## Optical diffraction tomography for high resolution live cell imaging

Optics Express, Vol. 17, Issue 1, pp. 266-277 (2009)

http://dx.doi.org/10.1364/OE.17.000266

Acrobat PDF (5036 KB)

### Abstract

We report the experimental implementation of optical diffraction tomography for quantitative 3D mapping of refractive index in live biological cells. Using a heterodyne Mach-Zehnder interferometer, we record complex field images of light transmitted through a sample with varying directions of illumination. To quantitatively reconstruct the 3D map of complex refractive index in live cells, we apply optical diffraction tomography based on the Rytov approximation. In this way, the effect of diffraction is taken into account in the reconstruction process and diffraction-free high resolution 3D images are obtained throughout the entire sample volume. The quantitative refractive index map can potentially serve as an intrinsic assay to provide the molecular concentrations without the addition of exogenous agents and also to provide a method for studying the light scattering properties of single cells.

© 2009 Optical Society of America

## 1. Introduction

1. F. Zernike, “Phase-contrast, a new method for microscopic observation of transparent objects. Part I.,” Physica **9**, 686–698 (1942). [CrossRef]

3. Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express **14**, 8263–8268 (2006). [CrossRef] [PubMed]

8. G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett. **97**, 218101 (2006). [CrossRef] [PubMed]

14. F. Charriere, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express **14**, 7005–7013 (2006). [CrossRef] [PubMed]

16. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nature Methods **4**, 717–719 (2007). [CrossRef] [PubMed]

20. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. **1**, 153–156 (1969). [CrossRef]

13. W. Gorski and W. Osten, “Tomographic imaging of photonic crystal fibers,” Opt. Lett. **32**, 1977–1979 (2007). [CrossRef] [PubMed]

15. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. **205**, 165–176 (2002). [CrossRef] [PubMed]

21. M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. **19**, (2008). [CrossRef]

13. W. Gorski and W. Osten, “Tomographic imaging of photonic crystal fibers,” Opt. Lett. **32**, 1977–1979 (2007). [CrossRef] [PubMed]

15. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. **205**, 165–176 (2002). [CrossRef] [PubMed]

21. M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. **19**, (2008). [CrossRef]

16. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nature Methods **4**, 717–719 (2007). [CrossRef] [PubMed]

22. W. S. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Extended depth of focus in tomographic phase microscopy using a propagation algorithm,” Opt. Lett. **33**, 171–173 (2008). [CrossRef] [PubMed]

23. Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA **105**, 13730–13735 (2008). [CrossRef] [PubMed]

24. W. Choi, C. C. Yu, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Field-based angle-resolved light-scattering study of single live cells,” Opt. Lett. **33**, 1596–1598 (2008). [CrossRef] [PubMed]

## 2. Theory of optical diffraction tomography

20. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. **1**, 153–156 (1969). [CrossRef]

25. A. J. Devaney, “Inverse-Scattering Theory within the Rytov Approximation,” Opt. Lett. **6**, 374–376 (1981). [CrossRef] [PubMed]

*U*(

*R*⃗), through the medium, can be described by the wave equation as follows:

*k*

_{0}= 2

*π*/

*λ*

_{0}is the wave number in the free space with

*λ*

_{0}the wavelength in the free space, and

*n*(

*R*⃗) is the complex refractive index. If the field is decomposed into the incident field

*U*

^{(I)}(

*R*⃗) and scattered field

*U*

^{(S)}(

*R*⃗),

*F*(

*R*⃗) = -(2

*π*

*n*/

_{m}*λ*

_{0})

^{2}((

*n*(

*R*⃗)/

*n*)

_{m}^{2}-1), and

*n*is the refractive index of the medium.

