Abstract

Diffusive wave phased arrays have been demonstrated to be a sensitive method of detecting inhomogeneities embedded in heavily scattering media. However, the increase in sensitivity is coupled with an increase in noise, so that the optimum performance may not be obtained when the sources are modulated in antiphase. The performance of a range of configurations in the presence of Gaussian noise is investigated by using probabilistic detection theory. A model of diffusive wave propagation through scattering media is used to demonstrate that the phase performance can be improved by controlling the relative phase difference between the two sources. However, the best performance is obtained by using the amplitude response of a single source system. The major benefit of a phased array system is therefore the rejection of common systematic noise.

© 2004 Optical Society of America

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References

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  1. M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. S. P. Morgan, K. Y. Yong, “Elimination of amplitude-phase crosstalk in frequency domain near infrared spectroscopy,” Rev. Sci. Instr. 72, 1982–1987 (2001).
    [CrossRef]

2002 (1)

2001 (2)

Y. Chen, C. Mu, X. Intes, B. Chance, “Signal to noise analysis for detection of small absorbing heterogeneity in turbid media with single-source and dual-interfering-source,” Opt. Express 9, 212–224 (2001).
[CrossRef] [PubMed]

S. P. Morgan, K. Y. Yong, “Elimination of amplitude-phase crosstalk in frequency domain near infrared spectroscopy,” Rev. Sci. Instr. 72, 1982–1987 (2001).
[CrossRef]

2000 (1)

1998 (1)

S. P. Morgan, M. G. Somekh, K. I. Hopcraft, “Probabilistic method for phased array detection in scattering media,” Opt. Eng. 37, 1618–1626 (1998).
[CrossRef]

1997 (3)

1996 (1)

D. G. Papaioannou, G. W. Hooft, S. B. Colak, J. T. Oostveen, “Detection limit in localizing objects hidden in a turbid medium using an optically scanned phased array,” J. Biomed. Opt. 1, 305–310 (1996).
[CrossRef] [PubMed]

1993 (2)

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. 90, 3423–3427 (1993).
[CrossRef]

A. Knuttel, J. M. Schmitt, J. R. Knutson, “Spatial localization of absorbing bodies by interfering diffusive photon density waves,” Appl. Opt. 32, 381–389 (1993).
[CrossRef]

Boas, D. A.

D. A. Boas, M. A. O’Leary, B. Chance, 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).
[CrossRef] [PubMed]

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

Brukilacchio, T. J.

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

Chance, B.

Chen, Y.

Colak, S. B.

D. G. Papaioannou, G. W. Hooft, S. B. Colak, J. T. Oostveen, “Detection limit in localizing objects hidden in a turbid medium using an optically scanned phased array,” J. Biomed. Opt. 1, 305–310 (1996).
[CrossRef] [PubMed]

Erickson, M. G.

Fantini, S.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Franchescini, M. A.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Gaida, G.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Gaudett, T.

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gratton, E.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

He, L.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. 90, 3423–3427 (1993).
[CrossRef]

Hooft, G. W.

D. G. Papaioannou, G. W. Hooft, S. B. Colak, J. T. Oostveen, “Detection limit in localizing objects hidden in a turbid medium using an optically scanned phased array,” J. Biomed. Opt. 1, 305–310 (1996).
[CrossRef] [PubMed]

Hopcraft, K. I.

S. P. Morgan, M. G. Somekh, K. I. Hopcraft, “Probabilistic method for phased array detection in scattering media,” Opt. Eng. 37, 1618–1626 (1998).
[CrossRef]

Intes, X.

Jess, H.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Kang, K.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. 90, 3423–3427 (1993).
[CrossRef]

Kaschke, M.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Knutson, J. R.

Knuttel, A.

Li, A.

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

Li, X. D.

Matulin, W. W.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Moesta, K. T.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Morgan, S. P.

S. P. Morgan, K. Y. Yong, “Elimination of amplitude-phase crosstalk in frequency domain near infrared spectroscopy,” Rev. Sci. Instr. 72, 1982–1987 (2001).
[CrossRef]

S. P. Morgan, K. Y. Yong, “Controlling the phase response of a diffusive wave phased array system,” Opt. Express 7, 540–546 (2000).
[CrossRef] [PubMed]

S. P. Morgan, M. G. Somekh, K. I. Hopcraft, “Probabilistic method for phased array detection in scattering media,” Opt. Eng. 37, 1618–1626 (1998).
[CrossRef]

S. P. Morgan, M. C. Pitter, M. G. Somekh, K. Y. Yong, “Conventional optics approach to diffraction of diffuse photon density waves,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 5–14 (1999).
[CrossRef]

Mu, C.

O’Leary, M. A.

Oostveen, J. T.

D. G. Papaioannou, G. W. Hooft, S. B. Colak, J. T. Oostveen, “Detection limit in localizing objects hidden in a turbid medium using an optically scanned phased array,” J. Biomed. Opt. 1, 305–310 (1996).
[CrossRef] [PubMed]

Papaioannou, D. G.

D. G. Papaioannou, G. W. Hooft, S. B. Colak, J. T. Oostveen, “Detection limit in localizing objects hidden in a turbid medium using an optically scanned phased array,” J. Biomed. Opt. 1, 305–310 (1996).
[CrossRef] [PubMed]

Pitter, M. C.

