## Phase imaging of cells by simultaneous dual-wavelength reflection digital holography

Optics Express, Vol. 16, Issue 15, pp. 10900-10911 (2008)

http://dx.doi.org/10.1364/OE.16.010900

Acrobat PDF (691 KB)

### Abstract

We present a phase-imaging technique to quantitatively study the three-dimensional structure of cells. The method, based on the simultaneous dual-wavelength digital holography, allows for higher axial range at which the unambiguous phase imaging can be performed. The technique is capable of nanometer axial resolution. The noise level, which increases as a result of using two wavelengths, is then reduced to the level of a single wavelength. The method compares favorably to software unwrapping, as the technique does not produce non-existent phase steps. Curvature mismatch between the reference and object beams is numerically compensated. The 3D images of SKOV-3 ovarian cancer cells are presented.

© 2008 Optical Society of America

## 1. Introduction

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

6. S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields
reconstruction by digital holography,” Opt. Express **9**, 294–302 (2001). [CrossRef] [PubMed]

9. L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. **40**, 5046–5051 (2001). [CrossRef]

12. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. **23**, 817–819 (1998). [CrossRef]

13. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. **24**, 291–293 (1999). [CrossRef]

14. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. **42**, 1938–1946 (2003). [CrossRef] [PubMed]

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

16. C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express **13**, 8693–8698 (2005). [CrossRef] [PubMed]

## 2. Experimental apparatus

17. K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE **6162**, 616203 (2006). [CrossRef]

22. N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express , **15**, 9239–9247 (2007). [CrossRef] [PubMed]

*λ*

_{1}=633 nm) and diode-pumped solid-state (

*λ*

_{2}=532 nm) lasers were used as coherent light sources. Both beams are attenuated by neutral density filters (ND) and then passed through the microscope objectives (OBJ11/OBJ12) which, together with the apertures A and collimating lenses L11/L12, produce plane waves. Their intensity is further controlled by the polarizing filters P1 and P2. Beam splitters BS1 and BS2 divide the beams into the reference and the object arms. Two separate reference arms are used to fine-tune the location of the first-order diffraction peaks and separate them in the Fourier domain. Lenses L21 and L22 and 20x microscope objective OBJ1 again collimate the beams in the object arm. The wave fronts in both reference arms remain spherical and the resulting curvature mismatch is digitally removed. An interference filter is placed into the reference arm of the diode-pumped solidstate (λ=532 nm) laser. It is designed to allow only this wavelength to pass and block the inverse reflection of the other laser. The interference pattern between the reflected reference waves and the object wave is recorded by the CCD camera. A relative angle can be introduced between the object and each of the two reference beams by slightly tilting the reference arms mirrors. By introducing different tilts in two orthogonal directions for two reference beams,we can separate each spectral component in Fourier space (see Fig. 2(b) below), which allows us to capture both wavelengths simultaneously.

## 3. Multi-wavelength digital holographic phase imaging

### 3.1 Angular spectrum method

*z*-direction) in accordance with the laws of diffraction. In the case of Fraunhofer diffraction, Fresnel-Kirchoff integral can be expressed as [27]:

*k*and

_{x}*k*are spatial frequencies corresponding to

_{y}*x*and

*y*respectively.

*E*

_{0}(

*x*,

*y*;

*z*=0) is the intensity distribution recorded by the CCD camera. This is the expression for Fourier transform and

*A*

_{0}(

*k*,

_{x}*k*;0) is the angular spectrum of the optical field

_{y}*E*

_{0}(

*x*,

*y*;

*z*=0) at the hologram plane

*z*=0. The object’s angular spectrum consists of a zero-order and a pair of first-order terms. One of the first-order terms is the angular spectrum of the object field and the other is its phase inverted version. Figure 2(a) shows the hologram of a USAF resolution target recorded by our dual wavelength experimental setup. The two crossing interference fringe patterns, formed by two wavelengths, can be clearly seen. Figure 2(b) presents the Fourier spectrum with the two pairs of first-order components,corresponding to the two wavelengths, clearly visible.

