Abstract

Digital holography is a convenient method for determining the phase induced by transparent objects. When the phase change is higher than 2π, an unwrapping algorithm is needed to provide a useful phase map. In the presence of noise, this process is not trivial and not fully resolved. In this paper a procedure is proposed to circumvent the need for unwrapping by estimating the phase from its gradient, which is directly computed from the reconstructed field. Application of the method to digital holograms of microscopic samples is demonstrated.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  17. A. Agrawal, R. Raskar, and R. Chellappa, “What Is the Range of Surface Reconstructions from a Gradient Field?” in Computer Vision – ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Lecture Notes in Computer Science (Springer Berlin Heidelberg, 2006), Vol. 3951, pp. 578–591.

2014 (1)

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (1)

2011 (1)

2009 (1)

2005 (1)

2004 (1)

C. Vérinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun. 233(1-3), 27–38 (2004).
[Crossref]

2003 (1)

2000 (1)

1999 (1)

1996 (1)

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Opt. 43(2), 289–293 (1996).
[Crossref]

Andrés, P.

Barbastathis, G.

Bevilacqua, F.

Chen, Z.

Colomb, T.

Cuche, E.

Dakoff, A.

Depeursinge, C.

Doblas, A.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, P. Andrés, and J. Garcia-Sucerquia, “Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging,” Opt. Lett. 38(8), 1352–1354 (2013).
[Crossref] [PubMed]

Emery, Y.

Garcia-Sucerquia, J.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, P. Andrés, and J. Garcia-Sucerquia, “Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging,” Opt. Lett. 38(8), 1352–1354 (2013).
[Crossref] [PubMed]

Gass, J.

Gorthi, S. S.

Huang, H. Y. H.

Iglesias, I.

I. Iglesias and F. Vargas-Martin, “Quantitative phase microscopy of transparent samples using a liquid crystal display,” J. Biomed. Opt. 18(2), 026015 (2013).
[Crossref] [PubMed]

I. Iglesias, “Pyramid phase microscopy,” Opt. Lett. 36(18), 3636–3638 (2011).
[Crossref] [PubMed]

Kim, M. K.

Li, H.

Liu, Y.

Magistretti, P. J.

Marquet, P.

Martínez-Corral, M.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, P. Andrés, and J. Garcia-Sucerquia, “Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging,” Opt. Lett. 38(8), 1352–1354 (2013).
[Crossref] [PubMed]

Ragazzoni, R.

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Opt. 43(2), 289–293 (1996).
[Crossref]

Rajshekhar, G.

Rappaz, B.

Rastogi, P.

Saavedra, G.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, P. Andrés, and J. Garcia-Sucerquia, “Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging,” Opt. Lett. 38(8), 1352–1354 (2013).
[Crossref] [PubMed]

Sánchez-Ortiga, E.

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, P. Andrés, and J. Garcia-Sucerquia, “Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging,” Opt. Lett. 38(8), 1352–1354 (2013).
[Crossref] [PubMed]

Tian, L.

Vargas-Martin, F.

I. Iglesias and F. Vargas-Martin, “Quantitative phase microscopy of transparent samples using a liquid crystal display,” J. Biomed. Opt. 18(2), 026015 (2013).
[Crossref] [PubMed]

Vérinaud, C.

C. Vérinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun. 233(1-3), 27–38 (2004).
[Crossref]

Zhang, Z.

Zhou, Y.

Appl. Opt. (1)

J. Biomed. Opt. (2)

I. Iglesias and F. Vargas-Martin, “Quantitative phase microscopy of transparent samples using a liquid crystal display,” J. Biomed. Opt. 18(2), 026015 (2013).
[Crossref] [PubMed]

A. Doblas, E. Sánchez-Ortiga, M. Martínez-Corral, G. Saavedra, and J. Garcia-Sucerquia, “Accurate single-shot quantitative phase imaging of biological specimens with telecentric digital holographic microscopy,” J. Biomed. Opt. 19(4), 046022 (2014).
[Crossref] [PubMed]

J. Mod. Opt. (1)

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Opt. 43(2), 289–293 (1996).
[Crossref]

Opt. Commun. (1)

C. Vérinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun. 233(1-3), 27–38 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (7)

SPIE Rev. (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2013).

Other (3)

R. Tyson, Principles of Adaptive Optics, Third Edition, Edición: 3 (CRC, 2010).

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in Computer Vision,2005. ICCV 2005. Tenth IEEE International Conference on (IEEE, 2005), Vol. 1, pp. 174–181.
[Crossref]

A. Agrawal, R. Raskar, and R. Chellappa, “What Is the Range of Surface Reconstructions from a Gradient Field?” in Computer Vision – ECCV 2006, A. Leonardis, H. Bischof, and A. Pinz, eds., Lecture Notes in Computer Science (Springer Berlin Heidelberg, 2006), Vol. 3951, pp. 578–591.

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Figures (2)

Fig. 1
Fig. 1 (a) Scheme of the data organization; (b) Response, m' , to a constant phase ramp with slope m.
Fig. 2
Fig. 2 (a) The modulus and (b) the phase of the reconstructed field of a digital hologram of a sample of human RBCs. (c) The modulus of the Fourier transform corresponding to the region marked I in (a) and the corresponding gradient x-component (upper inset) and y-component (bottom inset). (d) Normalized representation of the phase, corresponding to the equally labeled ROIs in (a). (e) The modulus of the reconstruction of the digital hologram of a slice of a Drosophila head and the corresponding phase, (f), and the integrated phase (g) for the marked ROIs. The color scale is valid for all the contour plots.

Equations (6)

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

U( m 2 )=FFT[ u H ( m 1 ) ]
U i (s,t) ( p i ) i=A,B,C,D
p i =( p i , q i ) i=A,B,C,D
p A [ 1,M/2 ]; q A [ 1,M/2 ] p B [ 1+M/2 ,M ]; q B [ 1,M/2 ] p C [ 1,M/2 ]; q C [ 1+M/2 ,M ] p D [ 1+M/2 ,M ]; q D [ 1+M/2 ,M ]
u i (s,t) ( v 1 )= FFT 1 [ U i (s,t) ( p i ) ] i=A,B,C,D
g x ( v 1 )=γ ( ( ( s,t ) | u A (s,t) | 2 + ( s,t ) | u B (s,t) | 2 )( ( s,t ) | u C (s,t) | 2 + ( s,t ) | u D (s,t) | 2 ) ) / i ( s,t ) | u i (s,t) | 2 g y ( v 1 )=γ ( ( ( s,t ) | u A (s,t) | 2 + ( s,t ) | u C (s,t) | 2 )( ( s,t ) | u B (s,t) | 2 + ( s,t ) | u D (s,t) | 2 ) ) / i ( s,t ) | u i (s,t) | 2

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