Abstract

In phase-shifting digital holographic microscopy (PS-DHM), the reconstructed phase map is obtained after processing several holograms of the same scene with a phase shift between them. Most of the reconstruction algorithms in PS-DHM require an accurate and known phase shift between the recorded holograms. This requirement limits the applicability of the method. To ease the use of PS-DHM, this paper presents an iterative-blind phase shift extraction method based on demodulation of the different components of the recorded holograms. The method uses a DHM system operating in a slightly off-axis architecture. The proposed method uses three-frame holograms with arbitrary and unequal phase shifts between them and therefore eases the use of the PS-DHM. We believe both simulated and experimental results demonstrate the goodness and feasibility of the proposed technique.

© 2019 Optical Society of America

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References

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    [Crossref]
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2019 (1)

G. A. Ayubi, I. Duarte, and J. A. Ferrari, “Optimal phase-shifting algorithm for interferograms with arbitrary steps and phase noise,” Opt. Lasers Eng. 114, 129–135 (2019).
[Crossref]

2017 (2)

D. Xie, D. Zhao, Y. Yang, and H. Zhai, “Phase-shift extraction algorithm for blind phase-shifting holography based on the quotient of inner products,” Opt. Commun. 393, 40–44 (2017).
[Crossref]

C. Meneses-Fabian and N. Tejeda-Muñoz, “Self-calibrating phase-shifting interferometry of three unequal phase steps by fitting background light to a polynomial of degree K,” Appl. Opt. 56, 4278–4283 (2017).
[Crossref]

2016 (1)

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

2014 (2)

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, 046022 (2014).
[Crossref]

E. Sánchez-Ortiga, A. Doblas, G. Saavedra, M. Martínez-Corral, and J. Garcia-Sucerquia, “Off-axis digital holographic microscopy: practical design parameters for operating at diffraction limit,” Appl. Opt. 53, 2058–2066 (2014).
[Crossref]

2013 (3)

2012 (1)

2010 (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 18005 (2010).
[Crossref]

2007 (3)

H. Guo, Y. Yu, and M. Chen, “Blind phase shift estimation in phase-shifting interferometry,” J. Opt. Soc. Am. A 24, 25–33 (2007).
[Crossref]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

P. Slangen and B. Gautier, “Nematic liquid crystal light valve: application to phase shifting speckle interferometry,” Proc. SPIE 6616, 66162U (2007).

2006 (1)

2002 (2)

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[Crossref]

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[Crossref]

2000 (1)

1997 (1)

1988 (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

Andrés, P.

Arévalo Aguilar, L. M.

Ayubi, G. A.

G. A. Ayubi, I. Duarte, and J. A. Ferrari, “Optimal phase-shifting algorithm for interferograms with arbitrary steps and phase noise,” Opt. Lasers Eng. 114, 129–135 (2019).
[Crossref]

Cai, L. Z.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[Crossref]

Chen, M.

Chen, Q.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Cherel, L.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[Crossref]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

Cuche, E.

De Nicola, S.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[Crossref]

Depeursinge, C.

Doblas, A.

Dong, G. Y.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[Crossref]

Duarte, I.

G. A. Ayubi, I. Duarte, and J. A. Ferrari, “Optimal phase-shifting algorithm for interferograms with arbitrary steps and phase noise,” Opt. Lasers Eng. 114, 129–135 (2019).
[Crossref]

Ferrari, J. A.

G. A. Ayubi, I. Duarte, and J. A. Ferrari, “Optimal phase-shifting algorithm for interferograms with arbitrary steps and phase noise,” Opt. Lasers Eng. 114, 129–135 (2019).
[Crossref]

Ferraro, P.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[Crossref]

Finizio, A.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[Crossref]

Garcia, J.

Garcia-Sucerquia, J.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, 1978).

Gautier, B.

P. Slangen and B. Gautier, “Nematic liquid crystal light valve: application to phase shifting speckle interferometry,” Proc. SPIE 6616, 66162U (2007).

Gu, H.

F. Zeng, H. Gu, and Q. Tan, “Application of the blind signal separation method for phase-shifting interferometry with random phase shifts,” Proc. SPIE 9046, 90460R (2013).
[Crossref]

Guerrero-Sánchez, F.

Guo, H.

Hou, X.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Ixba-Santos, V.

Juarez-Salazar, R.

Kim, M. K.

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 18005 (2010).
[Crossref]

Kothiyal, M.

R. Sirohi and M. Kothiyal, Optical Components, Systems, and Measurement Techniques, 1st ed. (Marcel Dekker, 1991).

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley, 2004).

Li, J.-C.