*E*

_{0}(

*x*,

*y*;

*z*=0) can be regarded as a projection of many plane waves propagating in different directions in space and with the complex amplitude of each component equal to

*A*

_{0}(

*k*,

_{x}*k*;0). The angular spectrum can then be propagated in space along the

_{y}*z*-axis:

*ik*] is the complex transfer function and

_{z}z*k*=2

*π*/

*λ*. Here, there is no requirement for

*z*to be larger than a certain minimum value, as in the case of Fresnel transform or Huygens convolution. The complex wave-field at an arbitrary

*z*can be obtained by performing the inverse Fourier transform:

### 3.2 Curvature correction

*E*

_{0}(

*x*,

*y*;

*z*=0) by the phase factor exp[

*i*], where

_{ϕ}*ϕ*=

*kd*is the phase difference between

*and*

**A***. Here,*

**O***k*=2

*π*/

*λ*,where

*λ*is the wavelength of light and

*d*is the optical path difference:

28. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. **42**, 1938–1946 (2003). [CrossRef] [PubMed]

*R*≫

*r*and

*r*¯

_{0}→0:

*mRλ*, where

*m*=

*0,1,2*…. Therefore, for a wavelength of 532 nm,

*R*=3 cm, the radius of a first fringe is 126 micron and there is a total of 3 fringes visible in 174 micron frame (see Fig. 4 below). If the field of view is increased, there are going to be more fringes visible and at some point the aliasing may occur. One can use this formula as an analytical expression to avoid fringe aliasing. For example, for the parameters above, in order for the fringes to alias (less than 2 pixel per fringe), one would have to have a field of view large enough for over 100 fringes.

### 3.3 Multi-wavelength phase imaging and optical thickness

*h*(

*x*,

*y*) is described by its phase map

*ϕ*(

*x*,

*y*) of the holographic reconstruction at a given wavelength by

*n*-

*n*

_{0}) is the refractive index difference between the cell and air. Figure 5(a) shows the phase map of the aluminum-covered USAF resolution target. The step size in Fig. 5(a) is approximately 2.2 radians, which can be converted to height using Eq. (8). This is consistent with the AFM scan of the same area, shown in Fig. 5(b), with the step height equal to approximately 100 nm in both images.

*π*, but since the two wavelengths are different, the discontinuities occur at different points of the image. It is possible to use this information to unwrap the phase by comparing the two maps.

*π*phase ambiguities can be resolved. The new phase map [see Fig. 6(c)] is equivalent to a phase map created by a wavelength:

_{1}=633 nm and λ

_{2}=532 nm, Λ

_{12}=3334 nm, which is high enough to remove the discontinuities seen in Figs. 6(a), 6(b).

*ϕ*

_{1}or

*ϕ*

_{2}), to produce the low noise “fine” phase map. The method (detailed in the reference 15) uses one of the original single wavelength (say

*λ*

_{1}) phase images and corrects the phase jumps using the coarse map as a guide. If the noise in the coarse phase map is too excessive, some of the single wavelength segments might still end up being vertically shifted from its correct position by

*λ*

_{1}[26

26. A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. **47**, 3203–3210 (2008). [CrossRef] [PubMed]

*λ*

_{1}, these errors can then be corrected in software by simply looking for such jumps and shifting them up or down back to their proper place. In comparison to the coarse map, the noise in the resulting fine map [see Fig. 6(d)] is much lower, while the axial range is still the same. Indeed, while the rms noise in the flat area of the resolution target is about 40 nm for the coarse map, for the fine map it is almost the same as for the single wavelength (both on the order of 6 nm).

### 4. Results

### 5. Conclusion

## Acknowledgments

## References and links

1. | W. Jueptner and U. Schnars, |

2. | U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am . |

3. | U. Schnars and W. P. Jueptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. |

4. | U. Schnars and W. P. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci.
Technol. |

5. | J. W. Goodman, |

6. | S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields
reconstruction by digital holography,” Opt. Express |

7. | L. F. Yu and L. L. Cai, “Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram,” J. Opt. Soc. Am. A |

8. | K. Matsushima, H. Schimmel, and F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A |

9. | L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. |

10. | W.S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. |

11. | W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci.USA |

12. | A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. |

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

14. | P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. |

15. | J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2 |

16. | C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express |

17. | K. Tobin and P. Bingham, “Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology,” Proc. SPIE |

18. | J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Realtime dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express |

19. | P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, “Quantitative Phase Microscopy of microstructures with extended measurement range and correction of
chromatic aberrations by multiwavelength digital holography,” Opt. Express |

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

21. | M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in |

22. | N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express , |

23. | A. Khmaladze and M. Kim, “Quantitative Phase Contrast Imaging of Cells by Multi-Wavelength Digital Holography,” in |

24. | A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography,” in |

25. | A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples,” in |

26. | A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, “Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples,” Appl. Opt. |

27. | M. Born and E. Wolfe, Principles of Optics, (Pergamon, 1964). |

28. | P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. |

**OCIS Codes**

(180.0180) Microscopy : Microscopy

(180.6900) Microscopy : Three-dimensional microscopy

(090.1995) Holography : Digital holography

**ToC Category:**

Microscopy

**History**

Original Manuscript: April 29, 2008

Revised Manuscript: June 27, 2008

Manuscript Accepted: June 30, 2008

Published: July 7, 2008

**Virtual Issues**

Vol. 3, Iss. 8 *Virtual Journal for Biomedical Optics*

**Citation**

Alexander Khmaladze, Myung Kim, and Chun-Min Lo, "Phase imaging of cells by simultaneous dual-wavelength
reflection digital holography," Opt. Express **16**, 10900-10911 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-15-10900

