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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 3 — Mar. 1, 1999
  • pp: 455–466

Analysis of the forward problem with diffuse photon density waves in turbid media by use of a diffraction tomography model

Charles L. Matson and Hanli Liu  »View Author Affiliations


JOSA A, Vol. 16, Issue 3, pp. 455-466 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000455


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Abstract

We extend our previously developed diffraction tomography model of diffuse photon density wave propagation in turbid media to analyze the forward problem associated with detecting and resolving both absorptive and scattering inhomogeneities. Our results assume that detection occurs in a plane but no restrictions are placed on the illumination source geometry. We then specialize these results to plane-wave illumination and derive the turbid media version of the Fourier diffraction theorem. We also develop a shot-noise-limited Fourier-domain signal-to-noise-ratio (SNR) expression to determine how background, system, and inhomogeneity parameters affect one’s ability to detect and resolve inhomogeneities. We show that, in general, scattering inhomogeneities are more easily resolved than absorbing inhomogeneities. We also show that lower temporal modulation frequencies enhance one’s ability to detect and resolve inhomogeneities. These theoretical results are compared with previously published image-domain SNR results, and qualitative agreement is demonstrated.

© 1999 Optical Society of America

OCIS Codes
(100.6950) Image processing : Tomographic image processing
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5280) Medical optics and biotechnology : Photon migration

Citation
Charles L. Matson and Hanli Liu, "Analysis of the forward problem with diffuse photon density waves in turbid media by use of a diffraction tomography model," J. Opt. Soc. Am. A 16, 455-466 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-3-455


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References

  1. G. H. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, and P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).
  2. D. S. Dilworth, E. N. Leith, and J. L. Lopez, “Imaging absorbing structures within thick diffusing media,” Appl. Opt. 29, 691–698 (1990).
  3. M. Catler, “Transillumination as an aid in the diagnosis of breast lesions. With special reference to its value in cases of bleeding nipple,” Surg. Gynecol. Obstet. 48, 721–729 (1929).
  4. B. Ohlsen, J. Gunderson, and D. M. Nilson, “Diaphanography: a method for evaluation of the female breast,” World J. Surg. 4, 701–706 (1980).
  5. S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, and N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 180–213 (1997).
  6. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
  7. J. A. Izatt, M. R. Hee, and G. M. Owen, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
  8. J. M. Schmitt, A. Knüttel, A. Gandjbakche, and M. A. Eckhaus, “Optical coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
  9. R. R. Alfano, X. Liang, L. Wang, and P. P. Ho, “Time-resolved imaging of translucent droplets in highly scattering turbid media,” Science 264, 1913–1915 (1994).
  10. B. B. Das, K. M. Yoo, and R. R. Alfano, “Ultrafast time-gated imaging in thick tissues—a step towards optical mammography,” Opt. Lett. 18, 1092–1094 (1993).
  11. M. S. Patterson, B. Chance, and B. C. Wilson, “Time-resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
  12. S. C. W. Hyde, N. P. Barry, R. Jones, J. C. Dainty, P. M. W. French, M. B. Klein, and B. A. Wechsler, “Depth-resolved holographic imaging through scattering media by photorefraction,” Opt. Lett. 20, 1331–1333 (1995).
  13. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).
  14. H. B. Jiang, K. D. Paulsen, U. L. Osterberg, and M. S. Patterson, “Frequency-domain optical-image reconstruction in turbid media—an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
  15. H. B. Jiang, K. D. Paulsen, U. L. Osterberg, and M. S. Patterson, “Frequency-domain optical-image reconstruction in turbid media—an experimental study of single-target detectability: erratum,” Appl. Opt. 36, 2995–2996 (1997).
  16. X. D. Li, T. Durduran, A. G. Yodh, B. Chance, and D. N. Pattanayak, “Diffraction tomography for biochemical imaging with diffuse-photon density waves,” Opt. Lett. 22, 573–575 (1997).
  17. C. L. Matson, N. Clark, L. McMackin, and J. S. Fender, “Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves,” Appl. Opt. 36, 214–220 (1997).
  18. A. J. Devaney, “Reconstructive tomography with diffracting wavefields,” Inverse Probl. 2, 161–183 (1986).
  19. A. Schatzberg and A. J. Devaney, “Super-resolution in diffraction tomography,” Inverse Probl. 8, 149–164 (1992).
  20. A. J. Devaney, “Linearised inverse scattering in attenuating media,” Inverse Probl. 3, 389–397 (1987).
  21. A. J. Devaney, “The limited-view problem in diffraction tomography,” Inverse Probl. 5, 501–521 (1989).
  22. C. L. Matson, “A diffraction tomographic model of the forward problem using diffuse photon density waves,” Opt. Express 1, 6–11 (1997).
  23. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
  24. A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).
  25. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Simultaneous scattering and absorption images of heterogeneous media using diffuse waves within the Rytov approximation,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. R. Alfano, eds., Proc. SPIE 2389, 320–327 (1995).
  26. A. Baños, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, UK, 1966).
  27. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
  28. H. Stark, “Sampling theorems in polar coordinates,” J. Opt. Soc. Am. 69, 1519–1525 (1979).
  29. H. Stark and M. Wengrovitz, “Comments and corrections on the use of polar sampling theorems in CT,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 1329–1331 (1983).
  30. C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
  31. C. L. Matson, “Resolution, linear filtering, and positivity,” J. Opt. Soc. Am. A 15, 33–41 (1998).
  32. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  33. A. Lannes, S. Roques, and M. J. Casanove, “Stabilized reconstruction in signal and image processing. I. Partial deconvolution and spectral extrapolation with limited field,” J. Mod. Opt. 34, 161–226 (1987).
  34. C. L. Matson, I. A. DeLarue, T. M. Gray, and I. E. Drunzer, “Optimal Fourier spectrum estimation from the bispectrum,” Comput. Electr. Eng. 18, 485–497 (1992).
  35. J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).
  36. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991), p. 418.
  37. M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1996).
  38. The PMI software was developed by D. Boas, M. A. O’Leary, X. Li, B. Chance, A. G. Yodh, M. A. Ostermeyer, and S. L. Jacques. It is available on the Web or from D. Boas (email, dboas@emerald.tufts.edu).

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