Abstract

Using the decomposition of an image field in two spatial components that can be controllably shifted in phase with respect to each other, a new quantitative-phase microscope has been developed. The new instrument, referred to as the fast Fourier phase microscope (f-FPM), provides a factor of 100 higher acquisition rate compared with our previously reported Fourier phase microscope. The resulting quantitative-phase images are characterized by diffraction limited transverse resolution and path-length stability better than 2  nm at acquisition rates of 10 frames∕s or more. These features make the f-FPM particularly appealing for investigating the structure and dynamics of live cells over a broad range of time scales. In addition, we demonstrate the possibility of examining subcellular structures by digitally processing the amplitude and phase information provided by the instrument. Thus we developed software that can emulate phase contrast and differential interference contrast microscopy images by numerically processing FPM images. This approach adds the flexibility of digitally varying the phase shift between the two interfering beams. The images obtained appear as if they were recorded by variable phase contrast or differential interference contrast microscopes that deliver an enhanced view to the subcellular structure when compared with the typical commercial microscope.

© 2007 Optical Society of America

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References

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  1. F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
    [CrossRef] [PubMed]
  2. F. H. Smith, "Microscopic interferometry," Research (London) 8, 385-395 (1955).
  3. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  4. C. G. Rylander, D. P. Dave, T. Akkin, T. E. Milner, K. R. Diller, and A. J. Welch, "Quantitative phase-contrast imaging of cells with phase-sensitive optical coherence microscopy," Opt. Lett. 29, 1509-1511 (2004).
    [CrossRef] [PubMed]
  5. T. Akkin, D. P. Dave, T. E. Milner, and H. G. Rylander, "Detection of neural activity using phase-sensitive optical low-coherence reflectometry," Opt. Express 12, 2377-2386 (2004).
    [CrossRef] [PubMed]
  6. C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, "Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer," Opt. Lett. 29, 2028-2030 (2004).
    [CrossRef] [PubMed]
  7. M. A. Choma, A. K. Ellerbee, C. H. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30, 1162-1164 (2005).
    [CrossRef] [PubMed]
  8. C. H. Yang, A. Wax, R. R. Dasari, and M. S. Feld, "Phase-dispersion optical tomography," Opt. Lett. 26, 686-688 (2001).
    [CrossRef]
  9. C. H. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
    [CrossRef]
  10. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics, Opt. Lett. 26, 1271-1273 (2001).
    [CrossRef]
  11. G. A. Dunn and D. Zicha, eds., Using DRIMAPS System of Transmission Interference Microscopy to Study Cell Behavior (Academic, 1997).
  12. D. Zicha and G. A. Dunn, "An image-processing system for cell behavior studies in subconfluent cultures," J. Microsc. 179, 11-21 (1995).
    [CrossRef]
  13. D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
    [PubMed]
  14. T. E. Gureyev, A. Roberts, and K. A. Nugent, "Phase retrieval with the transport-of-intensity equation--matrix solution with use of Zernike polynomials," J. Opt. Soc. Am. A 12, 1932-1941 (1995).
    [CrossRef]
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    [CrossRef]
  16. D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
    [CrossRef] [PubMed]
  17. T. Zhang and I. Yamaguchi, "Three-dimensional microscopy with phase-shifting digital holography," Opt. Lett. 23, 1221-1223 (1998).
    [CrossRef]
  18. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, "Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy," Opt. Lett. 30, 468-470 (2005).
    [CrossRef] [PubMed]
  19. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
    [CrossRef] [PubMed]
  20. F. Charriere, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
    [CrossRef] [PubMed]
  21. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, "Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29, 2503-2505 (2004).
    [CrossRef] [PubMed]
  22. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1168 (2005).
    [CrossRef] [PubMed]
  23. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, "Diffraction phase microscopy for quantifying cell structure and dynamics," Opt. Lett. 31, 775-777 (2006).
    [CrossRef] [PubMed]
  24. G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. Lett. 10, 060503 (2005).
    [CrossRef]
  25. H. Kadono, M. Ogusu, and S.Toyooka, "Phase-shifting common-path interferometer using a liquid-crystal modulator," Opt. Commun. 110, 391-400 (1994).
    [CrossRef]
  26. J. Gluckstad and P. C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001).
    [CrossRef]

2006 (2)

2005 (5)

2004 (4)

2001 (3)

2000 (1)

1999 (1)

D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
[PubMed]

1998 (1)

1995 (3)

1994 (1)

H. Kadono, M. Ogusu, and S.Toyooka, "Phase-shifting common-path interferometer using a liquid-crystal modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1955 (1)

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

1948 (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Akkin, T.

