Abstract

Reconstructions of a three-dimensional absorber embedded in a scattering medium by use of frequency domain measurements of the transmitted light in a single source–detector plane are presented. The reconstruction algorithm uses Bayesian regularization and iterative coordinate descent optimization, and it incorporates estimation of the detector noise level, the source–detector coupling coefficient, and the background diffusion coefficient in addition to the absorption image. The use of multiple modulation frequencies is also investigated. The results demonstrate the utility of this algorithm, the importance of a three-dimensional model, and that out-of-plane scattering permits recovery of three-dimensional features from measurements in a single plane.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. S. Reynolds, A. Przadka, S. Yeung, and K. J. Webb, Appl. Opt. 35, 3671 (1996).
    [CrossRef] [PubMed]
  2. S. R. Arridge, Inverse Prob. 15, R41 (1999).
    [CrossRef]
  3. J. C. Ye, K. J. Webb, C. A. Bouman, and R. P. Millane, J. Opt. Soc. Am. A 16, 2400 (1999).
    [CrossRef]
  4. J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, IEEE Trans. Image Process. 10, 909 (2001).
    [CrossRef]
  5. F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, and S. R. Arridge, Appl. Opt. 39, 3380 (2000).
    [CrossRef]
  6. N. Iftimia and H. Jiang, Appl. Opt. 39, 5256 (2000).
    [CrossRef]
  7. F. Gao, P. Poulet, and Y. Yamada, Appl. Opt. 39, 5898 (2000).
    [CrossRef]
  8. D. Boas, T. Gaudette, and S. Arridge, Opt. Express 8, 263 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  9. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, J. Opt. Soc. Am. A 11, 2727 (1994).
    [CrossRef]
  10. J. C. Ye, K. J. Webb, R. P. Millane, and T. J. Downar, J. Opt. Soc. Am. A 16, 1814 (1999).
    [CrossRef]

2001

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, IEEE Trans. Image Process. 10, 909 (2001).
[CrossRef]

D. Boas, T. Gaudette, and S. Arridge, Opt. Express 8, 263 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

2000

1999

1996

1994

Arridge, S.

Arridge, S. R.

Boas, D.

Bouman, C. A.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, IEEE Trans. Image Process. 10, 909 (2001).
[CrossRef]

J. C. Ye, K. J. Webb, C. A. Bouman, and R. P. Millane, J. Opt. Soc. Am. A 16, 2400 (1999).
[CrossRef]

Dehghani, H.

Delpy, D. T.

Downar, T. J.

Feng, T.-C.

Fry, M. E.

Gao, F.

Gaudette, T.

Haskell, R. C.

Hebden, J. C.

Hillman, E. M. C.

Iftimia, N.

Jiang, H.

McAdams, M. S.

Millane, R. P.

Poulet, P.

Przadka, A.

Reynolds, J. S.

Schmidt, F. E. W.

Schweiger, M.

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.-T.

Webb, K. J.

Yamada, Y.

Ye, J. C.

Yeung, S.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Culture flask with the absorbing cylinder embedded in a scattering Intralipid solution. (b) Apparatus used to collect the data.

Fig. 2
Fig. 2

Reconstructed images of the absorption coefficient with data at modulation frequencies of (a) 10, (b) 46, (c) 81, and (d) 10, 46, and 81 MHz.

Fig. 3
Fig. 3

Isosurfaces of the absorption coefficient images contoured at one quarter of the maximum value with data at (a) 10, (b) 46, (c) 81, and (d) 10, 46, and 81 MHz.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

·Drϕkr+-μar-jω/cϕkr=-δr-sk,
xˆ=arg maxx0 maxα maxγ[logp(y|x,α,γ)+logpx],
px=1σNzp exp-1pσpi,jNbi-jxi-xjp,  1p2,
xˆ= arg minx0minγminα1αy-γfxΛ2+P log α+1pσpi,jNbi-jxi-xjp,
γˆ=RefHxˆΛyfHxˆΛfxˆ,
ΔDˆ=ReeHfDHxˆΛzγˆeHfDHxˆΛfDxˆe,

Metrics