## Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition

Optics Express, Vol. 15, Issue 12, pp. 7231-7242 (2007)

http://dx.doi.org/10.1364/OE.15.007231

Acrobat PDF (2299 KB)

### Abstract

A technique to perform two-wavelengths digital holographic microscopy (DHM) measurements with a single hologram acquisition is presented. The vertical measurement range without phase ambiguity is extended to the micron-range, thanks to the resulting synthetic wavelength defined by the beating of two wavelengths with a separation of about 80nm. Real-time dual-wavelength imaging is made possible by using two reference waves having different wavelengths and propagation directions for the hologram recording. The principle of the method is exposed and experimental results concerning a 1.2*μ*m m high test sample as well as a moving micro-mirror are presented. To the extent of our knowledge, this is the first time that real-time synthetic beat-wavelength digital holography measurements are reported.

© 2007 Optical Society of America

## 1. Introduction

1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. **11**, 77–79 (1967). [CrossRef]

4. D. Gabor, “A new microscopic principle,” Nature **161**, 777–778 (1948). [CrossRef] [PubMed]

*λ*/150 due to the interferometric nature of the method [5

5. 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]

*π*. Consequently, optical path lengths (OPL) larger than one time the wavelength cannot be unequivocally measured, resulting in a phase ambiguity. In a majority of situations, phase unwrapping algorithms can be used to retrieve the true OPL map of the sample, but high aspect-ratio objects, such as specimens with step height, or high roughness surface, as well as noisy experimental conditions can make such algorithms failing. In addition, such unwrapping methods are often time-consuming making them inadequate for real-time measurements.

*et al*. [6

6. A. T. Forrester, W. E. Parkins, and E. Gerjuoy, “On the possibility of observing beat frequencies between lines in the visible spectrum,” Phys. Rev. **72**, 728–728 (1947). [CrossRef]

7. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. **12**, 2071–2074 (1973). [CrossRef] [PubMed]

10. B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. **57**, 155–162 (1967). [CrossRef]

*et al*. [13

13. C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. **39**, 79–85 (2000). [CrossRef]

14. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2 pi ambiguity by multiwavelength digital holography,” Opt. Lett. **28**, 1141–1143 (2003). [CrossRef] [PubMed]

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

16. 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]

17. S. de Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. **30**, 2706–2708 (2005). [CrossRef] [PubMed]

18. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting digital holography,” Appl. Opt. **45**, 975–983 (2006). [CrossRef] [PubMed]

19. R. J. Mahon, J. A. Murphy, and W. Lanigan, “Digital holography at millimetre wavelengths,” Opt. Commun. **260**, 469–473 (2006). [CrossRef]

20. F. Zhang, G. Pedrini, and W. Osten, “Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution,” Opt. Lett. **31**, 1633–1635 (2006). [CrossRef] [PubMed]

*et al*. in Ref. [21

21. R. Onodera and Y. Ishii, “Two-wavelength interferometry that uses a fourier-transform method,” Appl. Opt. **37**, 7988–7994 (1998). [CrossRef]

22. A. W. Lohmann, “Reconstruction of vectorial wavefronts,” Appl. Opt. **4**, 1667–1668 (1965). [CrossRef]

23. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. **54**, 1295–1301 (1964). [CrossRef]

26. D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarisation imaging with digital holography,” Electron. Lett. **35**, 2053–2055 (1999). [CrossRef]

30. T. Saucedo A., F. M. Santoyo, M. D. l. T. Ibarra, G. Pedrini, and W. Osten, “Simultaneous two-dimensional en-doscopic pulsed digital holography for evaluation of dynamic displacements,” Appl. Opt. **45**, 4534–4539 (2006). [CrossRef] [PubMed]

16. 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]

17. S. de Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. **30**, 2706–2708 (2005). [CrossRef] [PubMed]

## 2. Principle

**O**_{1}and

**O**_{2}at two different wavelengths

*λ*

_{1}and

*λ*

_{2}that interfere with two reference beams

**R**_{1}and

**R**_{2}, emitted by the same pair of laser sources, in a off-axis configuration (slight angle between object and reference beams). The intensity pattern, which results from an incoherent addition of both interferograms at

*λ*

_{1}and

*λ*

_{2}, can be expressed as

*I*being the hologram intensity;

_{H}*x*,

*y*the coordinates in the camera plane, and

^{*}denoting the complex conjugate.