Badizadegan, K.

Best, C. A.

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. Lett. 10, 060503 (2005).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Charriere, F.

Choma, M. A.

Chu, M. C.

Colomb, T.

Creazzo, T. L.

Cuche, E.

Dasari, R. R.

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, "Diffraction phase microscopy for quantifying cell structure and dynamics," Opt. Lett. 31, 775-777 (2006).
[CrossRef] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1168 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. Lett. 10, 060503 (2005).
[CrossRef]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, "Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29, 2503-2505 (2004).
[CrossRef] [PubMed]

C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, "Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer," Opt. Lett. 29, 2028-2030 (2004).
[CrossRef] [PubMed]

C. H. Yang, A. Wax, R. R. Dasari, and M. S. Feld, "Phase-dispersion optical tomography," Opt. Lett. 26, 686-688 (2001).
[CrossRef]

C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics, Opt. Lett. 26, 1271-1273 (2001).
[CrossRef]

C. H. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
[CrossRef]

Dave, D. P.

Deflores, L. P.

Depeursinge, C.

Diller, K. R.

Dunn, G. A.

D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
[PubMed]

D. Zicha and G. A. Dunn, "An image-processing system for cell behavior studies in subconfluent cultures," J. Microsc. 179, 11-21 (1995).
[CrossRef]

G. A. Dunn and D. Zicha, eds., Using DRIMAPS System of Transmission Interference Microscopy to Study Cell Behavior (Academic, 1997).

Ellerbee, A. K.

Emery, Y.

Fang-Yen, C.

Feld, M. S.

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, "Diffraction phase microscopy for quantifying cell structure and dynamics," Opt. Lett. 31, 775-777 (2006).
[CrossRef] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1168 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. Lett. 10, 060503 (2005).
[CrossRef]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, "Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29, 2503-2505 (2004).
[CrossRef] [PubMed]

C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, "Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer," Opt. Lett. 29, 2028-2030 (2004).
[CrossRef] [PubMed]

C. H. Yang, A. Wax, R. R. Dasari, and M. S. Feld, "Phase-dispersion optical tomography," Opt. Lett. 26, 686-688 (2001).
[CrossRef]

C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics, Opt. Lett. 26, 1271-1273 (2001).
[CrossRef]

C. H. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Genot, E.

D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
[PubMed]

Georgakoudi, I.

Gluckstad, J.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Gureyev, T. E.

Hahn, M. S.

Hanlon, E. B.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Ikeda, T.

Iwai, H.

Izatt, J. A.

Kadono, H.

H. Kadono, M. Ogusu, and S.Toyooka, "Phase-shifting common-path interferometer using a liquid-crystal modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Kramer, I. M.

D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
[PubMed]

Kuehn, J.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Magistretti, P. J.

Marian, A.

Marquet, P.

Milner, T. E.

Mogensen, P. C.

Montfort, F.

Nugent, K. A.

Ogusu, M.

H. Kadono, M. Ogusu, and S.Toyooka, "Phase-shifting common-path interferometer using a liquid-crystal modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Popescu, G.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Rappaz, B.

Roberts, A.

Rylander, C. G.

Rylander, H. G.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Seung, H. S.

Smith, F. H.

F. H. Smith, "Microscopic interferometry," Research (London) 8, 385-395 (1955).

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Toyooka, S.

H. Kadono, M. Ogusu, and S.Toyooka, "Phase-shifting common-path interferometer using a liquid-crystal modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Vaughan, J. C.

Wax, A.

Welch, A. J.

Yamaguchi, I.

Yang, C.

Yang, C. H.

Zernike, F.

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Zhang, T.

Zicha, D.

D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
[PubMed]

D. Zicha and G. A. Dunn, "An image-processing system for cell behavior studies in subconfluent cultures," J. Microsc. 179, 11-21 (1995).
[CrossRef]

G. A. Dunn and D. Zicha, eds., Using DRIMAPS System of Transmission Interference Microscopy to Study Cell Behavior (Academic, 1997).