S. P. Morgan, M. C. Pitter, M. G. Somekh, K. Y. Yong, “Conventional optics approach to diffraction of diffuse photon density waves,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 5–14 (1999).
[CrossRef]

Reynolds, J. S.

Schlag, P. M.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Schmitt, J. M.

Seeber, M.

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Sevick, E.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. 90, 3423–3427 (1993).
[CrossRef]

Somekh, M. G.

S. P. Morgan, M. G. Somekh, K. I. Hopcraft, “Probabilistic method for phased array detection in scattering media,” Opt. Eng. 37, 1618–1626 (1998).
[CrossRef]

S. P. Morgan, M. C. Pitter, M. G. Somekh, K. Y. Yong, “Conventional optics approach to diffraction of diffuse photon density waves,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 5–14 (1999).
[CrossRef]

Wang, L.

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

Webb, K. J.

Weng, J.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. 90, 3423–3427 (1993).
[CrossRef]

Yodh, A. G.

Yong, K. Y.

S. P. Morgan, K. Y. Yong, “Elimination of amplitude-phase crosstalk in frequency domain near infrared spectroscopy,” Rev. Sci. Instr. 72, 1982–1987 (2001).
[CrossRef]

S. P. Morgan, K. Y. Yong, “Controlling the phase response of a diffusive wave phased array system,” Opt. Express 7, 540–546 (2000).
[CrossRef] [PubMed]

S. P. Morgan, M. C. Pitter, M. G. Somekh, K. Y. Yong, “Conventional optics approach to diffraction of diffuse photon density waves,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 5–14 (1999).
[CrossRef]

Zhang, Q.

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

Appl. Opt. (3)

J. Biomed. Opt. (1)

D. G. Papaioannou, G. W. Hooft, S. B. Colak, J. T. Oostveen, “Detection limit in localizing objects hidden in a turbid medium using an optically scanned phased array,” J. Biomed. Opt. 1, 305–310 (1996).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

S. P. Morgan, M. G. Somekh, K. I. Hopcraft, “Probabilistic method for phased array detection in scattering media,” Opt. Eng. 37, 1618–1626 (1998).
[CrossRef]

Opt. Express (2)

Proc. Natl. Acad. Sci. (2)

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. 90, 3423–3427 (1993).
[CrossRef]

M. A. Franchescini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Matulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. 94, 6468–6473 (1997).
[CrossRef]

Rev. Sci. Instr. (1)

S. P. Morgan, K. Y. Yong, “Elimination of amplitude-phase crosstalk in frequency domain near infrared spectroscopy,” Rev. Sci. Instr. 72, 1982–1987 (2001).
[CrossRef]

Other (4)

M. A. Franchescini, V. Toronov, M. E. Filiaci, E. Gratton, S. Fantini, “On-line optical imaging of the human brain with 160-ms temporal resolution,” Opt. Express6, 49–57 (2000), http://www.opticsexpress.org .
[CrossRef]

S. P. Morgan, M. C. Pitter, M. G. Somekh, K. Y. Yong, “Conventional optics approach to diffraction of diffuse photon density waves,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 5–14 (1999).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Q. Zhang, T. J. Brukilacchio, T. Gaudett, L. Wang, A. Li, D. A. Boas, “Experimental comparison of using continuous-wave and frequency-domain diffuse optical imaging systems to detect heterogeneities,” in Optical Tomography and Spectroscopy of Tissue IV, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, E. M. Sevick-Muraca, eds., Proc. SPIE4250, 219–238 (2001).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

System configuration. A planar object of width W is positioned opposite one of the sources at the midplane of the scattering medium. The detector is positioned equidistant to the sources.

Fig. 2
Fig. 2

PDFs in the presence (dotted curve) and absence (solid curve) of an object; (a) amplitude, ϕ = 0; (b) phase, ϕ = 0; (c) amplitude, ϕ = π; (d) phase, ϕ = π.

Fig. 3
Fig. 3

Operating curves obtained from the PDFs shown in Fig. 2.

Fig. 4
Fig. 4

Operating curves for different object sizes.

Fig. 5
Fig. 5

Overlap areas of amplitude and phase PDFs for different relative phases for a source separation of 10 mm. The horizontal lines represent the area of overlap for the single-source case.

Fig. 6
Fig. 6

Effect of source separation on (a) amplitude (b) phase PDFs.

Fig. 7
Fig. 7

Effect of object phase contrast on the area of amplitude (curve with triangles) and phase (curve with dots) overlap; object amplitude attenuation 0.8; object phase delay (a) 0°, (b) 2.5°, (c) 5°, (d) 10°. Reference horizontal lines are the areas of overlap for the single-source amplitude (solid) and phase (dotted) responses.

Fig. 8
Fig. 8

Effect of object amplitude on the area of amplitude (curve with triangles) and phase (curve with dots) overlap; object phase delay = 0°; object attenuation (a) 0.95, (b) 0.9, (c) 0.8, (d) 0.6, (e) 0.4, (f) 0.2. Reference horizontal lines are the areas of overlap for the single source amplitude (solid) and phase (dotted) responses.

Tables (1)

Tables Icon

Table 1 Four Detection Cases

Equations (4)

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

Sph=A1 expiθ1+A2 expiθ2+φ,
PAa=aσ2exp-a2+s22σ2I0asσ2a>00otherwise,
PΘθ=exp-k2/22π+k cos θ2π×exp-k2 sin2 θ2Φk cos θ,
Φb=12π-bexp-y2/2dy

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