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

**O**_{i}(the virtual images), or their conjugate

**O**^{*}

_{i}(the real images), with the reference waves. These interferences appear as fringes at carrier spatial frequencies on the hologram. With

**O**_{i}collinear on the optical axis, these carrier frequencies are dependent on the k-vectors of

**R**_{1}and

**R**_{2}. Considering different incident angles for the two references waves, especially the configuration where their k-vector projections on the CCD plane are orthogonal, each interference term occupies different position in the Fourier plane. Providing that there is no overlap between interference terms, a condition which imposes restrictions regarding the spatial frequency content of the object spectrum, it is therefore straightforward to isolate each frequency component by spatial filtering [31

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

26. D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarisation imaging with digital holography,” Electron. Lett. **35**, 2053–2055 (1999). [CrossRef]

30. T. Saucedo A., F. M. Santoyo, M. D. l. T. Ibarra, G. Pedrini, and W. Osten, “Simultaneous two-dimensional en-doscopic pulsed digital holography for evaluation of dynamic displacements,” Appl. Opt. **45**, 4534–4539 (2006). [CrossRef] [PubMed]

**R**^{*}

_{1}

**O**_{1}and

**R**^{*}

_{2}

**O**_{2}independently.

*I*

^{F}

_{H,1}for

**R**^{*}

_{1}

**O**_{1}and and

*I*

^{F}

_{H,2}for

**R**^{*}

_{2}

**O**_{2}and and by using the convolution formulation, we obtain the following expression for the Fresnel propagation:

_{CF,i}is the reconstructed wavefront for wavelength

*λ*in the convolution formulation,

_{i}*Γ*and

^{I}_{i}*Γ*are digital phase masks (DPM) in the image plane and in the hologram plane respectively, used to compensate for aberrations (see Ref. [32

^{H}_{i}32. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. **45**, 851–863 (2006). [CrossRef] [PubMed]

*d*is the propagation distance for wavelength

_{i}*λ*, FFT is the Fast Fourier Transform operator, (

_{i}*k*,

*l*) and (

*m*,

*n*) are the couple of integers so that (-

*N*/2 <

*k*,

*l*,

*m*,

*n*≤

*N*/2) representing coordinates in the hologram plane, respectively the reconstruction plane,

*NxN*is the number of pixels of the CCD camera and Δ

*x*and Δ

*y*are the pixel sizes.

_{CF,i}in an independent manner: the DPMs can be adapted to compensate for each wavefront aberrations and the propagation distances

*d*can be adjusted differently to compensate for slight chromatic aberrations or specimen displacement with respect to the working distance of the MO. Let us mention that the DPM could also be used as digital magnification lenses to resize the images in the case of stronger chromatic aberrations [16

_{i}16. 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]

**O**_{1}and

**O**_{2}in the reconstruction plane contain information both in amplitude and in phase, providing a nanometer-scale resolution in the vertical axis but suffering from phase ambiguity for OPLs larger than the wavelength. The calculation of

**O**_{1}

**O**^{*}

_{2}in the reconstruction plane allows to obtain the following expression for the synthetic wavelength phase:

*x*is the OPL (twice the topography in reflection, for an homogeneous sample in air),

*ϕ*the reconstructed phase for the wavelength

_{i}*λ*, and Λ is the synthetic beat wavelength defined as:

_{i}*λ*

_{2}-

*λ*

_{1}), the larger the synthetic wavelength, typically within the range of micrometers to millimeters. The corresponding synthetic phase obtained with Eq. 3 enables to resolve much higher structures by removing the phase ambiguity in the range of the beat wavelength Λ, thus greatly increasing the range for the phase measurement.

