Abstract

The paper presents a novel algorithm based on digital holographic interferometry and being promising for evaluation of phase variations from highly noisy or modulated by speckle-structures digital holograms. The suggested algorithm simulates an interferogram in finite width fringes, by analogy with classical double exposure holographic interferometry. Thus obtained interferogram is then processed as a digital hologram. The advantages of the suggested approach are demonstrated in numerical experiments on calculations of differences in phase distributions of wave fronts modulated by speckle structure, as well as in a physical experiment on the analysis of laser-induced heating dynamics of an aqueous solution of a photosensitizer. It is shown that owing to the inherent capability of the approach to perform adjustable smoothing of compared wave fronts, the resulting difference undergoes noise filtering. This capability of adjustable smoothing may be used to minimize losses in spatial resolution. Since the method allows to vary an observation angle of compared wave fields, an opportunity to compensate misalignment of optical axes of these wave fronts arises. This feature can be required, for example, when using two different setups in comparative digital holography or for compensation of recording system displacements during a set of exposures in studies of dynamic processes.

© 2014 Optical Society of America

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References

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2013 (1)

2011 (1)

D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Four-dimensional visualization of single and multiple laser filaments using in-line holographic microscopy,” Phys. Rev. A 84, 053809 (2011).
[Crossref]

2010 (1)

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49, 125801 (2010).
[Crossref]

2009 (3)

2008 (2)

J.-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471–5480 (2008).
[Crossref] [PubMed]

D. Papazoglou and S. Tzortzakis, “In-line holography for the characterization of ultrafast laser filamentation in transparent media,” Appl. Phys. Lett. 93, 041120 (2008).
[Crossref]

2006 (1)

2005 (2)

2004 (2)

2003 (2)

2002 (1)

1999 (3)

1996 (1)

U. Schnars, T. M. Kreis, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[Crossref]

1994 (2)

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Laser Eng. 21, 199–239 (1994).
[Crossref]

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
[Crossref]

1990 (1)

1988 (1)

1986 (1)

1982 (1)

Abdollahpour, D.

D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Four-dimensional visualization of single and multiple laser filaments using in-line holographic microscopy,” Phys. Rev. A 84, 053809 (2011).
[Crossref]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Comm. 162, 205–210 (1999).
[Crossref]

Alexeenko, I.

Almazan-Cuellar, S.

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524–3531 (2003).
[Crossref]

Baumbach, T.

Berns, M. W.

Bioucas-Dias, J.

V. Katkovnik, J. Bioucas-Dias, and N. Petrov, “Digital phase-shifting holography based on sparse approximation of phase and amplitude,” in ”3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 2014,” (2014), pp. 1–4.

Blu, T.

Bryanston-Cross, P. J.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Laser Eng. 21, 199–239 (1994).
[Crossref]

Chen, Z.

Colomb, T.

Coppola, G.

Cuche, E.

Depeursinge, C.

Desse, J.-M.

Dudenkova, V. V.

Emery, Y.

Ferraro, P.

Finizio, A.

Fröning, P.

Fu, S.

Genc, S.

Grilli, S.

Gurevich, V.

Gusev, M.

Gusev, M. E.

Ina, H.

Judge, T. R.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Laser Eng. 21, 199–239 (1994).
[Crossref]

Jüptner, W.

Jüptner, W. P. O.

U. Schnars, T. M. Kreis, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[Crossref]

Katkovnik, V.

V. Katkovnik, J. Bioucas-Dias, and N. Petrov, “Digital phase-shifting holography based on sparse approximation of phase and amplitude,” in ”3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 2014,” (2014), pp. 1–4.

Kerr, D.

Kim, M.

Kim, M. K.

Kobayashi, S.

Kreis, T.

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49, 125801 (2010).
[Crossref]

T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
[Crossref]

Kreis, T. M.

U. Schnars, T. M. Kreis, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[Crossref]

Liebling, M.

Liu, X.

Lo, C.-M.

Magistretti, P. J.

Magro, C.

