Abstract

A phase unwrapping approach based on multiple-wavelength scanning is presented for digital holographic microscopy. It unwrapped the ambiguous phase image layer by layer by synthesizing the extracted continuous components from a set of multiple phase images obtained by varying the optical wavelength, where the discontinuities occur at different places and the phase speckle noise presents various distributions in state. The total time for data acquisition is approximately 22 min for 10 wavelengths. The simulation and experimental results demonstrate that the proposed method has a more accurate calculation and better counteraction of phase noise compared with those of previously reported approaches. In addition, the wrapped phase image of the object containing the steps has also been unwrapped successfully.

© 2014 Optical Society of America

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  1. B. Kemper and G. Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
    [CrossRef]
  2. M. M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
    [CrossRef]
  3. S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
    [CrossRef]
  4. F. Charrière, J. Kühn, T. Colomb, F. Montfort, and E. Cuche, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45, 829–835 (2006).
    [CrossRef]
  5. N. Demoli, “Real-time monitoring of vibration fringe patterns by optical reconstruction of digital holograms: mode beating detection,” Opt. Express 14, 2117–2122 (2006).
    [CrossRef]
  6. J. Gass, A. Dakoff, and M. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
    [CrossRef]
  7. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [CrossRef]
  8. D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49, 609–617 (2011).
    [CrossRef]
  9. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  10. C. Quan, C. J. Tay, L. Chen, and Y. Fu, “Spatial-fringe-modulation-based quality map for phase unwrapping,” Appl. Opt. 42, 7060–7065 (2003).
    [CrossRef]
  11. S. Liu, W. Xiao, F. Pang, F. J. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50, 322–327 (2012).
    [CrossRef]
  12. T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” Proceedings of the 1996 International Geoscience and Remote Sensing Symposium (IEEE, 1996), Vol. 4, pp. 2057–2059.
  13. A. Baldi, “Phase unwrapping by region growing,” Appl. Opt. 42, 2498–2505 (2003).
    [CrossRef]
  14. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994).
    [CrossRef]
  15. A. Khmaladze, T. Epstein, and Z. Chen, “Phase unwrapping by varying the reconstruction distance in digital holographic microscopy,” Opt. Lett. 35, 1040–1042 (2010).
    [CrossRef]
  16. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef]
  17. D. Parshall and M. Kim, “Digital holographic microscopy with dual-wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
    [CrossRef]
  18. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007).
    [CrossRef]
  19. N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express 15, 9239–9247 (2007).
    [CrossRef]
  20. A. Wada, M. Kato, and Y. Ishii, “Multiple-wavelength digital holographic interferometry using tunable laser diodes,” Appl. Opt. 47, 2053–2059 (2008).
    [CrossRef]
  21. D. Carl, M. Fratz, M. Pfeifer, D. M. Giel, and H. Höfler, “Multiwavelength digital holography with autocalibration of phase shifts and artificial wavelengths,” Appl. Opt. 48, H1–H8 (2009).
    [CrossRef]
  22. A. Khmaladze, M. Kim, and C.-M. Lo, “Phase imaging of cells by simultaneous dual-wavelength reflection digital holography,” Opt. Express 16, 10900–10910 (2008).
    [CrossRef]
  23. A. Khmaladze, A. Restrepo-Martínez, M. Kim, R. Castañeda, and A. Blandón, “Simultaneous dual-wavelength reflection digital holography applied to the study of the porous coal samples,” Appl. Opt. 47, 3203–3209 (2008).
    [CrossRef]
  24. C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16, 9753–9764 (2008).
    [CrossRef]
  25. E. Cuche, P. Marquet, and C. Depursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
    [CrossRef]
  26. S. De Nicola, A. Finizio, and G. Pierattini, “Recovering correct phase information in multiwavelength digtial holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
    [CrossRef]
  27. N. Pandey and B. Hennelly, “Effect of additive noise on phase measurement in digital holographic microscopy,” 3D Res. 2, 1–6 (2011).
    [CrossRef]

2012

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

2011

N. Pandey and B. Hennelly, “Effect of additive noise on phase measurement in digital holographic microscopy,” 3D Res. 2, 1–6 (2011).
[CrossRef]

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49, 609–617 (2011).
[CrossRef]

2010

2009

2008

2007

2006

2005

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

S. De Nicola, A. Finizio, and G. Pierattini, “Recovering correct phase information in multiwavelength digtial holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
[CrossRef]

2003

2000

1994

1988

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

1987

Allano, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Baldi, A.