_{m}*F*(

*R*⃗) is known as the object function. Based on Green’s theorem, the formal solution to Eq. (3) can be written as

*G*(

*r*) = exp(

*in*

_{m}k_{0}

*r*) / (4

*πr*) the Green’s function. Since the integrand contains the unknown variable,

*U*(

*R*⃗), we employ an approximation to obtain a closed form solution for

*U*

^{(S)}(

*R*⃗). The first Born approximation is the simplest we can introduce when the scattered field is much weaker than the incident field (

*U*

^{(s)}≪

*U*

^{(I)}), in which case the scattered field is given by the following equation:

*F*(

*R*⃗) and the scattered field

*U*

^{(s)}(

*R*⃗). By taking Fourier transform of both sides of Eq. (5), we obtain the following relation, known as the Fourier diffraction theorem [20

20. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. **1**, 153–156 (1969). [CrossRef]

*F*̂ and

*U*̂

^{(s)}are the 3D and 2D Fourier transform of

*F*and

*U*

^{(s)}, respectively;

*k*and

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

_{y}*x*and

*y*in the transverse image plane, respectively;

*z*

^{+}=0 is the axial coordinate of the detector plane, which is the plane of objective focus in the experiment. (

*K*,

_{x}*K*,

_{y}*K*, the spatial frequencies in the object frame, define the spatial frequency vector of (

_{z}*k*,

_{x}*k*,

_{y}*k*) relative to the spatial frequency vector of the incident beam (

_{z}*k*

*,*

_{x0}*k*

*,*

_{y0}*k*), and

_{z0}*k*is determined by the relation

_{z}*(K*. As a result, we can map different regions of the 3D frequency spectrum of the object function

_{x}, K_{y}, K_{z})*F*(

*R*⃗) with various 2D angular complex E-field images. After completing the mapping, we can take the inverse Fourier transform of

*F*̂ to get the 3D distribution of the complex refractive index.

*π*/2[19]. The thickness of single biological cells is typically about 10 μm, with index difference with respect to the medium about 0.03. Thus, the phase delay induced by typical cells is approximately π at a source wavelength of

*λ*= 633 nm. Therefore, one would not expect the Born approximation to be valid for imaging biological cells.

*gradient*of the refractive index. Specifically, the Rytov approximation is valid when the following condition is satisfied:

*n*is the index variation in the sample over the length scale of wavelength. This condition basically asserts that the Rytov approximation is independent of the specimen size and only limited by the phase gradient ∇

_{δ}_{ψ}

^{(s)}. For a weakly scattering sample such as biological cell, the phase change ∇

_{ψ}

^{(s)}is linearly proportional to

*n*to a first approximation, such that the relation is valid when

_{δ}*n*≪

_{δ}*1*. According to our previous work [16

16. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nature Methods **4**, 717–719 (2007). [CrossRef] [PubMed]

*n*

*is in the range of 0.03 – 0.04 for biological cells. As shown in the Section 4, we obtain a high quality image of a live cell when we use the Rytov approximation, while the Born approximation leads to significant distortions in the reconstructed image.*

_{δ}25. A. J. Devaney, “Inverse-Scattering Theory within the Rytov Approximation,” Opt. Lett. **6**, 374–376 (1981). [CrossRef] [PubMed]

*ϕ*(

*R*⃗), defined by

*U*(

*R*⃗) =

*e*

*, and substitute this into the wave equation (Eq. (1)). After applying the approximation of Eq. (7), we again obtain the Fourier diffraction theorem (Eq. (6)), but with*

^{ϕ(R⃗)}*U*

^{(s)}replaced by

*U*

_{Rytov}^{(s)}defined as

## 3. Experiment

**4**, 717–719 (2007). [CrossRef] [PubMed]

5. C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, “Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy,” Opt. Lett. **32**, 1572–1574 (2007). [CrossRef] [PubMed]

## 4. Data analysis

*ψ*(

*x*,

*y*;

*θ*) and an amplitude image

*A*(

*x*,

*y*;

*θ*) taken at each illumination angle,

*θ*, we can reconstruct the total E-field,

*U*(

*x*,

*y*;

*θ*) =

*A*(

*x*,

*y*;

*θ*)

*e*

^{iψ(x,y;θ)}, at the image plane. The measured field image is composed of the phase change induced by the sample and the phase ramp introduced by the tilted illumination. A corresponding set of images

*U*(

_{bg}*x*,

*y*;

*θ*) =

*A*(

_{bg}*x*,

*y*;

*θ*)

*e*

^{ikx0x + iky0y}taken when no sample is present provides the background field, which can be considered as the incident fields. Figure 2(a) shows the phase image

*ψ*(

*x*,

*y*;

*θ*= 0) of a 6 μm polystyrene bead (Polysciences. Inc.) taken at zero incidence angle. The refractive index of beads according to manufacturer specifications is 1.585 at 633 nm wavelength, and this value was used to validate experimental measurements. Figure 2(b) shows the typical amplitude image of

*U*̂(

*k*,

_{x}*k*;

_{y}*θ*) on a logarithmic scale.