Malacara-Hernandez, D.

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524–3531 (2003).
[Crossref]

Mann, C.

Marquet, P.

Mohanty, S.

Mundt, J.

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49, 125801 (2010).
[Crossref]

Muraveva, M. S.

Nicola, S. D.

Osten, W.

Papazoglou, D.

D. Papazoglou and S. Tzortzakis, “In-line holography for the characterization of ultrafast laser filamentation in transparent media,” Appl. Phys. Lett. 93, 041120 (2008).
[Crossref]

Papazoglou, D. G.

D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Four-dimensional visualization of single and multiple laser filaments using in-line holographic microscopy,” Phys. Rev. A 84, 053809 (2011).
[Crossref]

Pedrini, G.

Petrov, N.

V. Katkovnik, J. Bioucas-Dias, and N. Petrov, “Digital phase-shifting holography based on sparse approximation of phase and amplitude,” in ”3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 2014,” (2014), pp. 1–4.

Picart, P.

Pierattini, G.

Rappaz, B.

Rybnikov, A. I.

Santoyo, F. M.

Schedin, S.

Schnars, U.

U. Schnars, T. M. Kreis, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[Crossref]

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
[Crossref]

Sun, X.

Takeda, M.

Tankam, P.

Tiziani, H. J.

Tyrer, J. R.

Tzortzakis, S.

D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Four-dimensional visualization of single and multiple laser filaments using in-line holographic microscopy,” Phys. Rev. A 84, 053809 (2011).
[Crossref]

D. Papazoglou and S. Tzortzakis, “In-line holography for the characterization of ultrafast laser filamentation in transparent media,” Appl. Phys. Lett. 93, 041120 (2008).
[Crossref]

Unser, M.

Vest, C. M.

C. M. Vest, Holographic Interferometry, 1st ed. (Wiley-Interscience, 1979), Chap. 1.

von Kopylow, C.

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Comm. 162, 205–210 (1999).
[Crossref]

Yamaguchi, I.

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[Crossref]

Yang, X.

Yokota, M.

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[Crossref]

Yu, L.

Yu, Q.

Zakharov, Y. N.

Zhang, J.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

D. Papazoglou and S. Tzortzakis, “In-line holography for the characterization of ultrafast laser filamentation in transparent media,” Appl. Phys. Lett. 93, 041120 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Opt. Technol. (1)

Opt. Comm. (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Comm. 162, 205–210 (1999).
[Crossref]

Opt. Eng. (4)

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[Crossref]

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524–3531 (2003).
[Crossref]

J. Mundt and T. Kreis, “Digital holographic recording and reconstruction of large scale objects for metrology and display,” Opt. Eng. 49, 125801 (2010).
[Crossref]

U. Schnars, T. M. Kreis, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[Crossref]

Opt. Express (4)

Opt. Laser Eng. (1)

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Laser Eng. 21, 199–239 (1994).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Four-dimensional visualization of single and multiple laser filaments using in-line holographic microscopy,” Phys. Rev. A 84, 053809 (2011).
[Crossref]

Other (2)

C. M. Vest, Holographic Interferometry, 1st ed. (Wiley-Interscience, 1979), Chap. 1.

V. Katkovnik, J. Bioucas-Dias, and N. Petrov, “Digital phase-shifting holography based on sparse approximation of phase and amplitude,” in ”3DTV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 2014,” (2014), pp. 1–4.

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Figures (6)

Fig. 1
Fig. 1

Sequence of operations aimed for calculations of phase distributions difference without prior unwrapping. Recorded holograms (a, b); reconstructed amplitude (c, e, g) and phase (d, f, h) distributions for the first object wave (c, d), reference wave (e, f) and the second object wave (g, h); simulated phase distribution for the reference wave incoming onto photodetector at the angle α + β (j); interference pattern I3 obtained as a result of interaction of the first object wave with the synthesized reference wave (i); result of multiplication of two trigonometric functions responsible for interference fringes in intensity distributions I2 and I3 (k); normalized interferogram for two object waves A and B, recorded at the angle β (l); sought phase difference (m).