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### References

- W. Jueptner and U. Schnars, Digital Holography (Springer Verlag, 2004).
- U. Schnars, "Direct phase determination in hologram interferometry with use of digitally recorded holograms," J. Opt. Soc. Am. A 11, 2011-2015 (1994). [CrossRef]
- U. Schnars and W. P. Jueptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994). [CrossRef] [PubMed]
- U. Schnars and W. P. Jueptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics, 2nd ed (New York, McGraw-Hill, 1996).
- S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, "Whole optical wavefields reconstruction by digital holography," Opt. Express 9, 294-302 (2001). [CrossRef] [PubMed]
- L. F. Yu and L. L. Cai, "Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram," J. Opt. Soc. Am. A 18, 1033-1045 (2001). [CrossRef]
- K. Matsushima, H. Schimmel, and F. Wyrowski, "Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves," J. Opt. Soc. Am. A 20, 1755-1762 (2003). [CrossRef]
- L. Xu, X. Peng, J. Miao, and A. K. Asundi, "Studies of digital microscopic holography with applications to microstructure testing," Appl. Opt. 40, 5046-5051 (2001). [CrossRef]
- W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, "Fourier-transform holographic microscope," Appl. Opt. 31, 4973-4978 (1992). [CrossRef] [PubMed]
- W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography for biological applications," Proc. Natl. Acad. Sci. USA 98, 11301-10305 (2001). [CrossRef] [PubMed]
- A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, "Quantitative optical phase microscopy," Opt. Lett. 23, 817-819 (1998). [CrossRef]
- E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999). [CrossRef]
- P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, "Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging," Appl. Opt. 42, 1938-1946 (2003). [CrossRef] [PubMed]
- J. Gass, A. Dakoff, and M. K. Kim, "Phase imaging without 2?-ambiguity by multiple-wavelength digital holography," Opt. Lett. 28, 1141-1143 (2003). [CrossRef] [PubMed]
- C. J. Mann, L. Yu, C. M. Lo, and M. K. Kim, "High-resolution quantitative phase-contrast microscopy by digital holography," Opt. Express 13, 8693-8698 (2005). [CrossRef] [PubMed]
- K. Tobin and P. Bingham, "Optical Spatial Heterodyned Interferometry for applications in Semiconductor Inspection and Metrology," Proc. SPIE 6162,616203 (2006). [CrossRef]
- J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, "Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition," Opt. Express 15, 7231-7242 (2007). [CrossRef] [PubMed]
- P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, "Quantitative Phase Microscopy of microstructures with extended measurement range and correction of chromatic aberrations by multiwavelength digital holography," Opt. Express 15, 14591-14600, (2007). [CrossRef] [PubMed]
- D. Parshall and M. K. Kim, "Digital holographic microscopy with dual wavelength phase unwrapping," Appl. Opt. 45, 451-459 (2006). [CrossRef] [PubMed]
- M. K. Kim, L. Yu, and C. J. Mann, "Digital holography and multi-wavelength interference techniques," in Digital holography and three-dimensional display, T. C. Poon, ed. (Springer 2006).
- N. Warnasooriya and M. K. Kim, "LED-based multi-wavelength phase imaging interference microscopy," Opt. Express 15, 9239-9247 (2007). [CrossRef] [PubMed]
- A. Khmaladze and M. Kim, "Quantitative Phase Contrast Imaging of Cells by Multi-Wavelength Digital Holography," in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A. [CrossRef]
- A. Khmaladze, C. J. Mann, and M. K. Kim, "Phase Contrast Movies of Cell Migration by Multi-Wavelength Digital Holography," in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.
- A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, "The Application of Dual-Wavelength Reflection Digital Holography for Detection of Pores in Coal Samples," in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2008), paper DMB5.
- A. Khmaladze, A. Restrepo-Martínez, M. K. Kim, R. Castañeda, and A. Blandón, "Simultaneous Dual-Wavelength Reflection Digital Holography Applied to the Study of the Porous Coal Samples," Appl. Opt. 47, 3203-3210 (2008). [CrossRef] [PubMed]
- M. Born and E. Wolfe, Principles of Optics (Pergamon, 1964).
- P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, "Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging," Appl. Opt. 42, 1938-1946 (2003). [CrossRef] [PubMed]

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