daughter cell cycles of Saccharomyces Cerevisiae,” Mol. Cell. Biol. 4(11), 2529–2531 (1984).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Other (2)

D. C. Ghihlia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

M. Costantini, F. Malvarosa, F. Minati, L. Pietranera, and G. Milillo, “A three-dimensional phase unwrapping algorithm for processing of multitemporal SAR interferometric measurements,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2002), pp. 1741–1743.
[Crossref]

Supplementary Material (14)

NameDescription
» Visualization 1       True phase of simulated data
» Visualization 2       Phase reconstruction of simulated data with 2D phase unwrapping
» Visualization 3       Phase reconstruction of simulated data with angular phase unwrapping
» Visualization 4       Phase reconstruction of simulated data with temporal phase unwrapping
» Visualization 5       Phase reconstruction of simulated data with T/A phase unwrapping
» Visualization 6       Phase reconstruction of simulated data with A/T phase unwrapping
» Visualization 7       Phase reconstruction of simulated data with LBE phase unwrapping
» Visualization 8       Phase reconstruction of simulated data with RG phase unwrapping
» Visualization 9       Phase reconstruction of simulated data with DE phase unwrapping
» Visualization 10       Phase reconstruction of Euglena gracilis with 2D phase unwrapping
» Visualization 11       Phase reconstruction of Euglena gracilis with angular phase unwrapping
» Visualization 12       Phase reconstruction of Euglena gracilis with temporal phase unwrapping
» Visualization 13       Phase reconstruction of Euglena gracilis with T/A phase unwrapping
» Visualization 14       Phase reconstruction of Euglena gracilis with A/T phase unwrapping

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Figures (4)

Fig. 1
Fig. 1 (a) T/A algorithm (b) A/T algorithm. The dark rectangle in the bottom left indicates the optically thin phase map, which acts as the initial boundary condition (BC). Blue arrows are followed first, creating BCs for further unwrapping in the direction of the red arrows.
Fig. 2
Fig. 2 Phase reconstruction using different phase unwrapping algorithms, applied on simulative data. First column to the left: actual phase profile (Visualization 1). Second column: 2-D reliability-based phase unwrapping performed separately on each phase profile [14] (Visualization 2). Third column: angular phase unwrapping performed for each time stack separately [11] (Visualization 3). Fourth column: temporal phase unwrapping performed for each angular view separately (Visualization 4). Fifth column: T/A algorithm (Visualization 5). Sixth column: A/T algorithm (Visualization 6). Seventh column: LBE Algorithm [12] (Visualization 7). Eighth column: RG Algorithm [12] (Visualization 8). Ninth column: DE Algorithm [12] (Visualization 9). First row: optically-thin time and angle (boundary condition for the T/A and A/T algorithms). Note that in the visualizations, the time steps are shown from the end to the beginning, to show the budding process, where the last time step (shown here as the first) acts as the optically-thin time step.
Fig. 3
Fig. 3 Experimental demonstration: (a) Mach-Zehnder-based off-axis angular multiplexing interferometer, used for data acquisition. BS1, BS2: beam splitters; L1, L2: lenses; L3-L8: lenses, with each pair forming a 4f lens configuration, including MO1 and MO2; M1-M4: mirrors; MO1, MO2: microscope objectives. (b) Multiplexed off-axis hologram acquired with this setup at t = 0 sec. (c) Absolute value of the Fourier transform of the multiplexed hologram, featuring three different cross-correlation pairs in non-overlapping locations. ER: Fourier transform of reference beam wavefront, Es1: Fourier transform of the -7 °  sample beam wavefront, Es2: Fourier transform of the +21 ° sample beam wavefront. indicates the cross-correlation operator.
Fig. 4
Fig. 4 Phase reconstruction using different phase unwrapping algorithms, applied on experimental data of a dynamic micro-organism. First column to the left: 2-D reliability-based phase unwrapping performed on each phase profile separately [14] (Visualization 10). Second column: angular phase unwrapping performed on each time stack separately [11] (Visualization 11). Third column: temporal phase unwrapping performed on each angular view separately (Visualization 12). Fourth column: T/A algorithm [presented in Fig. 1(a)] (Visualization 13). Fifth column: A/T algorithm [presented in Fig. 1(b)] (Visualization 14). First row: optically-thin time and angle phase profiles (boundary condition for the T/A and A/T algorithms).

Equations (1)

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| Δν || dψ(x,y;ν) dν |π,

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