A diffraction tomographic model of the forward problem using diffuse photon density waves
Optics Express, Vol. 1, Issue 1, pp. 6-11 (1997)
http://dx.doi.org/10.1364/OE.1.000006
Acrobat PDF (98 KB)
Abstract
We present a model of the forward problem for diffuse photon density waves in turbid medium using a diffraction tomographic problem formulation. We consider a spatially-varying inhomogeneous structure whose absorption properties satisfy the Born approximation and whose scattering properties are identical to the homogeneous turbid media in which it is imbedded. The two-dimensional Fourier transform of the scattered field, measured in a plane, is shown to be related to the three-dimensional Fourier transform of the object evaluated on a surface which in many cases is approximately a plane.
© Optical Society of America
7 . A.J. Devaney , “ Reconstructive tomography with diffracting wavefields ,” Inverse Problems 2 , 161 – 183 ( 1986 ) [CrossRef]
14 . 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 ) [CrossRef] [PubMed]
15 . W.F. Cheong , S.A. Prahl , and A.J. Welch , “ A review of the optical properties of biological tissues ,” IEEE J. Quantum Electronics 26 , 2166 – 2185 ( 1990 ) [CrossRef]
16 . H. Heusmann , J. Koelzer , and G. Mitic , “ Characterization of female breasts in vivo by time-resolved and spectroscopic measurements in near infrared spectroscopy ,” J.Biomed.Opt. 1 , 425 – 434 ( 1996 ) [CrossRef]
References and Links
1 . | 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 ) [CrossRef] [PubMed] |
2 . | 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 ) [CrossRef] [PubMed] |
3 . | S.A. Walker , S. Fantini , and E. Gratton , “ Image reconstruction using back-projection from frequency-domain optical measurements in highly scattering media ,” Appl. Opt. 36 , 170 – 179 ( 1997 ) [CrossRef] [PubMed] |
4 . | S.B. Colak , D.G. Papioannou , G.W. Hooft , and M.B. van der Mark , “ Optical image reconstruction with deconvolution in light diffusing media ,” in Photon Propagation in Tissues , B. Chance , D.T. Delpy , and G.J. Mueller , eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2626 , 306 – 315 ( 1995 ) |
5 . | 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 ) [CrossRef] [PubMed] |
6 . | 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 ) [CrossRef] [PubMed] |
7 . | A.J. Devaney , “ Reconstructive tomography with diffracting wavefields ,” Inverse Problems 2 , 161 – 183 ( 1986 ) [CrossRef] |
8 . | A. Schatzberg and A.J. Devaney , “ Super-resolution in diffraction tomography ,” Inverse Problems 8 , 149 – 164 ( 1992 ) [CrossRef] |
9 . | A.J. Devaney , “ Linearised inverse scattering in attenuating media ,” Inverse Problems 3 , 389 – 397 ( 1987 ) [CrossRef] |
10 . | A.J. Devaney , “ The limited-view problem in diffraction tomography ,” Inverse Problems 5 , 501 – 521 ( 1989 ) [CrossRef] |
11 . | A. Kak and M. Slaney , Principles of Computerized Tomographic Imaging ( IEEE Press, New York , 1988 ) |
12 . | A. Baños Jr. , Dipole Radiation in the Presence of a Conducting Half-Space ( Pergamon Press, Oxford , 1966 ) |
13 . | K.B. Howell , “ Fourier transforms ,” in The Transforms and Applications Handbook , A.D. Poularikas , ed. ( CRC Press, Boca Raton , 1996 ) |
14 . | 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 ) [CrossRef] [PubMed] |
15 . | W.F. Cheong , S.A. Prahl , and A.J. Welch , “ A review of the optical properties of biological tissues ,” IEEE J. Quantum Electronics 26 , 2166 – 2185 ( 1990 ) [CrossRef] |
