Abstract

The field of three-dimensional quantitative phase imaging (3D QPI) is expanding rapidly with applications in biological, medical, and industrial research, development, diagnostics, and metrology. Much of this research has centered on developing optical diffraction tomography (ODT) for biomedical applications. In addition to technical difficulties associated with coherent noise, ODT is not congruous with optical microscopy utilizing partially coherent light, which is used in most biomedical laboratories. Thus, ODT solutions have, for the most part, been limited to customized optomechanical systems which would be relatively expensive to implement on a wide scale. In the present work, a new phase reconstruction method, called tomographic deconvolution phase microscopy (TDPM), is described which makes use of commercial microscopy hardware in realizing 3D QPI. TDPM is analogous to methods used in deconvolution microscopy which improve spatial resolution and 3D-localization accuracy of fluorescence micrographs by combining multiple through-focal scans which are deconvolved by the system point spread function. TDPM is based on the 3D weak object transfer function theory which is shown here to be capable of imaging “nonweak” phase objects with large phase excursions. TDPM requires no phase unwrapping and recovers the entire object spectrum via object rotation, mitigating the need to fill in the “missing cone” of spatial frequencies algorithmically as in limited-angle ODT. In the present work, TDPM is demonstrated using optical fibers, including single-mode, polarization-maintaining, and photonic-crystal fibers as well as an azimuthally varying CO2-laser-induced long-period fiber grating period as test phase objects.

© 2015 Optical Society of America

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References

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2015 (5)

2014 (5)

2013 (5)

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

T. Feng, M. H. Jenkins, F. Yan, and T. K. Gaylord, “Arc fusion splicing effects in large-mode-area single-mode ytterbium-doped fibers,” Appl. Opt. 52, 7706–7711 (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, 4170–4191 (2013).
[Crossref]

A. D. Yablon, “Multifocus tomographic algorithm for measuring optically thick specimens,” Opt. Lett. 38, 4393–4396 (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, 32269–32278 (2013).
[Crossref]

2012 (6)

2011 (4)

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).
[Crossref]

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

F. Staier, H. Eipel, P. Matula, A. V. Evsikov, M. Kozubek, C. Cremer, and M. Hausmann, “Micro axial tomography: a miniaturized, versatile stage device to overcome resolution anisotropy in fluorescence light microscopy,” Rev. Sci. Instrum. 82, 093701 (2011).
[Crossref]

S. S. Kou, L. Waller, G. Barbastathis, P. Marquet, C. Depeursinge, and C. J. R. Sheppard, “Quantitative phase restoration by direct inversion using the optical transfer function,” Opt. Lett. 36, 2671–2673 (2011).
[Crossref]

2010 (2)

Y. Wang, “Review of long period fiber gratings written by CO2 laser,” J. Appl. Phys. 108, 081101 (2010).
[Crossref]

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

2009 (1)

2008 (2)

S. B. Mehta and C. J. R. Sheppard, “Partially coherent image formation in differential interference contrast (DIC) microscope,” Opt. Express 16, 19462–19479 (2008).
[Crossref]

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71, 5–10 (2008).
[Crossref]

2007 (1)

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).
[Crossref]

2006 (1)

2005 (2)

G. Rego, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “Arc-induced long-period gratings,” Fiber Integr. Opt. 24, 245–259 (2005).
[Crossref]

K. Morishita and A. Kaino, “Adjusting resonance wavelengths of long-period fiber gratings by the glass-structure change,” Appl. Opt. 44, 5018–5023 (2005).
[Crossref]

2004 (3)

L. D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).
[Crossref]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref]

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, and J. Jasapara, “Refractive-index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84, 19–21 (2004).
[Crossref]

2002 (1)

R. Heintzmann and C. Cremer, “Axial tomographic confocal fluorescence microscopy,” J. Microsc. 206, 7–23 (2002).
[Crossref]

2001 (3)

1998 (1)

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302–303 (1998).
[Crossref]

1996 (1)

