## Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light

Optics Express, Vol. 17, Issue 17, pp. 14780-14790 (2009)

http://dx.doi.org/10.1364/OE.17.014780

Acrobat PDF (359 KB)

### Abstract

We present a wide-field method for obtaining three-dimensional images of turbid media. By projecting patterns of light of varying spatial frequencies on a sample, we reconstruct quantitative, depth resolved images of absorption contrast. Images are reconstructed using a fast analytic inversion formula and a novel correction to the diffusion approximation for increased accuracy near boundaries. The method provides more accurate quantification of optical absorption and higher resolution than standard diffuse reflectance measurements.

© 2009 OSA

## 1. Introduction

1. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. **50**(4), R1–R43 (2005). [PubMed]

2. B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. **35**(6), 2443–2451 (2008). [PubMed]

3. J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology **40**(4), 501–510 (2003). [PubMed]

4. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. **23**(3), 313–320 (2005). [PubMed]

5. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. **30**(11), 1354–1356 (2005). [PubMed]

7. A. Joshi, W. Bangerth, K. Hwang, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence optical tomography from time-dependent measurements with area illumination and detection,” Med. Phys. **33**(5), 1299–1310 (2006). [PubMed]

5. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. **30**(11), 1354–1356 (2005). [PubMed]

8. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. **14**(2), 024012 (2009). [PubMed]

9. D. Abookasis, C. C. Lay, M. S. Mathews, M. E. Linskey, R. D. Frostig, and B. J. Tromberg, “Imaging cortical absorption, scattering, and hemodynamic response during ischemic stroke using spatially modulated near-infrared illumination,” J. Biomed. Opt. **14**(2), 024033 (2009). [PubMed]

10. D. J. Cuccia, D. Abookasis, R. D. Frostig, and B. J. Tromberg, “Quantitative in vivo imaging of tissue absorption, scattering, and hemoglobin concentration in rat cortex using spatially-modulated structured light,” in *In Vivo Optical Imaging of Brain Function,* 2nd ed., R. D. Frostig, ed. (CRC, 2009).

12. V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(5), 056616 (2004). [PubMed]

14. S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, “Imaging complex structures with diffuse light,” Opt. Express **16**(7), 5048–5060 (2008). [PubMed]

16. V. Lukic, V. A. Markel, and J. C. Schotland, “Optical tomography with structured illumination,” Opt. Lett. **34**(7), 983–985 (2009). [PubMed]

16. V. Lukic, V. A. Markel, and J. C. Schotland, “Optical tomography with structured illumination,” Opt. Lett. **34**(7), 983–985 (2009). [PubMed]

## 2. Methods

### 2.1 Theory

12. V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(5), 056616 (2004). [PubMed]

*c*is the speed of light in the medium,

*ℓ*is the extrapolation length, and

**k**.

**k**, has intensity

**ρ**, Eq. (11) can be put in block diagonal form and inverted by analytical methods which have been previously described [12

_{d}12. V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(5), 056616 (2004). [PubMed]

*M*and

*θ*are the modulation depth and phase of the source. Since the diffusion equation is linear, we can obtain the data that would be generated by a source of the form of Eq. (10) by using the source described by Eq. (14). To do so, we acquire data for at least three phases, and add a linear combination of the resulting measurements of light intensity

### 2.2 Instrumentation

^{−1}with four phases each were used. The diffuse reflected light images were acquired at 650 nm with a Nuance Multispectral Imaging System (CRi Inc., Woburn, MA) which consists of a liquid crystal tunable filter capable of acquiring at discrete wavelengths (10nm bandwidth) between 650 nm and 1100 nm, and a 1040 x 1392 pixel, front illuminated charge coupled device (CCD). A 6x6 cm field of view was acquired by the CCD using 4x4 hardware binning and an exposure time of ~100 ms. Cross-polarizers were placed at the source and detector in order to eliminate any specular reflection.

### 2.3 Phantoms

21. http://www.bli.uci.edu/ntroi/phantoms.php, retrieved April 24th, 2009.

5. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. **30**(11), 1354–1356 (2005). [PubMed]

## 3. Results and discussion

14. S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, “Imaging complex structures with diffuse light,” Opt. Express **16**(7), 5048–5060 (2008). [PubMed]

## 5. Conclusion

## Acknowledgements

## References and links

1. | A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. |

2. | B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. |

3. | J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology |

4. | V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. |

5. | D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. |

6. | A. Bassi, C. D’Andrea, G. Valentini, R. Cubeddu, and S. Arridge, “Temporal propagation of spatial information in turbid media,” Opt. Lett. |

7. | A. Joshi, W. Bangerth, K. Hwang, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence optical tomography from time-dependent measurements with area illumination and detection,” Med. Phys. |

8. | D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. |

9. | D. Abookasis, C. C. Lay, M. S. Mathews, M. E. Linskey, R. D. Frostig, and B. J. Tromberg, “Imaging cortical absorption, scattering, and hemodynamic response during ischemic stroke using spatially modulated near-infrared illumination,” J. Biomed. Opt. |

10. | D. J. Cuccia, D. Abookasis, R. D. Frostig, and B. J. Tromberg, “Quantitative in vivo imaging of tissue absorption, scattering, and hemoglobin concentration in rat cortex using spatially-modulated structured light,” in |

11. | J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. in press. |

12. | V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

13. | J. C. Schotland and V. A. Markel, “Inverse scattering with diffusing waves,” J. Opt. Soc. Am. A |