16 . | H. Heusmann , J. Koelzer , and G. Mitic , “ Characterization of female breasts in vivo by time-resolved and spectroscopic measurements in near infrared spectroscopy ,” J.Biomed.Opt. 1 , 425 – 434 ( 1996 ) [CrossRef] |
17 . | D.C. Munson Jr. and J.L.C. Sanz , “ Image reconstruction from frequency-offset Fourier data ,” Proc. IEEE 72 , 661 – 669 ( 1984 ) [CrossRef] |
18 . | C.L. Matson , I.A. Delarue , T.M. Gray , and I.E. Drunzer , “ Optimal Fourier spectrum estimation from the bispectrum ,” Computers Elect. Engng 18 , 485 – 497 ( 1992 ) [CrossRef] |
OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3660) Medical optics and biotechnology : Light propagation in tissues
ToC Category:
Research Papers
History
Original Manuscript: June 19, 1997
Revised Manuscript: June 17, 1997
Published: July 7, 1997
Citation
Charles Matson, "A diffraction tomographic model of the forward problem using diffuse photon density waves," Opt. Express 1, 6-11 (1997)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-1-1-6
Sort: Journal | Reset
References
- M.A. OLeary, 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) [CrossRef] [PubMed]
- H.B. Jiang, K.D. Paulsen, U.L. Osterberg, M.S. Patterson, "Frequency-domain optical-image reconstruction in turbid media - an experimental study of single-target detectability," Appl. Opt. 36, 52-63 (1997) [CrossRef] [PubMed]
- S.A. Walker, S. Fantini, and E. Gratton, " Image reconstruction using back-projection from frequency-domain optical measurements in highly scattering media," Appl. Opt. 36, 170-179 (1997) [CrossRef] [PubMed]
- S.B. Colak, D.G. Papioannou, G.W. Hooft, and M.B. van der Mark, "Optical image reconstruction with deconvolution in light diffusing media," in Photon Propagation in Tissues, B. Chance, D.T. Delpy, and G.J. Mueller, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2626, 306-315 (1995)
- 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) [CrossRef] [PubMed]
- 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) [CrossRef] [PubMed]
- A.J. Devaney, "Reconstructive tomography with diffracting wavefields," Inverse Problems 2, 161-183 (1986) [CrossRef]
- A. Schatzberg and A.J. Devaney, "Super-resolution in diffraction tomography," Inverse Problems 8, 149-164 (1992) [CrossRef]
- A.J. Devaney, "Linearised inverse scattering in attenuating media," Inverse Problems 3, 389-397 (1987) [CrossRef]
- A.J. Devaney, "The limited-view problem in diffraction tomography," Inverse Problems 5, 501-521 (1989) [CrossRef]
- A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988)
- A. Baños, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon Press, Oxford, 1966)
- K.B. Howell, "Fourier transforms," in The Transforms and Applications Handbook, A.D. Poularikas, ed. (CRC Press, Boca Raton, 1996)
- D.A. Boas, M.A. OLeary, 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) [CrossRef] [PubMed]
- W.F. Cheong, S.A. Prahl, and A.J. Welch, "A review of the optical properties of biological tissues," IEEE J. Quantum Electronics 26, 2166-2185 (1990) [CrossRef]
- H. Heusmann, J. Koelzer, and G. Mitic, "Characterization of female breasts in vivo by time-resolved and spectroscopic measurements in near infrared spectroscopy," J.Biomed.Opt. 1, 425-434 (1996) [CrossRef]
- D.C. Munson, Jr. and J.L.C. Sanz, "Image reconstruction from frequency-offset Fourier data," Proc. IEEE 72, 661-669 (1984) [CrossRef]
- C.L. Matson, I.A. Delarue, T.M. Gray, and I.E. Drunzer, "Optimal Fourier spectrum estimation from the bispectrum," Computers Elect. Engng 18, 485-497 (1992) [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.
Figures
Figure 1 |
« Previous Article | Next Article »
OSA is a member of CrossRef.