Fig. 2
Fig. 2

Experimental setups used for digital holograms recording by means of DH (a) and DHM (b). 1 - laser, 2 - beam expander, 3 - beamsplitters, 4 - mirrors, 5 - object, 6 - lenses (comprising a bitelecentric system (a); or a condenser lens (b)), 7 - photodetector array, 8 -microlens (b).

Fig. 3
Fig. 3

Spatial phase distributions: undisturbed (a), and after disturbance (b); spatial distribution of the sought disturbance (c); interference pattern containing information on the undisturbed and disturbed phase difference (d) and phase distributions obtained from it: wrapped (e) and after unwrapping (f); cross-sections of phase distributions drawn across the black horizontal line shown on the interferogram (f), the reconstructed distribution is depicted by the solid line, the given initial distribution is depicted by the dashed line.

Fig. 4
Fig. 4

Spatial phase difference of two wavefronts obtained from a noisy hologram by means of different methods: of direct wavefronts division (a–c) with filtering performed by multiple consecutive application of the sin–cos (a); method (a); by reconstruction of recorded holograms with the processing window size equal to 8 (b) and 24 (c); and using the suggested method (d).

Fig. 5
Fig. 5

Misalignment of optical axes at two exposures may be caused by two factors. Top row: angular misalignment: optical axes may be inclined to each other at some angle (a); two identical phase distributions with a small angle between them (b), result of their subtraction without correction (c) Bottom row: lateral misalignment: optical axes may be shifted relative to each other (d). The result of application of the method of tangent arguments difference for detection of wave fields modulated by speckle structures causes singular points on the differential phase distribution (e). An application of the algorithm of simulated digital interferogram allows to eliminate these drawbacks (f).

Fig. 6
Fig. 6

Holograms recorded before (a) and after (b) the illumination of the aqueous solution of the photosensitizer by the excitation laser (c). Reconstructed spatial phase distributions in the area designated by the green rectangle in the image (b): before heating by the excitation laser (a), and on the 8th second of the heating process (b); spatial distributions of phase difference in the range (−π, π) obtained using: the suggested algorithm (f), direct wavefront dividing (g), direct wavefront dividing with sin-cos filtration (h) and direct wavefront dividing after holograms reconstruction with the processing window of 32 × 32 pixels (i). Phase difference calculated using direct wavefronts dividing: before (g) and after sin-cos filtration (h). Comparison of cross sections of phase distributions obtained by these algorithms (j). Phase distribution in absolute values (h) obtained as a result of deconvolution of the phase distribution (f).

Equations (12)

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

A = | A | exp ( i φ ) = Re A + i Im A ,
B = | B | exp ( i ( φ + ε ) ) = Re B + i Im B ,
ε = arg ( X ) .
X = A B = Re B Re A + Im B Im A ( Re A ) 2 + ( Im A ) 2 + Im B Re A Re B Im A ( Re A ) 2 + ( Im A ) 2 i ,
ε = arctan Im B Re A Re B Im A Re B Re A + Im B Im A .
I 1 = | A | 2 + | C | 2 + 2 | A | | C | cos ( φ γ α ) ,
I 2 = | B | 2 + | C | 2 + 2 | B | cos ( ϕ γ α ) .
I 3 = | A | 2 + | C | 2 + 2 | A | | C | cos ( φ ( γ α + θ β ) )
cos ( ϕ γ α ) cos ( φ ( γ α + θ β ) ) = cos ( ( ϕ φ ) + θ β ) 2 + cos ( ϕ + φ 2 γ α θ β ) 2 ,
cos ( ϕ γ α ) = I 2 | B | 2 | C | 2 2 | B | | C |
cos ( ( γ α + θ β ) ) = I 3 | A | 2 | C | 2 2 | A | | C | .
I 4 = | A + B | 2 + | C | 2 + 2 | A + B | | C | cos ( ε + θ β )

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