33. P. de Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. **30**, 4026–4033 (1991). [CrossRef] [PubMed]

*ϕ*

_{1}or

*ϕ*

_{2}is also amplified when converted in topography due to the important value of Λ. Thus, high stability laser sources are required as well as careful setup design to minimize noise sources and use of low temporal coherence sources to avoid parasitic interferences. Nevertheless, methods to keep the single-wavelength precision by using the synthetic phase only for phase ambiguity removal, like the ones presented in Refs. [14

14. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2 pi ambiguity by multiwavelength digital holography,” Opt. Lett. **28**, 1141–1143 (2003). [CrossRef] [PubMed]

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

*μ*m high with a synthetic wavelength of Λ = 6.4

*μ*m.

## 3. Experimental configuration

*λ*

_{1}= 679.57nm and

*λ*

_{2}= 759.91nm, yielding Λ = 6.428

*μ*m for the synthetic beat wavelength. The diodes were tested for wavelength stability with a wavemeter and showed a wavelength deviation smaller than 10pm over 8h. The corresponding measurement error for a 3

*μ*m high step (nearly Λ/2), caused by an unwanted change of Λ, is less than 1

*Å*. The diodes also emits a low coherence (coherence length about 0.3mm) linearly polarized light.

^{2}with 512×512 pixels, and a large depth-of-field of more than 50

*μ*m. We can mention that there is no limitation regarding the use of higher magnification. The CCD camera is a standard 8 bits black and white CCD camera with 6.45

*μ*m pixel size. Each reference arm comprise a delay line (DL) adjusted to match the optical path length of its respective object counterparts, in order to create an interference on the CCD for both wavelengths. By tilting the pair of mirrors M1 and M2 for the first wavelength reference beam, respectively M3 and M4 for the second one, one can finely tune each k-vector incident upon the CCD camera. In other words, each wavelength interferograms fringes can be independently tuned both in spatial frequency and orientation.

**R**_{i}

**O**^{*}

_{i}, or the virtual image components

**R**^{*}

_{i}

**O**_{i}, or any other set of interference terms, can be selected independently as depicted in Fig. 2(b), and this procedure is rendered easier by the clearly visible cut-off frequency of the MO (colored circles in Fig. 2(b). This experimental configuration for recording holograms is very similar to the one in Ref. [27

27. T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. **41**, 27–37 (2002). [CrossRef] [PubMed]

28. T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. **231**, 137–147 (2004). [CrossRef]

*μ*m has been measured with a USAF 1950 resolution test target and the system is diffraction-limited according to the NA of the MO.

**23**, 3177–3190 (2006). [CrossRef]

*d*

_{1}= 50mm for

*λ*

_{1}= 680nm and

*d*

_{2}= 50.5mm for

*λ*

_{2}= 760nm and they correspond to the distances between the image planes and the CCD plane. As the reconstruction distances difference is very small due to the achromatic conditions, the magnification difference can be considered negligible and the superposition conditions are fulfilled.

## 4. Results

_{2}staircase on a Si wafer with a gold coating to ensure a perfect reflectivity. It is made of five steps with the following height values: 375, 525, 975, 1200, 1275nm inducing up to 2.5

*μ*m in term of OPL, which represents about four times a typical red-range wavelength and out of range of classical single-wavelength DHM. A schematic of this test-object and experimental reconstruction images of this sample from the hologram of Fig. 2 with the two-wavelength setup of Fig. 1 are presented in Fig. 3

*λ*

_{2}= 760nm. Unwrapping algorithms are clearly useless for such micro-structures investigation. As we have recorded both wavefronts with the same hologram acquisition, the computation of the phase difference between Figs. 3(d) and 3(e) can be achieved according to Eq. 3. After inversion of the sign of the phase to render a topographic map (i.e. a conjugated phase map), as will be done for all synthetic phase-maps further on, we obtain the Λ = 6.428

*μ*m synthetic wavelength conjugated phase distribution presented in Fig. 4.

