## Iterative method for zero-order suppression in off-axis digital holography |

Optics Express, Vol. 18, Issue 15, pp. 15318-15331 (2010)

http://dx.doi.org/10.1364/OE.18.015318

Acrobat PDF (1295 KB)

### Abstract

We propose a method to suppress the so-called zero-order term in a hologram, based on an iterative principle. During the hologram acquisition process, the encoded information includes the intensities of the two beams creating the interference pattern, which do not contain information about the recorded complex wavefront, and that can disrupt the reconstructed signal. The proposed method selectively suppresses the zero-order term by employing the information obtained during wavefront reconstruction in an iterative procedure, thus enabling its suppression without any a priori knowledge about the object. The method is analyzed analytically and its convergence is studied. Then, its performance is shown experimentally. Its robustness is assessed by applying the procedure on various types of holograms, such as topographic images of microscopic specimens or speckle holograms.

© 2010 Optical Society of America

## 1. Introduction

1. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**, 6994–7001 (1999). [CrossRef]

2. J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. **19**, 074007 (2008). [CrossRef]

3. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. **30**, 468–470 (2005). [CrossRef] [PubMed]

6. P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain **44**, 57–69 (2008). [CrossRef]

9. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. **52**, 1123–1130 (1962). [CrossRef]

10. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. **29**, 2503–2505 (2004). [CrossRef] [PubMed]

1. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**, 6994–7001 (1999). [CrossRef]

11. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. **22**, 1268–1270 (1997). [CrossRef] [PubMed]

12. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. **29**, 1671–1673 (2004). [CrossRef] [PubMed]

13. P. Guo and A. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. **29**, 857–859 (2004). [CrossRef] [PubMed]

14. L. Cai, Q. Liu, and X. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. **28**, 1808–1810 (2003). [CrossRef] [PubMed]

15. G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A **17**, 380–390 (2000). [CrossRef]

18. Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. **38**, 4990–4996 (1999). [CrossRef]

19. M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE **7072**, 70721C (2008). [CrossRef]

20. T. Kreis and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. **36**, 2357–2360 (1997). [CrossRef]

21. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. **72**, 156–160 (1982). [CrossRef]

23. G.-L. Chen, C.-Y. Lin, M.-K. Kuo, and C.-C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express **15**, 8851–8856 (2007). [CrossRef] [PubMed]

24. J. Weng, J. Zhong, and C. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express **16**, 21971–21981 (2008). [CrossRef] [PubMed]

25. N. Pavillon, C. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. **48**, H186–H195 (2009). [CrossRef] [PubMed]

26. J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. **21**, 2758–2769 (1982). [CrossRef] [PubMed]

19. M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE **7072**, 70721C (2008). [CrossRef]

## 2. Off-axis digital holography reconstruction

*or*

^{*}is the image term, and

*o*

^{*}

*r*is its complex conjugate, i.e. the twin image. If the reference wave is considered as a plane wave with a propagation vector subtending an angle with the optical axis, the reference can be expressed as

*r*=

*R*exp[-i

*φ*(

*x*,

*y*)], where

*φ*(

*x*,

*y*) is a linear phase function defining the tilt, and

*R*a real constant value defining the overall amplitude of the plane wavefront. In this case, the different terms of Eq. (1) will be modulated in the spectral domain as

*ω*

_{0,x},

*ω*

_{0,y}) corresponds to the frequency shift induced by the tilt function

*φ*(

*x*,

*y*). The reference having a constant intensity, its spectrum results in a Dirac function

*δ*. The result of the interference is illustrated in Fig. 1, where a simulation of a hologram has been performed, resulting in the image shown in Fig. 1(a), to which corresponds the spatial spectrum shown in Fig. 1(b), where the different terms of Eq. (1) are identified.

*ω*. In this case, the object autocorrelation will have a spectral bandwidth of [-2

_{c}*ω*,2

_{c}*ω*], which can lead to spectral overlap with the imaging order. However, as it can be seen in Fig. 1(b), the spectral bandwidth can appear as smaller in the case of smooth objects. Finally, the twin image has a bandwidth identical to the imaging order, but is modulated in the opposite side of the spectrum. Therefore, in the case the modulation is large enough compared to the bandwidth of the imaging orders, i.e.