14. | S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, “Imaging complex structures with diffuse light,” Opt. Express |

15. | Z. M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, “Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets,” Opt. Lett. |

16. | V. Lukic, V. A. Markel, and J. C. Schotland, “Optical tomography with structured illumination,” Opt. Lett. |

17. | G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, “Superresolution and corrections to the diffusion approximation in optical tomography,” Appl. Phys. Lett. |

18. | V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. II. Role of boundary conditions,” J. Opt. Soc. Am. A |

19. | V. A. Markel, V. Mital, and J. C. Schotland, “Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition,” J. Opt. Soc. Am. A |

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

21. | http://www.bli.uci.edu/ntroi/phantoms.php, retrieved April 24th, 2009. |

22. | F. Bevilacqua, A. J. Berger, A. E. Cerussi, D. Jakubowski, and B. J. Tromberg, “Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods,” Appl. Opt. |

23. | H. P. Tuan, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. |

24. | B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. |

25. | J. C. Schotland and V. A. Markel, “Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation,” Inverse Problems and Imaging |

26. | G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “Radiative Transport Equation in Rotated Reference Frames,” J. Phys. A |

27. | V. A. Markel, “Modified spherical hamonics method for solving the radiative transport equation,” Waves Random Media |

**OCIS Codes**

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

(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics

(110.0113) Imaging systems : Imaging through turbid media

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: June 9, 2009

Revised Manuscript: August 3, 2009

Manuscript Accepted: August 4, 2009

Published: August 5, 2009

**Virtual Issues**

Vol. 4, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Soren D. Konecky, Amaan Mazhar, David Cuccia, Anthony J. Durkin, John C. Schotland, and Bruce J. Tromberg, "Quantitative optical tomography of sub-surface heterogeneities using spatially modulated structured light," Opt. Express **17**, 14780-14790 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14780

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### References

- A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005). [PubMed]
- B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35(6), 2443–2451 (2008). [PubMed]
- J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology 40(4), 501–510 (2003). [PubMed]
- V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005). [PubMed]
- D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30(11), 1354–1356 (2005). [PubMed]
- A. Bassi, C. D’Andrea, G. Valentini, R. Cubeddu, and S. Arridge, “Temporal propagation of spatial information in turbid media,” Opt. Lett. 33(23), 2836–2838 (2008). [PubMed]
- A. Joshi, W. Bangerth, K. Hwang, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence optical tomography from time-dependent measurements with area illumination and detection,” Med. Phys. 33(5), 1299–1310 (2006). [PubMed]
- D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009). [PubMed]
- D. Abookasis, C. C. Lay, M. S. Mathews, M. E. Linskey, R. D. Frostig, and B. J. Tromberg, “Imaging cortical absorption, scattering, and hemodynamic response during ischemic stroke using spatially modulated near-infrared illumination,” J. Biomed. Opt. 14(2), 024033 (2009). [PubMed]
- D. J. Cuccia, D. Abookasis, R. D. Frostig, and B. J. Tromberg, “Quantitative in vivo imaging of tissue absorption, scattering, and hemoglobin concentration in rat cortex using spatially-modulated structured light,” in In Vivo Optical Imaging of Brain Function, 2nd ed., R. D. Frostig, ed. (CRC, 2009).
- J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. in press.
- V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 056616 (2004). [PubMed]
- J. C. Schotland and V. A. Markel, “Inverse scattering with diffusing waves,” J. Opt. Soc. Am. A 18(11), 2767–2777 (2001).
- S. D. Konecky, G. Y. Panasyuk, K. Lee, V. Markel, A. G. Yodh, and J. C. Schotland, “Imaging complex structures with diffuse light,” Opt. Express 16(7), 5048–5060 (2008). [PubMed]
- Z. M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, “Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets,” Opt. Lett. 30(24), 3338–3340 (2005).
- V. Lukic, V. A. Markel, and J. C. Schotland, “Optical tomography with structured illumination,” Opt. Lett. 34(7), 983–985 (2009). [PubMed]
- G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, “Superresolution and corrections to the diffusion approximation in optical tomography,” Appl. Phys. Lett. 87(10), 101111 (2005).
- V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. II. Role of boundary conditions,” J. Opt. Soc. Am. A 19(3), 558–566 (2002).
- V. A. Markel, V. Mital, and J. C. Schotland, “Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition,” J. Opt. Soc. Am. A 20(5), 890–902 (2003).
- A. C. Kak, and M. Slaney, Principles of Computerized Imaging (IEEE, 1988).
- http://www.bli.uci.edu/ntroi/phantoms.php , retrieved April 24th, 2009.
- F. Bevilacqua, A. J. Berger, A. E. Cerussi, D. Jakubowski, and B. J. Tromberg, “Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods,” Appl. Opt. 39(34), 6498–6507 (2000).
- H. P. Tuan, O. Coquoz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71(6), 2500–2513 (2000).
- B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38(13), 2950–2961 (1999).
- J. C. Schotland and V. A. Markel, “Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation,” Inverse Problems and Imaging 1, 147–154 (2007).
- G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “Radiative Transport Equation in Rotated Reference Frames,” J. Phys. A 39(1), 115–137 (2006).
- V. A. Markel, “Modified spherical hamonics method for solving the radiative transport equation,” Waves Random Media 14(1), L13–L19 (2004).

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