P. Picart and J.-C. Li, Digital Holography (Wiley, 2012).

Liu, F.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Marquet, P.

Martínez-Corral, M.

Meneses-Fabian, C.

Meng, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[Crossref]

Micó, V.

Patorski, K.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Picart, P.

P. Picart and J.-C. Li, Digital Holography (Wiley, 2012).

Pierattini, G.

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[Crossref]

Popescu, G.

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

Robledo-Sanchez, C.

Rodriguez-Zurita, G.

Roy, M.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[Crossref]

Saavedra, G.

Sánchez-Ortiga, E.

Shen, X. X.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[Crossref]

Sheppard, C. J. R.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[Crossref]

Sirohi, R.

R. Sirohi and M. Kothiyal, Optical Components, Systems, and Measurement Techniques, 1st ed. (Marcel Dekker, 1991).

Slangen, P.

P. Slangen and B. Gautier, “Nematic liquid crystal light valve: application to phase shifting speckle interferometry,” Proc. SPIE 6616, 66162U (2007).

Svahn, P.

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[Crossref]

Tan, Q.

F. Zeng, H. Gu, and Q. Tan, “Application of the blind signal separation method for phase-shifting interferometry with random phase shifts,” Proc. SPIE 9046, 90460R (2013).
[Crossref]

Tejeda-Muñoz, N.

Trusiak, M.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Wan, Y.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Wang, J.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Wang, Y. R.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

Wu, F.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Wu, Y.

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

Xie, D.

D. Xie, D. Zhao, Y. Yang, and H. Zhai, “Phase-shift extraction algorithm for blind phase-shifting holography based on the quotient of inner products,” Opt. Commun. 393, 40–44 (2017).
[Crossref]

Xu, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006).
[Crossref]

Yamaguchi, I.

Yang, X. L.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

Yang, Y.

D. Xie, D. Zhao, Y. Yang, and H. Zhai, “Phase-shift extraction algorithm for blind phase-shifting holography based on the quotient of inner products,” Opt. Commun. 393, 40–44 (2017).
[Crossref]

Yu, Y.

Zalevsky, Z.

Zeng, F.

F. Zeng, H. Gu, and Q. Tan, “Application of the blind signal separation method for phase-shifting interferometry with random phase shifts,” Proc. SPIE 9046, 90460R (2013).
[Crossref]

Zhai, H.

D. Xie, D. Zhao, Y. Yang, and H. Zhai, “Phase-shift extraction algorithm for blind phase-shifting holography based on the quotient of inner products,” Opt. Commun. 393, 40–44 (2017).
[Crossref]

Zhang, H.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

Zhang, T.

Zhao, D.

D. Xie, D. Zhao, Y. Yang, and H. Zhai, “Phase-shift extraction algorithm for blind phase-shifting holography based on the quotient of inner products,” Opt. Commun. 393, 40–44 (2017).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, “Generalized phase-shifting interferometry with arbitrary unknown phase shifts: direct wave-front reconstruction by blind phase shift extraction and its experimental verification,” Appl. Phys. Lett. 90, 121124 (2007).
[Crossref]

J. Biomed. Opt. (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, 046022 (2014).
[Crossref]

J. Opt. (1)

F. Liu, J. Wang, Y. Wu, F. Wu, M. Trusiak, K. Patorski, Y. Wan, Q. Chen, and X. Hou, “Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert–Huang prefiltering,” J. Opt. 18, 105604 (2016).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

D. Xie, D. Zhao, Y. Yang, and H. Zhai, “Phase-shift extraction algorithm for blind phase-shifting holography based on the quotient of inner products,” Opt. Commun. 393, 40–44 (2017).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (3)

G. A. Ayubi, I. Duarte, and J. A. Ferrari, “Optimal phase-shifting algorithm for interferograms with arbitrary steps and phase noise,” Opt. Lasers Eng. 114, 129–135 (2019).
[Crossref]

M. Roy, P. Svahn, L. Cherel, and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[Crossref]

S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002).
[Crossref]

Opt. Lett. (4)

Proc. SPIE (2)

P. Slangen and B. Gautier, “Nematic liquid crystal light valve: application to phase shifting speckle interferometry,” Proc. SPIE 6616, 66162U (2007).

F. Zeng, H. Gu, and Q. Tan, “Application of the blind signal separation method for phase-shifting interferometry with random phase shifts,” Proc. SPIE 9046, 90460R (2013).
[Crossref]

Prog. Opt. (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

SPIE Rev. (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 18005 (2010).
[Crossref]

Other (5)

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

P. Picart and J.-C. Li, Digital Holography (Wiley, 2012).

R. Sirohi and M. Kothiyal, Optical Components, Systems, and Measurement Techniques, 1st ed. (Marcel Dekker, 1991).

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley, 2004).