*k*,

_{x}*k*) on the right hand side into (

_{y}*K*,

_{x}*K*) as follows.

_{y}*U*̂

^{(s)}(

*k*,

_{x}*k*;

_{y}*θ*) (Eq. (2)) or

*U*̂

_{Rytov}

^{(s)}(

*k*,

_{x}*k*;

_{y}*θ*)(Eq. (8)) from measured complex fields. We then shift them by (-

*k*

_{x0},-

*k*

_{y0}) in spatial frequency space following the right hand side of Eq. (9). In mapping the experimental data, we divide them by the incident field

*U*(

_{bg}*x*,

*y*;

*θ*), which is equivalent to shifting them in Fourier space. In other words, the scattered field used in the Fourier diffraction theorem in the experiment is as follows:

*(*

*K*,

_{x}*K*,

_{y}*K*=

_{z}*0)*and

*(K*planes, respectively. The data along the blue line in Fig. 2(b) is mapped onto the blue half-circle on the

_{x}, K_{y}=0,K_{z})*(K*space of Fig. 2(d). Different angular images are mapped onto different spaces such that they eventually cover a significant portion of the

_{x}, K_{z})*(K*space of the object function

_{x}, K_{y}, K_{z})*F*(

*R*⃗). Looking at the frequency spectrum of Figs. 2(c)-(d), ring patterns are clearly visible after mapping various angular images, which is expected for the spherical shape of the sample. By taking the inverse Fourier transform of the entire 3D frequency spectrum, we obtain the 3D distribution of refractive index and absorption coefficient of the object.

17. K. C. Tam and V. Perezmendez, “Tomographical Imaging with Limited-Angle Input,” J. Opt. Soc. Am. **71**, 582–592 (1981). [CrossRef]

18. B. P. Medoff, W. R. Brody, M. Nassi, and A. Macovski, “Iterative Convolution Backprojection Algorithms for Image-Reconstruction from Limited Data,” J. Opt. Soc. Am. **73**, 1493–1500 (1983). [CrossRef]

## 5. Experimental results

**4**, 717–719 (2007). [CrossRef] [PubMed]

## 6. Discussion

15. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. **205**, 165–176 (2002). [CrossRef] [PubMed]

23. Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA **105**, 13730–13735 (2008). [CrossRef] [PubMed]

24. W. Choi, C. C. Yu, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Field-based angle-resolved light-scattering study of single live cells,” Opt. Lett. **33**, 1596–1598 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | F. Zernike, “Phase-contrast, a new method for microscopic observation of transparent objects. Part I.,” Physica |

2. | G. Nomarski, “Microinterféromètre différentiel à ondes polarisées,” J. Phys. Radium |

3. | Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express |

4. | G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. |

5. | C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, “Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy,” Opt. Lett. |

6. | 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. |

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

8. | G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett. |

9. | B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express |

10. | N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Live cell refractometry using microfluidic devices,” Opt. Lett. |

11. | B. Rappaz, F. Charriere, C. Depeursinge, P. J. 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. |

12. | A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. |

13. | W. Gorski and W. Osten, “Tomographic imaging of photonic crystal fibers,” Opt. Lett. |

14. | F. Charriere, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express |

15. | V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. |

16. | W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nature Methods |

17. | K. C. Tam and V. Perezmendez, “Tomographical Imaging with Limited-Angle Input,” J. Opt. Soc. Am. |

18. | B. P. Medoff, W. R. Brody, M. Nassi, and A. Macovski, “Iterative Convolution Backprojection Algorithms for Image-Reconstruction from Limited Data,” J. Opt. Soc. Am. |

19. | A. C. Kak and M. Slaney, |

20. | E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. |

21. | M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. |

22. | W. S. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Extended depth of focus in tomographic phase microscopy using a propagation algorithm,” Opt. Lett. |

23. | Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. USA |

24. | W. Choi, C. C. Yu, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Field-based angle-resolved light-scattering study of single live cells,” Opt. Lett. |