Appl. Opt. (1)

J. Biomed. Opt. Lett. (1)

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Erythrocyte structure and dynamics quantified by Hilbert phase microscopy," J. Biomed. Opt. Lett. 10, 060503 (2005).
[CrossRef]

J. Cell Sci. (1)

D. Zicha, E. Genot, G. A. Dunn, and I. M. Kramer, "TGF beta 1 induces a cell-cycle-dependent increase in motility of epithelial cells," J. Cell Sci. 112, 447-454 (1999).
[PubMed]

J. Microsc. (1)

D. Zicha and G. A. Dunn, "An image-processing system for cell behavior studies in subconfluent cultures," J. Microsc. 179, 11-21 (1995).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. Kadono, M. Ogusu, and S.Toyooka, "Phase-shifting common-path interferometer using a liquid-crystal modulator," Opt. Commun. 110, 391-400 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (12)

C. Fang-Yen, M. C. Chu, H. S. Seung, R. R. Dasari, and M. S. Feld, "Noncontact measurement of nerve displacement during action potential with a dual-beam low-coherence interferometer," Opt. Lett. 29, 2028-2030 (2004).
[CrossRef] [PubMed]

M. A. Choma, A. K. Ellerbee, C. H. Yang, T. L. Creazzo, and J. A. Izatt, "Spectral-domain phase microscopy," Opt. Lett. 30, 1162-1164 (2005).
[CrossRef] [PubMed]

C. H. Yang, A. Wax, R. R. Dasari, and M. S. Feld, "Phase-dispersion optical tomography," Opt. Lett. 26, 686-688 (2001).
[CrossRef]

C. H. Yang, A. Wax, I. Georgakoudi, E. B. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
[CrossRef]

C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics, Opt. Lett. 26, 1271-1273 (2001).
[CrossRef]

C. G. Rylander, D. P. Dave, T. Akkin, T. E. Milner, K. R. Diller, and A. J. Welch, "Quantitative phase-contrast imaging of cells with phase-sensitive optical coherence microscopy," Opt. Lett. 29, 1509-1511 (2004).
[CrossRef] [PubMed]

F. Charriere, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, "Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29, 2503-2505 (2004).
[CrossRef] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1168 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, "Diffraction phase microscopy for quantifying cell structure and dynamics," Opt. Lett. 31, 775-777 (2006).
[CrossRef] [PubMed]

T. Zhang and I. Yamaguchi, "Three-dimensional microscopy with phase-shifting digital holography," Opt. Lett. 23, 1221-1223 (1998).
[CrossRef]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, "Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy," Opt. Lett. 30, 468-470 (2005).
[CrossRef] [PubMed]

Science (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Other (2)

F. H. Smith, "Microscopic interferometry," Research (London) 8, 385-395 (1955).

G. A. Dunn and D. Zicha, eds., Using DRIMAPS System of Transmission Interference Microscopy to Study Cell Behavior (Academic, 1997).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

(a) Intensity versus voltage associated with the PCF in amplitude mode. (b) Wrapped and unwrapped phase versus voltage calibration curve. (c) Phase grating during the PCF phase mode of operation. (d) Intensity variation versus step voltage for top and bottom areas on the phase grating in (c). The dotted line is a guide to the eye for the saturation level.

Fig. 3
Fig. 3

(Color online) (a) Quantitative phase image of background. The shaded bar indicates the phase in radians. The limited field of view is to enlarge the diffraction spot at the Fourier plane of the dc component. (b) Histogram of temporal path-length standard deviations associated with pixels within the rectangular region shown in (a). (c) Profile of the phase grating obtained using the f-FPM. The shaded bar indicates the phase in radians. (d) Phase values measured in each pixel of the two rectangular regions shown in (c).

Fig. 4
Fig. 4

(Color online) (a) f-FPM image of a live HeLa cell. (b) Digital DIC image obtained from the image in (a). The visual interface for numerical processing is also shown.

Fig. 5
Fig. 5

(Color online) (a)–(h) Series of f-FPM images of a dissolving sugar crystal. The shaded bar indicates the phase in radians. (i) Temporal evolution of the volume enclosed by the surface ϕ ( x , y ) .

Equations (3)

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

I sin 2 [ Γ ( V ) / 2 ] ,
Δ ϕ ( x , y ) = arctan ( I 1.5 π ( x , y ) I 2.5 π ( x , y ) I π ( x , y ) I 2 π ( x , y ) ) ,
ϕ ( x , y ) = arctan ( β   sin [ Δ ϕ ( x , y ) ] 1 + β   cos [ Δ ϕ ( x , y ) ] ) .

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