_{c}*ω*>

_{o}*ω*, this term will not overlap with the imaging term in the off-axis configuration, and thus can be filtered out. This condition can be in fact usually readily fulfilled in most implementations, as using one quadrant of the Fourier spectrum for the imaging order makes it possible to reach diffraction-limited resolution when any magnifying optics is employed [25

_{c}25. N. Pavillon, C. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. **48**, H186–H195 (2009). [CrossRef] [PubMed]

*Ŵ*(

*ω*) is a window function to select the imaging term. After having selected the imaging term, one can employ a phase mask, commonly called numerical parametric lens (NPL) [27

_{x},ω_{y}27. T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express **14**, 4300–4306 (2006). [CrossRef] [PubMed]

28. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A **23**, 3177–3190 (2006). [CrossRef]

29. U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. **13**, R85–R101 (2002). [CrossRef]

30. F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A **23**, 2944–2953 (2006). [CrossRef]

30. F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A **23**, 2944–2953 (2006). [CrossRef]

25. N. Pavillon, C. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. **48**, H186–H195 (2009). [CrossRef] [PubMed]

## 3. Functioning principle of the iterative method

### 3.1. Iterative method principle

*r*|

^{2}can simply be recorded by the camera by blocking the object wave, for instance, in order to get an estimator |

*r*|

_{exp}^{2}. As the reference wave is commonly well controlled and constant in time, this operation can be considered as a calibration step before the experiment. The fact of using a measurement enables the suppression of the experimental noise occurring on the reference wave. It is however more complicated to compensate for the object wave intensity term |

*o*|

^{2}, since its profile is specimen-dependent.

*r*|

_{exp}^{2}≈

*R*

^{2}. This equation provides an estimation of the object wave intensity, so that it is possible to get a hologram with an attenuated zero-order by subtracting those terms as

18. Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. **38**, 4990–4996 (1999). [CrossRef]

19. M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE **7072**, 70721C (2008). [CrossRef]

*I*′ of Eq. (5) at step

*k*in order to get a more accurate estimator |

*o*|

_{est,k+1}^{2}for further suppression.

- Compensate for the reference intensity by subtracting the term |
*r*|_{exp}^{2}. - Extract the imaging term (
*or*^{*})_{0}(*x,y*) from the hologram*I*(*x,y*) − |*r*|_{exp}^{2}according to Eq. (3). - Extract the new imaging term (
*or*^{*})_{k+1}(*x,y*) from*I*′_{k}(*x,y*). - Repeat 3.-5. until full suppression.

### 3.2. Discussion on convergence

*O*(

_{W}*x,y*) = |

*o*|

^{2}⊗

*W*(

*x,y*), the zero-order estimator at the first iteration becomes

*k*as

*O*(

*f*) is a polynomial function. One can note that the parasitic terms of Eq. (8) are powers of

*R*> |

*o*|, so that the summation in Eq. (8) does not diverge. Indeed, the error in the estimation at first iteration will be once again multiplied by the factor

*K*at the next iteration, making them thus decrease.

*r*|

_{exp}^{2}, in order to minimize the error induced by the first term on the right hand of Eq. (8).

## 4. Results on synthesized holograms

### 4.1. Topographic holography

*ω*,

_{c}*ω*] range.

_{c}*λ*= 661 nm and a camera sampling of Δ

*x*= 6.45

*µ*m. The object is then propagated to the camera plane (

*d*= 5 cm), where its interference with a tilted plane wave has been calculated to generate the hologram. The ratio

*K*has been taken in this case as 1/5.

*K*or the spectral overlap between terms, more iterations could possibly be needed in order to get sufficient extinction. The speed of convergence for this hologram is shown in Fig. 4 by representing the sum of

*ε*—defined in Eq. (8)—on the field of view for each iteration which has been normalized by the object intensity.

### 4.2. Speckle hologram simulations

*π*/2,

*π*/2]. This simulation considers a low aperture optical system, composed of a 2

*f*lens system. The field diffracted by the specimen is propagated to the first lens of the optical system, where a low-pass filter is applied to account for the optical component aperture. The field is next propagated to the second lens where its curvature is compensated. Then, it is propagated to the hologram plane where the interference with a tilted reference wave is computed. The optical system was taken for a numerical aperture of 0.045, a wavelength of

*λ*= 760 nm and Δ

*x*= 6.45

*µ*m.

## 5. Experiments

### 5.1. Topographic measurements

1. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**, 6994–7001 (1999). [CrossRef]

*λ*= 661 nm, through a 20× MO (NA = 0.4). The reflected light then interferes with a reference wave, which profile is well controlled and curvature matched with the object wave. The interference pattern is recorded by a CCD camera, with a pixel size of Δ

*x*= 6.45

*µ*m, for a field of view of 512×512.

*d*= 4.8 cm. The amplitude of the reconstruction for the standard method [cf. Fig. 6(a)] contains a strong part of zero-order, which is suppressed with the iterative technique as shown in Fig. 6(b).

### 5.2. Speckle hologram

*E*generated in the bandwidth of the aperture can be clearly identified, giving a similar signal as in the simulations of Section 4.2. This behavior is due to the roughness of the coin, which generates approximately random phasors in some parts of the field of view.