Bally, G.

Bingham, P. R.

Blandón, A.

Carl, D.

Castañeda, R.

Cen, K. F.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Charrière, F.

Chen, L.

Chen, Z.

Colomb, T.

Cong, L.

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

Creath, K.

Cuche, E.

Da, F.

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49, 609–617 (2011).
[CrossRef]

Dakoff, A.

De Nicola, S.

Demoli, N.

Depeursinge, C.

Depursinge, C.

Emery, Y.

Epstein, T.

Finizio, A.

Flynn, T. J.

T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” Proceedings of the 1996 International Geoscience and Remote Sensing Symposium (IEEE, 1996), Vol. 4, pp. 2057–2059.

Fratz, M.

Fu, Y.

Gass, J.

Ghiglia, D. C.

Giel, D. M.

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]

Hennelly, B.

N. Pandey and B. Hennelly, “Effect of additive noise on phase measurement in digital holographic microscopy,” 3D Res. 2, 1–6 (2011).
[CrossRef]

Höfler, H.

Hossain, M. M.

Ishii, Y.

Kato, M.

Kemper, B.

Khmaladze, A.

Kim, M.

Kim, M. K.

Kühn, J.

Lebrun, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Liu, S.

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

Lo, C.-M.

Malek, M.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Mann, C. J.

Marquet, P.

Montfort, F.

Pandey, N.

N. Pandey and B. Hennelly, “Effect of additive noise on phase measurement in digital holographic microscopy,” 3D Res. 2, 1–6 (2011).
[CrossRef]

Pang, F.

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

Paquit, V. C.

Parshall, D.

Patte-Rouland, B.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Pfeifer, M.

Pierattini, G.

Pritt, M. D.

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

Pu, S. L.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

Quan, C.

Restrepo-Martínez, A.

Romero, L. A.

Shakher, C.

Tay, C. J.

Tobin, K. W.

Wada, A.

Wang, F. J.

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

Warnasooriya, N.

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

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]

Zheng, D.

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49, 609–617 (2011).
[CrossRef]

3D Res.

N. Pandey and B. Hennelly, “Effect of additive noise on phase measurement in digital holographic microscopy,” 3D Res. 2, 1–6 (2011).
[CrossRef]

Appl. Opt.

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef]

E. Cuche, P. Marquet, and C. Depursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

A. Baldi, “Phase unwrapping by region growing,” Appl. Opt. 42, 2498–2505 (2003).
[CrossRef]

D. Parshall and M. Kim, “Digital holographic microscopy with dual-wavelength phase unwrapping,” Appl. Opt. 45, 451–459 (2006).
[CrossRef]

F. Charrière, J. Kühn, T. Colomb, F. Montfort, and E. Cuche, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45, 829–835 (2006).
[CrossRef]

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

A. Wada, M. Kato, and Y. Ishii, “Multiple-wavelength digital holographic interferometry using tunable laser diodes,” Appl. Opt. 47, 2053–2059 (2008).
[CrossRef]

A. Khmaladze, A. Restrepo-Martínez, M. Kim, R. Castañeda, and A. Blandón, “Simultaneous dual-wavelength reflection digital holography applied to the study of the porous coal samples,” Appl. Opt. 47, 3203–3209 (2008).
[CrossRef]

C. Quan, C. J. Tay, L. Chen, and Y. Fu, “Spatial-fringe-modulation-based quality map for phase unwrapping,” Appl. Opt. 42, 7060–7065 (2003).
[CrossRef]

M. M. Hossain and C. Shakher, “Temperature measurement in laminar free convective flow using digital holography,” Appl. Opt. 48, 1869–1877 (2009).
[CrossRef]

D. Carl, M. Fratz, M. Pfeifer, D. M. Giel, and H. Höfler, “Multiwavelength digital holography with autocalibration of phase shifts and artificial wavelengths,” Appl. Opt. 48, H1–H8 (2009).
[CrossRef]

Exp. Fluids

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lasers Eng.

