OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 20 — Jul. 10, 2013
  • pp: 4933–4940

Virtual source method for diffuse optical imaging

Hakan Erkol and Mehmet Burcin Unlu  »View Author Affiliations

Applied Optics, Vol. 52, Issue 20, pp. 4933-4940 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (517 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The Green’s function for diffusive wave propagation can be obtained by utilizing the representation theorems of the convolution type and the correlation type. In this work, the Green’s function is retrieved by making use of the Robin boundary condition and the representation theorems for diffusive media. The diffusive Green’s function between two detectors for photon flux is calculated by combining detector readings due to point light sources and utilizing virtual light sources at the detector positions in optical tomography. Two dimensional simulations for a circular region with eight sources and eight detectors located on the boundary are performed using a finite element method to demonstrate the feasibility of virtual sources. The most important potential application would be the replacement of noisy measurements with synthetic measurements that are provided by the virtual sources. This becomes an important issue in small animal and human studies. In addition, the same method may also be used to reduce the imaging time.

© 2013 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5270) Medical optics and biotechnology : Photon density waves

ToC Category:
Medical Optics and Biotechnology

Original Manuscript: January 31, 2013
Revised Manuscript: April 16, 2013
Manuscript Accepted: May 20, 2013
Published: July 9, 2013

Virtual Issues
Vol. 8, Iss. 8 Virtual Journal for Biomedical Optics

Hakan Erkol and Mehmet Burcin Unlu, "Virtual source method for diffuse optical imaging," Appl. Opt. 52, 4933-4940 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Wapenaar, E. Slob, and R. Snieder, “Seismic and electromagnetic controlled-source interferometry in dissipative media,” Geophys. Prospect. 56, 419–434 (2008). [CrossRef]
  2. D. Halliday, A. Curtis, and K. Wapenaar, “Generalized PP+ PS= SS from seismic interferometry,” Geophys. J. Int. 189, 1015–1024 (2012). [CrossRef]
  3. G. Melo, A. Malcolm, and M. Fehler, “Comparison of microearthquake locations using seismic interferometry principles,” in SEG Technical Program Expanded Abstracts 2012 (Society of Exploration Geophysicists, 2012), pp. 1–5.
  4. K. Wapenaar, E. Slob, and R. Snieder, “Unified Green’s function retrieval by cross correlation,” Phys. Rev. Lett. 97, 234301 (2006). [CrossRef]
  5. R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001). [CrossRef]
  6. R. Weaver and O. Lobkis, “On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons,” Ultrasonics 40, 435–439 (2002). [CrossRef]
  7. K. Wapenaar, “Retrieving the elastodynamic Green’s function of an arbitrary inhomogeneous medium by cross correlation,” Phys. Rev. Lett. 93, 254301 (2004). [CrossRef]
  8. M. Campillo and A. Paul, “Long-range correlations in the diffuse seismic coda,” Science 299, 547–549 (2003). [CrossRef]
  9. J. T. Fokkema and P. M. van den Berg, Seismic Applications of Acoustic Reciprocity (Elsevier, 1993).
  10. R. Snieder, “Retrieving the Green’s function of the diffusion equation from the response to a random forcing,” Phys. Rev. E 74, 0466201 (2006). [CrossRef]
  11. R. Snieder, “Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves,” J. Acoust. Soc. Am. 121, 2637–2643 (2007). [CrossRef]
  12. B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005). [CrossRef]
  13. B. J. Tromberg, “Optical scanning and breast cancer,” Acad. Radiol. 12, 923–924 (2005). [CrossRef]
  14. 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, 2443–2451 (2008). [CrossRef]
  15. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005). [CrossRef]
  16. A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006). [CrossRef]
  17. A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007). [CrossRef]
  18. B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003). [CrossRef]
  19. B. W. Pogue, “Near-infrared characterization of disease via vascular permeability probes,” Acad. Radiol. 13, 1–3 (2006). [CrossRef]
  20. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999). [CrossRef]
  21. A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).
  22. M. B. Unlu and G. Gulsen, “Effects of the time dependence of a bioluminescent source on the tomographic reconstruction,” Appl. Opt. 47, 799–806 (2008). [CrossRef]
  23. M. B. Unlu, O. Birgul, and G. Gulsen, “A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (dce-dot),” Phys. Med. Biol. 53, 3189–3200 (2008). [CrossRef]
  24. M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008). [CrossRef]
  25. H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999). [CrossRef]
  26. H. Dehghani, S. R. Arridge, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1670 (2000). [CrossRef]
  27. J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).
  28. P. Giacometti and S. G. Diamond, “Diffuse optical tomography for brain imaging: continuous wave instrumentation and linear analysis methods,” in Optical Methods and Instrumentation in Brain Imaging and Therapy (Springer, 2013), pp. 57–85.
  29. T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002). [CrossRef]
  30. B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998). [CrossRef]
  31. S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992). [CrossRef]
  32. A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001). [CrossRef]
  33. S. Thomsen and D. Tatman, “Physiological and pathological factors of human breast disease that can influence optical diagnosis,” Ann. N.Y. Acad. Sci. 838, 171–193 (1998). [CrossRef]
  34. B. W. Pogue, H. Jiang, K. D. Paulsen, and U. L. Osterberg, “Frequency-domain diffuse optical tomography of breast tissue: detector size and imaging geometry,” in Proceedings of the IEEE Conference on Engineering in Medicine and Biology Society (IEEE, 1997), p. 2745.
  35. M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997). [CrossRef]
  36. A. D. Hoop and H. Stam, “Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems,” Wave Motion 10, 479–489 (1988). [CrossRef]
  37. M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006). [CrossRef]
  38. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995). [CrossRef]
  39. K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995). [CrossRef]
  40. H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003). [CrossRef]
  41. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993). [CrossRef]
  42. S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000). [CrossRef]
  43. Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007). [CrossRef]
  44. T. Nielsen, T. Koehler, M. van der Mark, and G. t’Hooft, “Fully 3D reconstruction of attenuation for diffuse optical tomography using a finite element model,” in Proceedings of IEEE Conference on Nuclear Science (IEEE, 2005), p. 2283.
  45. D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34, 4293–4301 (2007). [CrossRef]
  46. M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.
  47. T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50, 4913–4930 (2005). [CrossRef]
  48. P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006). [CrossRef]
  49. J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited