Abstract

A fast reliability-guided phase unwrapping algorithm, using an optimized quality map and combining it with look-up table operation, is proposed for digital holographic microscopy. First, by detecting the residues in the wrapped phase map, an intensity threshold is calculated in the normalized intensity image and the measured region is distinguished into the reliable region and the doubtful region. An optimized quality map is derived by the method in which the intensity values in the reliable region are set to 1 and those in the doubtful region remain unchanged. Then the flood fill algorithm by look-up table is implemented with the optimized quality map to retrieve true phase map. The experimental results demonstrate that not only does the proposed algorithm perform well, but also the speed is significantly faster than that of the conventional flood fill algorithm using insert sorting.

© 2012 Optical Society of America

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References

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  1. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  2. L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Partition calculation for zero-order and conjugate image removal in digital in-line holography,” Opt. Express 20, 1805–1815 (2012).
    [CrossRef]
  3. M. León-Rodríguez, R. Rodríguez-Vera, J. A. Rayas, and S. Calixto, “High topographical accuracy by optical shot noise reduction in digital holographic microscopy,” J. Opt. Soc. Am. A 29, 498–506 (2012).
    [CrossRef]
  4. C. Furlong and R. J. Pryputniewics, “Optoelectronic characterization of shape and deformations of MEMS accelerometers used in transportation applications,” Opt. Eng. 42, 1223–1231(2003).
    [CrossRef]
  5. T. Kozacki, M. Józwik, and K. Liżewski, “High-numerical-aperture microlens shape measurement with digital holographic microscopy,” Opt. Lett. 36, 4419–4421 (2011).
    [CrossRef]
  6. W. J. Qu, C. O. Choo, Y. J. Yu, and A. Asundi, “Microlens characterization by digital holographic microscopy with physical spherical phase compensation,” Appl. Opt. 49, 6448–6454 (2010).
    [CrossRef]
  7. L. H. Ma, H. Wang, H. Z. Jin, and Y. Li, “Experimental study on quantitative phase imaging by digital holographic microscopy,” Zhongguo Jiguang/Chin. J. Lasers 39, 0309002 (2012).
    [CrossRef]
  8. M. H. Jericho, H. J. Kreuzer, M. Kanka, and R. Riesenberg, “Quantitative phase and refractive index measurements with point-source digital in-line holographic microscopy,” Appl. Opt. 51, 1503–1515 (2012).
    [CrossRef]
  9. B. Kemper and G. v. Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
    [CrossRef]
  10. P. Langehanenberg, L. Ivanova, and I. Bernhardt, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
    [CrossRef]
  11. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).
  12. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [CrossRef]
  13. Y. G. Lu, X. Z. Wang, and G. T. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
    [CrossRef]
  14. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
    [CrossRef]
  15. S. Fang, L. Meng, L. J. Wang, P. C. Yang, and M. Komori, “Quality-guided phase unwrapping algorithm based on reliability evaluation,” Appl. Opt. 50, 5446–5452 (2011).
    [CrossRef]
  16. S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
    [CrossRef]
  17. S. Fang, L. Meng, L. Wang, P. Yang, and M. Komori, “Quality-guided phase unwrapping algorithm based on reliability evaluation,” Appl. Opt. 50, 5446–5452 (2011).
    [CrossRef]
  18. T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
    [CrossRef]
  19. W. Xu, “A region growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
    [CrossRef]
  20. M. A. Schofield and Y. M. Zhu, “Fast phase unwrapping algorithm for interferometric applications,” Opt. Lett. 28, 1194–1196 (2003).
    [CrossRef]
  21. J. Arines, “Least-squares modal estimation of wrapped phases: application to phase unwrapping,” Appl. Opt. 42, 3373–3378 (2003).
    [CrossRef]
  22. Y. G. Lua, X. Z. Wang, and X. P. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
    [CrossRef]
  23. D. Kerr, G. H. Kaufmann, and G. E. Galizzi, “Unwrapping of interferometric phase-fringe maps by the discrete cosine transform,” Appl. Opt. 35, 810–816 (1996).
    [CrossRef]
  24. A. Anand and W. S. Zhou, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
    [CrossRef]
  25. Y. Li and X. Su, “Fast algorithm for reliability-guided phase unwrapping,” Opt. Electron. Eng. 32, 76–79 (2005).
  26. M. Zhao, L. Huang, Q. C. Zhang, X. Y. Su, A. Asundi, and K. M. Qian, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50, 6214–6224 (2011).
    [CrossRef]
  27. L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Effect of system parameters on the reconstructed image quality in digital holographic microscopy,” Acta Photonica Sinica 40, 300–306 (2011).
    [CrossRef]
  28. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
    [CrossRef]
  29. T. Colomb, E. Cuche, F. Charriére, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45, 851–863 (2006).
    [CrossRef]
  30. W. Qu, C. Choo, V. Singh, Y. Yu, and A. Asundi, “Quasi-physical phase compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 26, 2005–2011 (2009).
    [CrossRef]