25. | A. J. Devaney, “Inverse-Scattering Theory within the Rytov Approximation,” Opt. Lett. |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(180.0180) Microscopy : Microscopy

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: October 7, 2008

Revised Manuscript: November 20, 2008

Manuscript Accepted: December 11, 2008

Published: January 2, 2009

**Virtual Issues**

Vol. 4, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

Yongjin Sung, Wonshik Choi, Christopher Fang-Yen, Kamran Badizadegan, Ramachandra R. Dasari, and Michael S. Feld, "Optical diffraction tomography for high resolution live cell imaging," Opt. Express **17**, 266-277 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-266

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### References

- F. Zernike, "Phase-contrast, a new method for microscopic observation of transparent objects. Part I.," Physica 9, 686-698 (1942). [CrossRef]
- Q1. G. Nomarski, "Microinterféromètre différentiel à ondes polarisées," J. Phys. Radium 16, 9S-11S (1955).
- Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Diffraction phase and fluorescence microscopy," Opt. Express 14, 8263-8268 (2006). [CrossRef] [PubMed]
- G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, "Diffraction phase microscopy for quantifying cell structure and dynamics," Opt. Lett. 31, 775-777 (2006). [CrossRef] [PubMed]
- C. Fang-Yen, S. Oh, Y. Park, W. Choi, S. Song, H. S. Seung, R. R. Dasari, and M. S. Feld, "Imaging voltage-dependent cell motions with heterodyne Mach-Zehnder phase microscopy," Opt. Lett. 32, 1572-1574 (2007). [CrossRef] [PubMed]
- 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]
- A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, "Quantitative optical phase microscopy," Opt. Lett. 23, 817-819 (1998). [CrossRef]
- G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, "Optical measurement of cell membrane tension," Phys. Rev. Lett. 97, 218101 (2006). [CrossRef] [PubMed]
- B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005). [CrossRef] [PubMed]
- N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, "Live cell refractometry using microfluidic devices," Opt. Lett. 31, 2759-2761 (2006). [CrossRef] [PubMed]
- B. Rappaz, F. Charriere, C. Depeursinge, P. J. 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]
- A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000). [CrossRef]
- W. Gorski and W. Osten, "Tomographic imaging of photonic crystal fibers," Opt. Lett. 32, 1977-1979 (2007). [CrossRef] [PubMed]
- F. Charriere, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, "Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba," Opt. Express 14, 7005-7013 (2006). [CrossRef] [PubMed]
- V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002). [CrossRef] [PubMed]
- W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, "Tomographic phase microscopy," Nature Methods 4, 717-719 (2007). [CrossRef] [PubMed]
- K. C. Tam and V. Perezmendez, "Tomographical Imaging with Limited-Angle Input," J. Opt. Soc. Am. 71, 582-592 (1981). [CrossRef]
- B. P. Medoff, W. R. Brody, M. Nassi, and A. Macovski, "Iterative Convolution Backprojection Algorithms for Image-Reconstruction from Limited Data," J. Opt. Soc. Am. 73, 1493-1500 (1983). [CrossRef]
- A. C. Kak, and M. Slaney, Principles of Computerized Tomographic Imaging (Academic Press, New York, 1999).
- E. Wolf, "Three-dimensional structure determination of semi-transparent objects from holographic data," Opt. Commun. 1, 153-156 (1969). [CrossRef]
- Q2. M. Debailleul, B. Simon, V. Georges, O. Haeberle, and V. Lauer, "Holographic microscopy and diffractive microtomography of transparent samples," Meas. Sci. Technol. 19, (2008). [CrossRef]
- W. S. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Extended depth of focus in tomographic phase microscopy using a propagation algorithm," Opt. Lett. 33, 171-173 (2008). [CrossRef] [PubMed]
- Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, "Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum," Proc. Natl. Acad. Sci. USA 105, 13730-13735 (2008). [CrossRef] [PubMed]
- W. Choi, C. C. Yu, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Field-based angle-resolved light-scattering study of single live cells," Opt. Lett. 33, 1596-1598 (2008). [CrossRef] [PubMed]
- A. J. Devaney, "Inverse-Scattering Theory within the Rytov Approximation," Opt. Lett. 6, 374-376 (1981). [CrossRef] [PubMed]

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