C. J. Cogswell, K. G. Larkin, and H. U. Klemm, “Fluorescence microtomography: multi-angle image acquisition and 3D digital reconstruction,” Proc. SPIE 2655, 109–115 (1996).
[Crossref]

1992 (1)

J. Bradl, M. Hausmann, V. Ehemann, D. Komitowski, and C. Cremer, “A tilting device for three-dimensional microscopy: application to in situ imaging of interphase cell nuclei,” J. Microsc. 168, 47–57 (1992).
[Crossref]

1990 (1)

1989 (2)

P. J. Shaw, D. A. Agard, Y. Hiraoka, and J. W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55, 101–110 (1989).
[Crossref]

C. J. R. Sheppard and X. Q. Mao, “Three-dimensional imaging in a microscope,” J. Opt. Soc. Am. A 6, 1260–1269 (1989).
[Crossref]

1986 (1)

M. A. Fiddy, “Inversion of optical scattered field data,” J. Phys. D. 19, 301–317 (1986).

1985 (1)

1984 (1)

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref]

1983 (2)

S. X. Pan and A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered backpropagation,” IEEE Trans. Acoust. Speech Signal Process. 31, 1262–1275 (1983).
[Crossref]

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73, 1434–1441 (1983).
[Crossref]

1982 (1)

A. J. Devaney, “A filtered back-propagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).

1978 (1)

1977 (1)

J. P. Guigay, “Fourier-transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).

1952 (1)

R. Barer, “Interference microscopy and mass determination,” Nature 169, 366–367 (1952).
[Crossref]

Agard, D. A.

P. J. Shaw, D. A. Agard, Y. Hiraoka, and J. W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55, 101–110 (1989).
[Crossref]

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[Crossref]

Ahn, T. J.

Aknoun, S.

Alieva, T.

Auth, T.

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

Babacan, S. D.

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

Backman, V.

Badizadegan, K.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref]

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).
[Crossref]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Balla, A. K.

T. H. Nguyen, S. Sridharan, V. Macias, A. K. Balla, M. N. Do, and G. Popescu, “Prostate cancer diagnosis using quantitative phase imaging and machine learning algorithms,” Proc. SPIE 9336, 933619 (2015).
[Crossref]

Barbastathis, G.

Barer, R.

R. Barer, “Interference microscopy and mass determination,” Nature 169, 366–367 (1952).
[Crossref]

Barty, A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref]

Bashir, R.

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

Bednarz, M.

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

Best, C. A.

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

Birks, T. A.

Bon, P.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 6th ed. (Pergamon, 1980).

Bradl, J.

J. Bradl, M. Hausmann, V. Ehemann, D. Komitowski, and C. Cremer, “A tilting device for three-dimensional microscopy: application to in situ imaging of interphase cell nuclei,” J. Microsc. 168, 47–57 (1992).
[Crossref]

Brox, T.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Carney, P. S.

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

Chandramohanadas, R.

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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. Nat. Acad. Sci. USA 108, 13124–13129 (2011).

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

B. H. Kim, Y. Park, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657–1659 (2001).
[Crossref]

Paterson, D.

Pavillon, N.

Peele, A. G.

Phillips, K. G.

K. G. Phillips, S. L. Jacques, and O. J. T. McCarty, “Measurement of single cell refractive index, dry mass, volume, and density using a transillumination microscope,” Phys. Rev. Lett. 109, 118105 (2012).
[Crossref]

Popescu, G.

R. Zhou, C. Edwards, G. Popescu, and L. Goddard, “Semiconductor defect metrology using laser-based quantitative phase imaging,” Proc. SPIE 9336, 93361I (2015).
[Crossref]

T. H. Nguyen, S. Sridharan, V. Macias, A. K. Balla, M. N. Do, and G. Popescu, “Prostate cancer diagnosis using quantitative phase imaging and machine learning algorithms,” Proc. SPIE 9336, 933619 (2015).
[Crossref]

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

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. Nat. Acad. Sci. USA 108, 13124–13129 (2011).

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

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

Prasanth, S. G.

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. Nat. Acad. Sci. USA 108, 13124–13129 (2011).

Preiser, P. R.