2012 (5)

2011 (5)

2010 (1)

2009 (2)

P. Langehanenberg, L. Ivanova, and I. Bernhardt, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

W. Qu, C. Choo, V. Singh, Y. Yu, and A. Asundi, “Quasi-physical phase compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 26, 2005–2011 (2009).
[CrossRef]

2008 (1)

2007 (1)

Y. G. Lua, X. Z. Wang, and X. P. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

2006 (1)

2005 (2)

Y. Li and X. Su, “Fast algorithm for reliability-guided phase unwrapping,” Opt. Electron. Eng. 32, 76–79 (2005).

Y. G. Lu, X. Z. Wang, and G. T. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

2004 (1)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

2003 (4)

1999 (2)

W. Xu, “A region growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Anand, A.

Arines, J.

Aspert, N.

Asundi, A.

Bally, G. v.

Bernhardt, I.

P. Langehanenberg, L. Ivanova, and I. Bernhardt, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Bevilacqua, F.

Calixto, S.

Charriére, F.

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Choo, C.

Choo, C. O.

Colomb, T.

Cong, L.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
[CrossRef]

Coppola, G.

Cuche, E.

De Nicola, S.

Depeursinge, C.

Fang, S.

Ferraro, P.

Finizio, A.

Flynn, T. J.

Furlong, C.

C. Furlong and R. J. Pryputniewics, “Optoelectronic characterization of shape and deformations of MEMS accelerometers used in transportation applications,” Opt. Eng. 42, 1223–1231(2003).
[CrossRef]

Galizzi, G. E.

Ghiglia, D. C.

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

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Grilli, S.

He, G. T.

Y. G. Lu, X. Z. Wang, and G. T. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

Huang, L.

Ivanova, L.

P. Langehanenberg, L. Ivanova, and I. Bernhardt, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Jericho, M. H.

Jin, H. Z.

L. H. Ma, H. Wang, H. Z. Jin, and Y. Li, “Experimental study on quantitative phase imaging by digital holographic microscopy,” Zhongguo Jiguang/Chin. J. Lasers 39, 0309002 (2012).
[CrossRef]

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Partition calculation for zero-order and conjugate image removal in digital in-line holography,” Opt. Express 20, 1805–1815 (2012).
[CrossRef]

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Effect of system parameters on the reconstructed image quality in digital holographic microscopy,” Acta Photonica Sinica 40, 300–306 (2011).
[CrossRef]

Józwik, M.

Kanka, M.

Kaufmann, G. H.

Kemper, B.

Kerr, D.

Komori, M.

Kozacki, T.

Kreuzer, H. J.

Kühn, J.

Langehanenberg, P.

P. Langehanenberg, L. Ivanova, and I. Bernhardt, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

León-Rodríguez, M.

Li, Y.

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Partition calculation for zero-order and conjugate image removal in digital in-line holography,” Opt. Express 20, 1805–1815 (2012).
[CrossRef]

L. H. Ma, H. Wang, H. Z. Jin, and Y. Li, “Experimental study on quantitative phase imaging by digital holographic microscopy,” Zhongguo Jiguang/Chin. J. Lasers 39, 0309002 (2012).
[CrossRef]

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Effect of system parameters on the reconstructed image quality in digital holographic microscopy,” Acta Photonica Sinica 40, 300–306 (2011).
[CrossRef]

Y. Li and X. Su, “Fast algorithm for reliability-guided phase unwrapping,” Opt. Electron. Eng. 32, 76–79 (2005).

Liu, S.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
[CrossRef]

Lizewski, K.

Lu, Y. G.

Y. G. Lu, X. Z. Wang, and G. T. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

Lua, Y. G.

Y. G. Lua, X. Z. Wang, and X. P. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Ma, L. H.

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Partition calculation for zero-order and conjugate image removal in digital in-line holography,” Opt. Express 20, 1805–1815 (2012).
[CrossRef]

L. H. Ma, H. Wang, H. Z. Jin, and Y. Li, “Experimental study on quantitative phase imaging by digital holographic microscopy,” Zhongguo Jiguang/Chin. J. Lasers 39, 0309002 (2012).
[CrossRef]

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Effect of system parameters on the reconstructed image quality in digital holographic microscopy,” Acta Photonica Sinica 40, 300–306 (2011).
[CrossRef]

Magro, C.

Marquet, P.

Meng, L.

Montfort, F.

Pan, F.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
[CrossRef]

Pierattini, G.

Pritt, M. D.

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

Pryputniewics, R. J.

C. Furlong and R. J. Pryputniewics, “Optoelectronic characterization of shape and deformations of MEMS accelerometers used in transportation applications,” Opt. Eng. 42, 1223–1231(2003).
[CrossRef]

Qian, K. M.

Qu, W.

Qu, W. J.

Rayas, J. A.

Riesenberg, R.

Rodríguez-Vera, R.

Schofield, M. A.

Singh, V.

Su, X.

Y. Li and X. Su, “Fast algorithm for reliability-guided phase unwrapping,” Opt. Electron. Eng. 32, 76–79 (2005).

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Su, X. Y.

Wang, F.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
[CrossRef]

Wang, H.

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Partition calculation for zero-order and conjugate image removal in digital in-line holography,” Opt. Express 20, 1805–1815 (2012).
[CrossRef]

L. H. Ma, H. Wang, H. Z. Jin, and Y. Li, “Experimental study on quantitative phase imaging by digital holographic microscopy,” Zhongguo Jiguang/Chin. J. Lasers 39, 0309002 (2012).
[CrossRef]

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Effect of system parameters on the reconstructed image quality in digital holographic microscopy,” Acta Photonica Sinica 40, 300–306 (2011).
[CrossRef]

Wang, L.

Wang, L. J.

Wang, X. Z.

Y. G. Lua, X. Z. Wang, and X. P. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Y. G. Lu, X. Z. Wang, and G. T. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Xiao, W.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
[CrossRef]

Xu, W.

W. Xu, “A region growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

Yang, P.

Yang, P. C.

Yu, Y.

Yu, Y. J.

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Zhang, Q. C.

Zhang, X. P.

Y. G. Lua, X. Z. Wang, and X. P. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Zhao, M.

Zhou, W. S.

Zhu, Y. M.

Acta Photonica Sinica (1)

L. H. Ma, H. Wang, Y. Li, and H. Z. Jin, “Effect of system parameters on the reconstructed image quality in digital holographic microscopy,” Acta Photonica Sinica 40, 300–306 (2011).
[CrossRef]

Appl. Opt. (11)

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
[CrossRef]

T. Colomb, E. Cuche, F. Charriére, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45, 851–863 (2006).
[CrossRef]

J. Arines, “Least-squares modal estimation of wrapped phases: application to phase unwrapping,” Appl. Opt. 42, 3373–3378 (2003).
[CrossRef]

D. Kerr, G. H. Kaufmann, and G. E. Galizzi, “Unwrapping of interferometric phase-fringe maps by the discrete cosine transform,” Appl. Opt. 35, 810–816 (1996).
[CrossRef]

A. Anand and W. S. Zhou, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
[CrossRef]

M. Zhao, L. Huang, Q. C. Zhang, X. Y. Su, A. Asundi, and K. M. Qian, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50, 6214–6224 (2011).
[CrossRef]

M. H. Jericho, H. J. Kreuzer, M. Kanka, and R. Riesenberg, “Quantitative phase and refractive index measurements with point-source digital in-line holographic microscopy,” Appl. Opt. 51, 1503–1515 (2012).
[CrossRef]