*μ*m straightforwardly provides a phase jumps-free result and a real 3D-topography of this up to 1.275

*μ*m high specimen as illustrated in Fig. 4(b). To assess the method, quantitative profiles measurements on the synthetic map of Fig. 4 are given in Fig. 5 and compared with results obtained with a white light interferometer.

*μ*m and 1.275

*μ*m steps. Furthermore, the precision can be enhanced by spatially averaging 100 profiles as in Fig. 5(b), where the measure seems even more accurate than with the white light interferometer. This spatial averaging is done for a single reconstruction, and it applies on both the setup and the speckle noise (shot noise at the instant of acquisition).

_{2}staircases with the same heights staircases, and the sequence is recorded at the maximum frame rate of 25 images/s (1’000 acquisitions). Results illustrating the real-time synthetic wavelength phase maps are presented as multimedia movies in Fig. 6.

^{2}micro-mirror oscillating at 1Hz, for a single wavelength [Fig. 7(a)] and for synthetic wavelength [Fig. 7(b,c)].

*λ*/2) between two acquisition (as for example between 0.12 and 0.25 second in Fig. 8), a temporal phase unwrapping method may fail.

_{i}## 5. Conclusion

*μ*m high test-target imaged at 25 frames/s with a 6.4

*μ*m synthetic wavelength are in good agreement with white light interferometer measurements. Further on, this method allows for observing fast phenomena and the dynamic performance has been illustrated with a 1Hz oscillating micro-mirror monitoring at video frequency.

## References and links

1. | J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. |

2. | U. Schnars and W. Jüptner, “Direct recording of holograms by a ccd target and numerical reconstruction,” Appl. Opt. |

3. | E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. |

4. | D. Gabor, “A new microscopic principle,” Nature |

5. | 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. |

6. | A. T. Forrester, W. E. Parkins, and E. Gerjuoy, “On the possibility of observing beat frequencies between lines in the visible spectrum,” Phys. Rev. |

7. | C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. |

8. | F. Bien, M. Camac, H. J. Caulfield, and S. Ezekiel, “Absolute distance measurements by variable wavelength interferometry,” Appl. Opt. |

9. | R. Dändliker, R. Thalmann, and D. Prongué, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. |

10. | B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am. |

11. | J. S. Zelenka and J. R. Varner, “A new method for generating depth contours holographically,” Appl. Opt. |

12. | J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. |

13. | C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. |

14. | J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2 pi ambiguity by multiwavelength digital holography,” Opt. Lett. |

15. | D. Parshall and M. Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. |

16. | 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 |

17. | S. de Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. |

18. | I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting digital holography,” Appl. Opt. |

19. | R. J. Mahon, J. A. Murphy, and W. Lanigan, “Digital holography at millimetre wavelengths,” Opt. Commun. |

20. | F. Zhang, G. Pedrini, and W. Osten, “Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution,” Opt. Lett. |

21. | R. Onodera and Y. Ishii, “Two-wavelength interferometry that uses a fourier-transform method,” Appl. Opt. |

22. | A. W. Lohmann, “Reconstruction of vectorial wavefronts,” Appl. Opt. |

23. | E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. |

24. | E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. |

25. | J. D. Armitage and A. W. Lohmann, “Theta modulation in optics,” Appl. Opt. |

26. | D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarisation imaging with digital holography,” Electron. Lett. |

27. | T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. |

28. | T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, “Jones vector imaging by use of digital holography: simulation and experimentation,” Opt. Commun. |

29. | A. T. Saucedo, F. M. Santoyo, M. D. l. Torre-Ibarra, G. Pedrini, and W. Osten, “Endoscopic pulsed digital holography for 3d measurements,” Opt. Lett. |

30. | T. Saucedo A., F. M. Santoyo, M. D. l. T. Ibarra, G. Pedrini, and W. Osten, “Simultaneous two-dimensional en-doscopic pulsed digital holography for evaluation of dynamic displacements,” Appl. Opt. |