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

D. Zheng and F. Da, “A novel algorithm for branch cut phase unwrapping,” Opt. Lasers Eng. 49, 609–617 (2011).
[CrossRef]

Opt. Lett.

Radio Sci.

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

Other

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

T. J. Flynn, “Consistent 2-D phase unwrapping guided by a quality map,” Proceedings of the 1996 International Geoscience and Remote Sensing Symposium (IEEE, 1996), Vol. 4, pp. 2057–2059.

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Figures (10)

Fig. 1.
Fig. 1.

Phase unwrapping by varying the illumination wavelength.

Fig. 2.
Fig. 2.

Simulated results: (a) and (b) the amplitude image and phase image of simulated object wave, respectively; (c) and (d) the amplitude image and wrapped phase image with noise corruption (L=0.1), respectively. All of them are 1024×1024 pixels of size 6.7μm×6.7μm.

Fig. 3.
Fig. 3.

MWS unwrapping: (a)–(d) various stages of unwrapping; (e) 3D pseudocolor rendering of the unwrapped phase image in (d); and (f) phase distributions and corresponding calculated height values of the black line scan indicated in (d).

Fig. 4.
Fig. 4.

Quality map-guided unwrapping based on the PDV: (a) unwrapped phase image; (b) 3D pseudocolor rendering of the unwrapped phase image in (a); and (c) phase distributions and corresponding calculated height values of the black line scan indicated in (a).

Fig. 5.
Fig. 5.

Standard deviation of the phase distribution associated with the methods based on MWS and the quality-guided method based on the PDV map when noise level L=0.1,0.2,1.

Fig. 6.
Fig. 6.

Schematic diagram of the experimental setup. The inset is a detailed diagram of off-axis geometry. M, mirror; HWP, half-wave plate; PBS, polarizing beam splitter; BE, beam expander with spatial filter; MO, microscope objective (4×, NA=0.1); S, sample; O, object wave; R, reference wave; BS, beam splitter; α, incidence angle between the reference wave and object wave.

Fig. 7.
Fig. 7.

Measurement results obtained from WLI: (a) 3D surface and (b) cross-section profile obtained from (a).

Fig. 8.
Fig. 8.

Experimental results for microlens array with continuous profile distribution: (a) digital hologram at λ is 642.0 nm; (b), (c) reconstructed amplitude image and wrapped phase image, respectively; (d) unwrapped phase image by MWS; (e) unwrapped phase image by PDV; (f), (g) phase values and corresponding calculated height distributions of the black line scan indicated in (d) and (e), respectively; (h), (i) 3D pseudocolor rendering of the unwrapped phase images in (d) and (e), respectively.

Fig. 9.
Fig. 9.

Measurement results obtained from WLI: (a) 3D surface and (b) cross-section profile obtained from (a).

Fig. 10.
Fig. 10.

Experiment results for microlens array with the profile containing steps: (a) digital hologram at λ is 642.0 nm; (b), (c) reconstructed amplitude image and wrapped phase image, respectively; (d) unwrapped phase image by MWS; (e) unwrapped phase image by PDV; (f), (g) phase values and corresponding calculated height distributions of the black line scan indicated in (d) and (e), respectively; (h), (i) 3D pseudocolor rendering of the unwrapped phase images in (d) and (e), respectively.

Equations (3)

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h(xo,yo)=λ14πϕ1(xo,yo)+N1(xo,yo)·λ12=λ24πϕ2(xo,yo)+N2(xo,yo)·λ22=λn4πϕn(xo,yo)+Nn(xo,yo)·λn2,
ϕm(xo,yo)=λ1λmϕ1(xo,yo)+2π[λ1λmN1(xo,yo)Nm(xo,yo)].
U(xo,yo)=o(xo,yo)+r(xo,yo)=Ao(xo,yo)exp[jϕo(xo,yo)]+L{Rr(xo,yo)+jIr(xo,yo)},

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