B. Kemper and G. v. Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
[CrossRef]

W. J. Qu, C. O. Choo, Y. J. Yu, and A. Asundi, “Microlens characterization by digital holographic microscopy with physical spherical phase compensation,” Appl. Opt. 49, 6448–6454 (2010).
[CrossRef]

S. Fang, L. Meng, L. J. Wang, P. C. Yang, and M. Komori, “Quality-guided phase unwrapping algorithm based on reliability evaluation,” Appl. Opt. 50, 5446–5452 (2011).
[CrossRef]

S. Fang, L. Meng, L. Wang, P. Yang, and M. Komori, “Quality-guided phase unwrapping algorithm based on reliability evaluation,” Appl. Opt. 50, 5446–5452 (2011).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

W. Xu, “A region growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999).
[CrossRef]

J. Biomed. Opt. (1)

P. Langehanenberg, L. Ivanova, and I. Bernhardt, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Electron. Eng. (1)

Y. Li and X. Su, “Fast algorithm for reliability-guided phase unwrapping,” Opt. Electron. Eng. 32, 76–79 (2005).

Opt. Eng. (2)

Y. G. Lu, X. Z. Wang, and G. T. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

C. Furlong and R. J. Pryputniewics, “Optoelectronic characterization of shape and deformations of MEMS accelerometers used in transportation applications,” Opt. Eng. 42, 1223–1231(2003).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (2)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327(2012).
[CrossRef]

Opt. Lett. (3)

Optik (1)

Y. G. Lua, X. Z. Wang, and X. P. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Zhongguo Jiguang/Chin. J. Lasers (1)

L. H. Ma, H. Wang, H. Z. Jin, and Y. Li, “Experimental study on quantitative phase imaging by digital holographic microscopy,” Zhongguo Jiguang/Chin. J. Lasers 39, 0309002 (2012).
[CrossRef]

Other (1)

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

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of transmission digital holographic microscopy. NF, neutral density filter; BS, beam splitter; BE, beam expander with spatial filter; L, collimating lens; M, mirror; MO, microscopic objective.

Fig. 2.
Fig. 2.

Schematic diagram of the implementation of the proposed method.

Fig. 3.
Fig. 3.

Experimental setup for transmission digital holographic microscopy.

Fig. 4.
Fig. 4.

Experimental results of red blood cells. (a) Image-plane digital hologram, (b) reconstructed intensity image, (c) wrapped phase map, (d) optimized intensity parameter map, (e) 2D map of unwrapped image, and (f) 3D map of unwrapped image.

Fig. 5.
Fig. 5.

2D map of unwrapped image (a) with Diamond algorithm, (b) with Goldstein’s branch cut algorithm, (c) with the conventional flood fill algorithm with intensity image quality map.

Fig. 6.
Fig. 6.

Experimental results of phase-type sinusoidal grating. (a) Image-plane digital hologram, (b) wrapped phase map, (c) 2D map of unwrapped image, and (d) 3D map of unwrapped image.

Fig. 7.
Fig. 7.

2D map of unwrapped image (a) with diamond algorithm, (b) with Goldstein’s branch cut algorithm, (c) with the conventional flood fill algorithm with intensity image quality map.

Tables (1)

Tables Icon

Table 1. Comparison of Phase Unwrapping Time for Different Algorithms for 512×512 Array Size on a Personal Computer [Intel(R) core E7300, RAM 3.0 GB] with Windows XP Pro

Equations (6)

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

I(xH,yH)=|R(xH,yH)+O(xH,yH)|2=|R(xH,yH)|2+|O(xH,yH)|2+R*(xH,yH)O(xH,yH)+R(xH,yH)O*(xH,yH).
IC(xH,yH)=R(xH,yH)O*(xH,yH).
UH(xH,yH)=RD(xH,yH)IC(xH,yH)=RD(xH,yH)R(xH,yH)O*(xH,yH).
I(xi,yi)=|U(xi,yi)|2,
φ(xi,yi)=arctan[ImU(xi,yi)ReU(xi,yi)],
s(i,j)=[(φ(i,j+1)φ(i,j))/2π]+[(φ(i,j)φ(i+1,j))/2π]+[(φ(i+1,j)φ(i+1,j+1))/2π]+[(φ(i+1,j+1)φ(i,j+1))/2π],

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