*S*= 97.8% for the measurements shown in Fig. 8, indicating that most of the spectral energy carried by the zero-order has been suppressed.

## 6. Conclusions

## Acknowledgments

## References

1. | E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. |

2. | J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. |

3. | P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. |

4. | B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. |

5. | B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium,” Opt. Lett. |

6. | P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain |

7. | X. C. de Lega and P. Jacquot, “Deformation measurement with object-induced dynamic phase shifting,” Appl. Opt. |

8. | Y. Fu, G. Pedrini, and W. Osten, “Vibration measurement by temporal Fourier analyses of digital hologram sequence,” Appl. Opt. |

9. | E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. |

10. | G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. |

11. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

12. | Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. |

13. | P. Guo and A. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. |

14. | L. Cai, Q. Liu, and X. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. |

15. | G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A |

16. | G. Indebetouw and P. Klysubun, “Spatiotemporal digital microholography,” J. Opt. Soc. Am. A |

17. | M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express |

18. | Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. |

19. | M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE |

20. | T. Kreis and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. |

21. | M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. |

22. | T. Kreis, “Digital Recording and Numerical Reconstruction of Wave Fields,” in |

23. | G.-L. Chen, C.-Y. Lin, M.-K. Kuo, and C.-C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express |

24. | J. Weng, J. Zhong, and C. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express |

25. | N. Pavillon, C. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. |

26. | J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. |

27. | T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express |

28. | T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A |

29. | U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. |

30. | F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A |

31. | J. W. Goodman, |

**OCIS Codes**

(100.2000) Image processing : Digital image processing

(100.3010) Image processing : Image reconstruction techniques

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(180.3170) Microscopy : Interference microscopy

(090.1995) Holography : Digital holography

(100.3175) Image processing : Interferometric imaging

**ToC Category:**

Holography

**History**

Original Manuscript: April 26, 2010

Revised Manuscript: June 21, 2010

Manuscript Accepted: June 26, 2010

Published: July 2, 2010

**Citation**

Nicolas Pavillon, Cristian Arfire, Isabelle Bergoënd, and Christian Depeursinge, "Iterative method for zero-order suppression in off-axis digital holography," Opt. Express **18**, 15318-15331 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15318

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### References

- E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999). [CrossRef]
- J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008). [CrossRef]
- P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]
- B. Kemper, and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008). [CrossRef] [PubMed]
- B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye–enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008). [CrossRef] [PubMed]
- P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008). [CrossRef]
- X. C. de Lega, and P. Jacquot, “Deformation measurement with object-induced dynamic phase shifting,” Appl. Opt. 35, 5115–5121 (1996). [CrossRef]
- Y. Fu, G. Pedrini, and W. Osten, “Vibration measurement by temporal Fourier analyses of digital hologram sequence,” Appl. Opt. 46, 5719–5727 (2007). [CrossRef] [PubMed]
- E. N. Leith, and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962). [CrossRef]
- G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29, 2503–2505 (2004). [CrossRef] [PubMed]
- I. Yamaguchi, and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997). [CrossRef] [PubMed]
- Z. Wang, and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004). [CrossRef] [PubMed]
- P. Guo, and A. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004). [CrossRef] [PubMed]
- L. Cai, Q. Liu, and X. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28, 1808–1810 (2003). [CrossRef] [PubMed]
- G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000). [CrossRef]
- G. Indebetouw, and P. Klysubun, “Spatiotemporal digital microholography,” J. Opt. Soc. Am. A 18, 319–325 (2001). [CrossRef]
- M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629–9635 (2005). [CrossRef] [PubMed]
- Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999). [CrossRef]
- M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE 7072, 70721C (2008). [CrossRef]
- T. Kreis, and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997). [CrossRef]
- M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
- T. Kreis, “Digital Recording and Numerical Reconstruction of Wave Fields,” in Handbook of Holographic Interferometry, T. Kreis, ed. (Wiley-VCH Verlag, 2005), pp. 81–183.
- G.-L. Chen, C.-Y. Lin, M.-K. Kuo, and C.-C. Chang, “Numerical suppression of zero-order image in digital holography,” Opt. Express 15, 8851–8856 (2007). [CrossRef] [PubMed]
- J. Weng, J. Zhong, and C. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express 16, 21971–21981 (2008). [CrossRef] [PubMed]
- N. Pavillon, C. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. 48, H186–H195 (2009). [CrossRef] [PubMed]
- J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
- T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006). [CrossRef] [PubMed]
- T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 23, 3177–3190 (2006). [CrossRef]
- U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002). [CrossRef]
- F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A 23, 2944–2953 (2006). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics (McGraw Hill Higher Education, 1996), 2nd ed.

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