Abstract

We present a multielement phased-array approach to diffuse optical imaging based on postprocessing of continuous-wave data for the improvement of spatial resolution. In particular, we present a theoretical and experimental analysis of the performance of a three-element source array in the study of an optically turbid medium with two embedded cylindrical inclusions. We find that the proposed phased-array approach is able to resolve two cylinders with side-to-side separation of 10 mm that are not resolved by the intensity associated with a single light source.

© 2005 Optical Society of America

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  1. Special Section on Optical Imaging, G. Gratton, M. Fabiani, T. Elbert, and B. Rockstroh, eds., Psychophysiology 40, 487–571 (2003).
    [CrossRef]
  2. Special Section on Optics in Breast Cancer, S. Fantini, K. T. Moesta, and B. W. Pogue, eds., J. Biomed. Opt. 9, 1121–1181 (2004).
    [CrossRef]
  3. B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
    [CrossRef]
  4. K. A. Kang, D. F. Bruley, and B. Chance, Biomed. Instrum. Technol. 31, 373 (1997).
    [PubMed]
  5. J. M. Schmitt, A. Knüttel, and J. R. Knutson, J. Opt. Soc. Am. A 9, 1832 (1992).
    [CrossRef] [PubMed]
  6. Y. Chen, C. Mu, X. Intes, and B. Chance, Appl. Opt. 41, 7325 (2002).
    [CrossRef] [PubMed]
  7. J. B. Fishkin and E. Gratton, J. Opt. Soc. Am. A 10, 127 (1993).
    [CrossRef] [PubMed]
  8. J.-M. Kaltenbach and M. Kaschke, in Medical Optical Tomography:?Functional Imaging and Monitoring, G. J. Müller, 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. (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.
  9. V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
    [CrossRef] [PubMed]

2004 (1)

Special Section on Optics in Breast Cancer, S. Fantini, K. T. Moesta, and B. W. Pogue, eds., J. Biomed. Opt. 9, 1121–1181 (2004).
[CrossRef]

2003 (2)

Special Section on Optical Imaging, G. Gratton, M. Fabiani, T. Elbert, and B. Rockstroh, eds., Psychophysiology 40, 487–571 (2003).
[CrossRef]

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

2002 (1)

1997 (1)

K. A. Kang, D. F. Bruley, and B. Chance, Biomed. Instrum. Technol. 31, 373 (1997).
[PubMed]

1993 (2)

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

J. B. Fishkin and E. Gratton, J. Opt. Soc. Am. A 10, 127 (1993).
[CrossRef] [PubMed]

1992 (1)

Bruley, D. F.

K. A. Kang, D. F. Bruley, and B. Chance, Biomed. Instrum. Technol. 31, 373 (1997).
[PubMed]

Chance, B.

Y. Chen, C. Mu, X. Intes, and B. Chance, Appl. Opt. 41, 7325 (2002).
[CrossRef] [PubMed]

K. A. Kang, D. F. Bruley, and B. Chance, Biomed. Instrum. Technol. 31, 373 (1997).
[PubMed]

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

Chen, Y.

Fantini, S.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Fishkin, J. B.

Gotz, L.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Gratton, E.

He, L.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

Heffer, E. L.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Heinig, A.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Heywang-Kobrunner, S.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Intes, X.

Kaltenbach, J.-M.

J.-M. Kaltenbach and M. Kaschke, in Medical Optical Tomography:?Functional Imaging and Monitoring, G. J. Müller, 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. (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.

Kang, K.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

Kang, K. A.

K. A. Kang, D. F. Bruley, and B. Chance, Biomed. Instrum. Technol. 31, 373 (1997).
[PubMed]

Kaschke, M.

J.-M. Kaltenbach and M. Kaschke, in Medical Optical Tomography:?Functional Imaging and Monitoring, G. J. Müller, 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. (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.

Knutson, J. R.

Knüttel, A.

Mu, C.

Pera, V. E.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Schmitt, J. M.

Schutz, O.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Sevick, E.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

Siebold, H.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

Weng, J.

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

Appl. Opt. (1)

Biomed. Instrum. Technol. (1)

K. A. Kang, D. F. Bruley, and B. Chance, Biomed. Instrum. Technol. 31, 373 (1997).
[PubMed]

J. Biomed. Opt. (2)

Special Section on Optics in Breast Cancer, S. Fantini, K. T. Moesta, and B. W. Pogue, eds., J. Biomed. Opt. 9, 1121–1181 (2004).
[CrossRef]

V. E. Pera, E. L. Heffer, H. Siebold, O. Schutz, S. Heywang-Kobrunner, L. Gotz, A. Heinig, and S. Fantini, J. Biomed. Opt. 8, 517 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Proc. Natl. Acad. Sci. USA (1)

B. Chance, K. Kang, L. He, J. Weng, and E. Sevick, Proc. Natl. Acad. Sci. USA 90, 3423 (1993).
[CrossRef]

Psychophysiology (1)

Special Section on Optical Imaging, G. Gratton, M. Fabiani, T. Elbert, and B. Rockstroh, eds., Psychophysiology 40, 487–571 (2003).
[CrossRef]

Other (1)

J.-M. Kaltenbach and M. Kaschke, in Medical Optical Tomography:?Functional Imaging and Monitoring, G. J. Müller, 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. (SPIE Press, Bellingham, Wash., 1993), pp. 65–86.

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Figures (3)

Fig. 1
Fig. 1

Representative phased-array consisting of three sources with the indicated amplitude Ai and phase αi factors. These factors are defined in Eq. (1). The detector faces the central source at a distance of 6 cm, and the intersource separation is 1 cm.

Fig. 2
Fig. 2

Spatial distribution of the sensitivity function on the xy plane defined by the detector and the source array for (a) one source and one detector located at 0,-3 and 0,3, respectively, and (b) the three-source array of Fig. 1 consisting of sources located at -1,-3, 0,-3, and 1,-3. In both panels, the sensitivity function is defined relative to the value at x=0 (i.e., along the line through the detector and the central source). The optical coefficients used in Eq. (3) to calculate these sensitivity functions are μa0=0.047 cm-1 and μs0=15 cm-1.

Fig. 3
Fig. 3

Experimental results (thin curves) and theoretical fits (thick curves) for center-source intensity I2 and phased-array intensity IPA in the linear scans performed in a highly scattering liquid sample containing two absorbing cylinders located halfway between the source and detector scanning lines. The black dots indicate the positions of the two absorbing cylinders. The side-to-side separation between the cylinders is 70 mm in (a), 20 mm in (b), and 10 mm in (c).

Equations (4)

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

IPA=i=1NAiIiI0icosαi,
I0=vP4πD0exp-vμa0/D01/2rd-rsrd-rs,
ΔIr=-v2ΔμaPV4πD02×exp-vμa0/D01/2r-rs+rd-rr-rsrd-r,
Ir=I0+ΔIr.

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