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, 1978).

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Figures (6)

Fig. 1.
Fig. 1. (a) Optical configuration of a digital holographic microscope based on a Mach–Zehnder interferometer. (b) Illustration of the DHM performance through the Fourier transform of the digital hologram based on the angle between the object (O) and the reference (R) waves. Note that the size of the DC diffraction order (light blue) is always the double of the $ \pm {1}$ terms (yellow) if the DHM system operates in the telecentric regime (the aperture stop of the MO is located at the front focal plane of the TL). The remaining components of the system are denoted as: CL, converging lens; BS, beamsplitter; M, mirror; MO, microscope objective; TL, tube lens.
Fig. 2.
Fig. 2. Demonstration of the proposed cost minimization function in our approach. The panels are: (a) True complex (amplitude and phase) distributions of the simulated object. (b) Hologram and its Fourier transform using a reference slightly tilted. (c) Fourier transform of the demodulated components using Eq. (6) for different values of the phase steps ( $\Delta \varphi _2^\prime $ and $\Delta \varphi _3^\prime $ ). (d) Quantitative phase image obtained from the demodulated component ${\text{d}_{ + 1}}$ . The true phase steps were $\Delta \varphi _2^\prime = {60}$ and $\Delta \varphi _3^\prime = {180}\,\text{deg}$ , respectively. The values of the cost function and the MSE are shown in images of panel (c) and (d). Note that only when the phase steps coincide with the true ones, the demodulated components have a unique order, and the MSE error is almost null.
Fig. 3.
Fig. 3. Flowchart of the proposed algorithm.
Fig. 4.
Fig. 4. Evaluation of the accuracy and the repeatability of our proposed method. The panels are: (a) Estimated quantitative phase image for a single realization. (b) Fourier transform of the demodulated components for the estimated phase steps ( $\Delta \varphi _2^\prime $ and $\Delta \varphi _3^\prime $ ) provided by our approach. (c) MSE between the true and estimated phase maps for different realization. For each realization, initialization of the phase steps is different. The mean and standard deviation of the MSE values are ${3.6} \times {{10}^{ - 16}}$ [red line in panel (c)] and ${5} \times {{10}^{ - 16}}$ , respectively. The small values of the mean and standard deviation in the MSE values are correlated, respectively, with the accuracy and the repeatability of our method.
Fig. 5.
Fig. 5. Experimental validation of the proposed method. Panel (a) shows at left-hand side one of the recorded holograms; at right-hand side is the corresponding spectrum of the Fourier transform of (a). Panel (b) presents the three recovered Fourier orders ${\text{D}_{ + 1}}$ , ${\text{D}_0}$ , and ${\text{D}_{ - 1}}$ from left- to right-hand side. Panel (c) shows a 3D rendering of the phase map of the reconstructed object and the height profiles measured at the line over the 3D phase map.
Fig. 6.
Fig. 6. Experimental verification of the proposed approach using a complex biological specimen: 3D rendering of the quantitative phase image of a section of the head of a Drosophila melanogaster fly.

Tables (1)

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Table 1. Performance of the Proposed Algorithm Under Noise Conditions: SNR, Δ φ 2 , Δ φ 3 , and MSE a

Equations (8)

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u IP ( x ) = 1 M 2 e i 2 k 0 ( f MO + f TL ) { o ( x M ) 2 P ( x λ 0 f TL ) } ,
h ( x ) = | u IP ( x ) | 2 + | r ( x ) | 2 + u IP ( x ) r ( x ) + u IP ( x ) r ( x ) ,
H ( u ) = DC ( u ) + U IP ( u sin θ / λ 0 ) + U IP ( u + sin θ / λ 0 ) .
u ^ synth ( x ) = r ^ 1 h 1 + r ^ 2 h 2 + r ^ 3 h 3 + r ^ 4 h 4 .
h n ( x ) = d 0 ( x ) + e i Δ φ n d 1 ( x ) + e i Δ φ n d 1 ( x ) ,
( d 0 d + 1 d 1 ) = ( 1 1 1 1 e i Δ φ 2 e i Δ φ 2 1 e i Δ φ 3 1 e i Δ φ 3 1 ) 1 ( h 1 h 2 h 3 ) .
J = 2 | D + 1 ( sin θ / λ 0 ) | | D + 1 ( sin θ / λ 0 ) | + | D + 1 ( sin θ / λ 0 ) | .
J = 2 | D 1 ( sin θ / λ 0 ) | | D 1 ( sin θ / λ 0 ) | + | D 1 ( sin θ / λ 0 ) | .

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