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).
[Crossref]

Quinn, D.

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).
[Crossref]

Rappaz, B.

Raty, L.

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

Reed, W. A.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, and J. Jasapara, “Refractive-index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84, 19–21 (2004).
[Crossref]

Rego, G.

G. Rego, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “Arc-induced long-period gratings,” Fiber Integr. Opt. 24, 245–259 (2005).
[Crossref]

Roberts, A.

N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71, 5–10 (2008).
[Crossref]

Rodrigo, J. A.

Rogers, J. D.

Roichman, Y.

Ronneberger, O.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Russell, P. St. J.

Safran, S. A.

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

Salgado, H. M.

G. Rego, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “Arc-induced long-period gratings,” Fiber Integr. Opt. 24, 245–259 (2005).
[Crossref]

Santos, J. L.

G. Rego, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “Arc-induced long-period gratings,” Fiber Integr. Opt. 24, 245–259 (2005).
[Crossref]

Schaefer, L. H.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).

Schmidt, T.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Scholten, R. E.

Sedat, J. W.

P. J. Shaw, D. A. Agard, Y. Hiraoka, and J. W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55, 101–110 (1989).
[Crossref]

Shaked, N. T.

Shaw, P. J.

P. J. Shaw, D. A. Agard, Y. Hiraoka, and J. W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55, 101–110 (1989).
[Crossref]

Shen, Z.

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. Nat. Acad. Sci. USA 108, 13124–13129 (2011).

Sheppard, C. J. R.

Shin, S.

Singer, W.

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Physical Image Formation (Wiley, 2006).

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

So, P. T. C.

Sridharan, S.

T. H. Nguyen, S. Sridharan, V. Macias, A. K. Balla, M. N. Do, and G. Popescu, “Prostate cancer diagnosis using quantitative phase imaging and machine learning algorithms,” Proc. SPIE 9336, 933619 (2015).
[Crossref]

Staier, F.

F. Staier, H. Eipel, P. Matula, A. V. Evsikov, M. Kozubek, C. Cremer, and M. Hausmann, “Micro axial tomography: a miniaturized, versatile stage device to overcome resolution anisotropy in fluorescence light microscopy,” Rev. Sci. Instrum. 82, 093701 (2011).
[Crossref]

Stoyneva, V.

Streibl, N.

Subramanian, H.

Sung, Y.

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

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).
[Crossref]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref]

Suresh, S.

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).
[Crossref]

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

Swedlow, J. R.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).

Taflove, A.

Teague, M. R.

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73, 1434–1441 (1983).
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M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Totzeck, M.

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Physical Image Formation (Wiley, 2006).

Tran, C. Q.

Turner, L. D.

Vengsarkar, A. M.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302–303 (1998).
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Vollmer, A.

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

Wallace, W.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).

Waller, L.

Wang, Y.

Y. Wang, “Review of long period fiber gratings written by CO2 laser,” J. Appl. Phys. 108, 081101 (2010).
[Crossref]

Wang, Z.

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. Nat. Acad. Sci. USA 108, 13124–13129 (2011).

Wattellier, B.

Wisk, P.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, and J. Jasapara, “Refractive-index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84, 19–21 (2004).
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Wolf, E.

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A. D. Yablon, “Multifocus tomographic algorithm for measuring optically thick specimens,” Opt. Lett. 38, 4393–4396 (2013).
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A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, and J. Jasapara, “Refractive-index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84, 19–21 (2004).
[Crossref]

Yan, F.

Yan, M. F.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, and J. Jasapara, “Refractive-index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84, 19–21 (2004).
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Yang, S.

Yaqoob, Z.

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

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

Ye, J. C.

Zhou, R.

R. Zhou, C. Edwards, G. Popescu, and L. Goddard, “Semiconductor defect metrology using laser-based quantitative phase imaging,” Proc. SPIE 9336, 93361I (2015).
[Crossref]

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

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A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, and J. Jasapara, “Refractive-index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84, 19–21 (2004).
[Crossref]

Biophys. J. (1)

P. J. Shaw, D. A. Agard, Y. Hiraoka, and J. W. Sedat, “Tilted view reconstruction in optical microscopy, three-dimensional reconstruction of Drosophila melanogaster embryo nuclei,” Biophys. J. 55, 101–110 (1989).
[Crossref]

Biotechniques (1)

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).