31. | E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. |

32. | T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. |

33. | P. de Groot and S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. |

34. | Y. Emery, E. Cuche, F. Marquet, N. Aspert, P. Marquet, J. Kühn, M. Botkine, T. Colomb, F. Montfort, F. Charrière, C. Depeursinge, P. Debergh, and R. Conde, “Digital holographic microscopy (DHM) for metrology and dynamic characterization of MEMS and MOEMS”, Proc. SPIE |

**OCIS Codes**

(090.1760) Holography : Computer holography

(090.4220) Holography : Multiplex holography

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

(180.3170) Microscopy : Interference microscopy

**ToC Category:**

Holography

**History**

Original Manuscript: April 6, 2007

Revised Manuscript: May 16, 2007

Manuscript Accepted: May 22, 2007

Published: May 29, 2007

**Virtual Issues**

Vol. 2, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Jonas Kühn, Tristan Colomb, Frédéric Montfort, Florian Charrière, Yves Emery, Etienne Cuche, Pierre Marquet, and Christian Depeursinge, "Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition," Opt. Express **15**, 7231-7242 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7231

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### References

- J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967). [CrossRef]
- U. Schnars and W. Jüptner, "Direct recording of holograms by a ccd target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994). [CrossRef] [PubMed]
- E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999). [CrossRef]
- D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948). [CrossRef] [PubMed]
- 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]
- A. T. Forrester, W. E. Parkins, and E. Gerjuoy, "On the possibility of observing beat frequencies between lines in the visible spectrum," Phys. Rev. 72, 728-728 (1947). [CrossRef]
- C. Polhemus, "Two-wavelength interferometry," Appl. Opt. 12, 2071-2074 (1973). [CrossRef] [PubMed]
- F. Bien, M. Camac, H. J. Caulfield, and S. Ezekiel, "Absolute distance measurements by variable wavelength interferometry," Appl. Opt. 20, 400-402 (1981). [CrossRef] [PubMed]
- R. Dändliker, R. Thalmann, and D. Prongué, "Two-wavelength laser interferometry using superheterodyne detection," Opt. Lett. 13, 339-341 (1988). [CrossRef] [PubMed]
- B. P. Hildebrand and K. A. Haines, "Multiple-wavelength and multiple-source holography applied to contour generation," J. Opt. Soc. Am. 57, 155-162 (1967). [CrossRef]
- J. S. Zelenka and J. R. Varner, "A new method for generating depth contours holographically," Appl. Opt. 7, 2107-2110 (1968). [CrossRef] [PubMed]
- J. C. Wyant, "Testing aspherics using two-wavelength holography," Appl. Opt. 10, 2113-2118 (1971). [CrossRef] [PubMed]
- C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000). [CrossRef]
- J. Gass, A. Dakoff, and M. K. Kim, "Phase imaging without 2 pi ambiguity by multiwavelength digital holography," Opt. Lett. 28, 1141-1143 (2003). [CrossRef] [PubMed]
- D. Parshall and M. Kim, "Digital holographic microscopy with dual wavelength phase unwrapping," Appl. Opt. 45, 451-459 (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]
- S. de Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, "Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations," Opt. Lett. 30, 2706-2708 (2005). [CrossRef] [PubMed]
- I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, "Image reconstruction only by phase data in phaseshifting digital holography," Appl. Opt. 45, 975-983 (2006). [CrossRef] [PubMed]
- R. J. Mahon, J. A. Murphy, and W. Lanigan, "Digital holography at millimetre wavelengths," Opt. Commun. 260, 469-473 (2006). [CrossRef]
- F. Zhang, G. Pedrini, and W. Osten, "Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution," Opt. Lett. 31, 1633-1635 (2006). [CrossRef] [PubMed]
- R. Onodera and Y. Ishii, "Two-wavelength interferometry that uses a fourier-transform method," Appl. Opt. 37, 7988-7994 (1998). [CrossRef]
- A. W. Lohmann, "Reconstruction of vectorial wavefronts," Appl. Opt. 4, 1667-1668 (1965). [CrossRef]
- E. N. Leith and J. Upatnieks, "Wavefront reconstruction with diffused illumination and three-dimensional objects," J. Opt. Soc. Am. 54, 1295-1301 (1964). [CrossRef]
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