Electron. Lett. (1)

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302–303 (1998).
[Crossref]

Fiber Integr. Opt. (1)

G. Rego, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “Arc-induced long-period gratings,” Fiber Integr. Opt. 24, 245–259 (2005).
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Y. Wang, “Review of long period fiber gratings written by CO2 laser,” J. Appl. Phys. 108, 081101 (2010).
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J. Biomed. Opt. (1)

A. Kus, M. Dudek, B. Kemper, M. Kujawinska, and A. Vollmer, “Tomographic phase microscope of living three-dimensional cell cultures,” J. Biomed. Opt. 19, 046009 (2014).
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N. M. Dragomir, X. M. Goh, and A. Roberts, “Three-dimensional refractive index reconstruction with quantitative phase tomography,” Microsc. Res. Tech. 71, 5–10 (2008).
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Nat. Methods (1)

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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Nat. Photonics (1)

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

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P. Bon, S. Aknoun, S. Monneret, and B. Wattellier, “Enhanced 3D spatial resolution in quantitative phase microscopy using spatially incoherent illumination,” Opt. Express 22, 8654–8671 (2014).
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Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
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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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F. Charriere, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express 14, 7005–7013 (2006).
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K. Kim, K. S. Kim, H. Park, J. C. Ye, and Y. Park, “Real-time visualization of 3-D dynamic microscopic objects using optical diffraction tomography,” Opt. Express 21, 32269–32278 (2013).
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S. B. Mehta and C. J. R. Sheppard, “Partially coherent image formation in differential interference contrast (DIC) microscope,” Opt. Express 16, 19462–19479 (2008).
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S. S. Kou, L. Waller, G. Barbastathis, P. Marquet, C. Depeursinge, and C. J. R. Sheppard, “Quantitative phase restoration by direct inversion using the optical transfer function,” Opt. Lett. 36, 2671–2673 (2011).
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L. Cherkezyan, H. Subramanian, V. Stoyneva, J. D. Rogers, S. Yang, D. Damania, A. Taflove, and V. Backman, “Targeted alteration of real and imaginary refractive index of biological cells by histological staining,” Opt. Lett. 37, 1601–1603 (2012).
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A. D. Yablon, “Multifocus tomographic algorithm for measuring optically thick specimens,” Opt. Lett. 38, 4393–4396 (2013).
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P. Bon, B. Wattellier, and S. Monneret, “Modeling quantitative phase image formation under tilted illuminations,” Opt. Lett. 37, 1718–1720 (2012).
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G. Kakarantzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, “Miniature all-fiber devices based on CO2 laser microstructuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001).
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B. H. Kim, Y. Park, T. J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W. T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657–1659 (2001).
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K. Kim, Z. Yaqoob, K. Lee, J. W. Kang, Y. Choi, P. Hosseini, P. T. C. So, and Y. Park, “Diffraction optical tomography using a quantitative phase imaging unit,” Opt. Lett. 39, 6935–6938 (2014).
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Phys. Rev. Lett. (1)

K. G. Phillips, S. L. Jacques, and O. J. T. McCarty, “Measurement of single cell refractive index, dry mass, volume, and density using a transillumination microscope,” Phys. Rev. Lett. 109, 118105 (2012).
[Crossref]

PLoS ONE (2)

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).
[Crossref]

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

Proc. Nat. Acad. Sci. USA (2)

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. Nat. Acad. Sci. USA 108, 13124–13129 (2011).

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

Proc. SPIE (3)

T. H. Nguyen, S. Sridharan, V. Macias, A. K. Balla, M. N. Do, and G. Popescu, “Prostate cancer diagnosis using quantitative phase imaging and machine learning algorithms,” Proc. SPIE 9336, 933619 (2015).
[Crossref]

R. Zhou, C. Edwards, G. Popescu, and L. Goddard, “Semiconductor defect metrology using laser-based quantitative phase imaging,” Proc. SPIE 9336, 93361I (2015).
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Sci. Rep. (1)

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography—a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (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, 4170–4191 (2013).
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M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

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M. R. Hutsel, “Characterization of the stress and refractive-index distributions in optical fibers and fiber-based devices,” Ph.D. thesis (Georgia Institute of Technology, 2011).

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

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Physical Image Formation (Wiley, 2006).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 6th ed. (Pergamon, 1980).

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Figures (12)

Fig. 1.
Fig. 1.

Magnitudes of the on-axis coherent (a) AOTF and (b) POTF derived from simulating the scattered complex field amplitude due to a point scatterer. All figures are plotted as a function of normalized frequency coordinates ρ λ / n 0 and have rotational symmetry about ρ ^ z .

Fig. 2.
Fig. 2.

Partially coherent (a) AOTF and (b) POTF plotted as a function of normalized frequency coordinates ρ λ / n 0 .

Fig. 3.
Fig. 3.

(a) Image of objective BFP with no sample in place. (b) Gaussian fit to (a) serving as input source distribution in the calculation of OTFs in Fig. 2. Both figures are plotted as a function of normalized frequency coordinates in the illumination pupil ρ λ / n 0 .

Fig. 4.
Fig. 4.

Block diagram representation of TDPM RI recovery for high spatial frequencies.

Fig. 5.
Fig. 5.

Block diagram representation of TDPM RI recovery for low spatial frequencies.

Fig. 6.
Fig. 6.

(a) NMSEs of various BPM simulations with and without OF correction [Eq. (21)] for normal ( ρ = 0 ) and marginal ( ρ = ρ c ρ ^ x = N A c ρ ^ x / λ ) incidence. (b) Simulated (with OF correction) and (c) analytic intensities with Δ n = 0.025 . Simulation parameters: λ = 546 nm , n 0 = 1 , Δ x = Δ z = 245 nm , N A o = 0.75 , and N A c = 0.375 .

Fig. 7.
Fig. 7.

RI contrast Δ n ( r ) of modified Shepp–Logan phantom.

Fig. 8.
Fig. 8.

Reconstructions obtained using filtered back-propagation under the [(a), (d), (g)] Born and [(b), (e), (h)] Rytov approximations as well as [(c), (f), (i)] TDPM for maximum RI contrast values of [(a), (b), (c)] Δ n max = 0.004 , [(d), (e), (f)] Δ n max = 0.02 , and [(g), (h), (i)] Δ n max = 0.1 . The resulting RMSEs are (a) 0.00042, (b) 0.00015, (c) 0.00017, (d) 0.00580, (e) 0.00088, (f) 0.00106, (g) 0.02681, (h) 0.01124, and (i) 0.01293.

Fig. 9.
Fig. 9.

TDPM reconstructions obtained with additive noise with a normalized standard deviation of σ = 0.01 and (a)  Δ n max = 0.004 and (b)  Δ n max = 0.04 . The resulting RMSEs are (a) 0.00026 and (b) 0.00294.

Fig. 10.
Fig. 10.

2D TDPM cross-sectional tomograms obtained on (a) single-mode, (b) polarization-maintaining, and (c) photonic-crystal fibers. All colorbars indicate RI units.

Fig. 11.
Fig. 11.

RI modification induced via CO 2 -laser exposure. (a) Unperturbed single-mode fiber reconstructed 150 μm away from the center of exposure. (b) Reconstruction near the center of the exposed region showing azimuthal variation. (c) Multiple slices showing the 3D nature of TDPM data plotted with a reduced colormap range to highlight both azimuthal and axial changes in the fiber cladding facing the exposure. All colorbars indicate RI units.

Fig. 12.
Fig. 12.

Line profiles showing the axial variation of RI in selected regions of CO 2 exposed single-mode fiber.

Equations (32)

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[ 2 + k 2 ( r ) ] u ( r ) = 0 .
[ 2 + ( k 0 n 0 ) 2 ] u ( r ) = V ( r ) u ( r ) .
u ( r ) = u 0 ( r ) + u s ( r ) ,
u s ( r ) = V V ( r ) u ( r ) g ( | r r | ) d r = [ V ( r ) u ( r ) ] * g ( r ) ,
u B ( r ) = [ V ( r ) u 0 ( r ) ] * g ( r ) .
u ( r ) = u 0 ( r ) exp [ ϕ s ( r ) ] ,
ϕ s ( r ) = 1 u 0 ( r ) { V ( r ) + [ ϕ s ( r ) ] 2 } u 0 ( r ) g ( | r r | ) d r ,
ϕ R ( r ) = u B ( r ) u 0 ( r ) ,
V ( r ) + [ ϕ s ( r ) ] 2 V ( r ) ,
I ( r , ρ ) = u ( r , ρ ) u * ( r , ρ ) = S ( ρ ) exp { 2 Re [ ϕ R ( r , ρ ) ] } .
| 2 Re [ ϕ R ( r , ρ ) ] | 1 ,
I ( r , ρ ) = S ( ρ ) { 1 + 2 Re [ ϕ R ( r , ρ ) ] } .
I ( r , ρ ) = S ( ρ ) [ 1 + 2 Re ( i u 0 ( r , ρ ) { [ A ( r ) u 0 ( r , ρ ) ] * g ( r ) } ) + 2 Re ( 1 u 0 ( r , ρ ) { [ P ( r ) u 0 ( r , ρ ) ] * g ( r ) } ) ] ,
V ( r ) = P ( r ) + i A ( r ) ,
I ( ρ , ρ ) = S ( ρ ) { δ ( ρ ) + i A ( ρ ) [ G ( ρ + ρ ) G * ( ρ ρ ) ] + P ( ρ ) [ G ( ρ + ρ ) + G * ( ρ ρ ) ] } ,
G ( ρ ) = G ( ρ ) P ( ρ ) U ( ρ z ) ,
circ ( ζ ) = { 1 , | ζ | 1 , 0 , | ζ | > 1 ,
U ( ζ ) = { 1 , ζ 0 , 0 , ζ < 0 .
I ( ρ ) = B δ ( ρ ) + A ( ρ ) H A ( ρ ) + P ( ρ ) H P ( ρ ) ,
B = S ( ρ ) d ρ ,
H A ( ρ ) = i S ( ρ ) [ G ( ρ + ρ ) G * ( ρ ρ ) ] d ρ ,
H P ( ρ ) = S ( ρ ) [ G ( ρ + ρ ) + G * ( ρ ρ ) ] d ρ ,
I ( r ) = B + A ( r ) * h A ( r ) + P ( r ) * h P ( r ) ,
| A ( r ) * 2 i Im [ g ( r , ρ ) ] | 1 ,
| P ( r ) * 2 Re [ g ( r , ρ ) ] | 1 ,
min ϵ = j = 0 N 1 | P ( ρ ) H P ( ρ ) I θ j ( ρ ) / B | 2 + α | P ( ρ ) | 2 .
P ( ρ ) = j = 0 N 1 [ I θ j ( ρ ) / B ] H P * ( ρ ) / [ j = 0 N 1 | H P j ( ρ ) | 2 + α ] .
j = 0 N 1 | H P j ( ρ ) | 2 = I [ j = 0 N 1 h P j ( r ) * h P j * ( r ) ] .
OF ( r ) = 1 1 [ | ϕ ( r ) | / k 0 n 0 ] 2 .
u z + Δ z 2 ( r ) = I 1 ( I [ u z ( r ) ] exp { i k 0 n 0 [ 1 ( λ ρ n 0 ) 2 ] Δ z 2 } ) ,
u z + Δ z 2 ( r ) = u z + Δ z 2 ( r ) exp { i k 0 [ n ( r ) n 0 ] OF ( r ) Δ z } .
NMSE [ I S ( r ) ] = [ I S ( r ) I A ( r ) ] 2 [ I A ( r ) I ¯ A ] 2 .

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