Abstract

Previous studies have suggested that the phased-array detection can achieve high sensitivity in detecting and localizing inhomogeneities embedded in turbid media by illuminating with dual interfering sources. In this paper, we analyze the sensitivity of single-source and dual-interfering-source (phased array) systems with signal-to-noise ratio criteria. Analytical solutions are presented to investigate the sensitivity of detection using different degrees of absorption perturbation by varying the size and contrast of the object under similar configurations for single- and dual-source systems. The results suggest that dual-source configuration can provide higher detection sensitivity. The relation between the amplitude and phase signals for both systems is also analyzed using a vector model. The results can be helpful for optimizing the experimental design by combining the advantages of both single- and dual-source systems in object detection and localization.

© Optical Society of America

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References

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  1. D. Watmough, "Transillumination of breast tissues: factors governing optimal imaging of lesions," Radiology 147, 89-92 (1983).
    [PubMed]
  2. F. F. Jobsis, "Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameter," Science 198, 1264-1267 (1977).
    [CrossRef] [PubMed]
  3. A. G. Yodh, B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48, 34-40 (1995).
    [CrossRef]
  4. A. Villringer, B. Chance, "Noninvasive optical spectroscopy and imaging of human brain function," Trends Neurosci. 20, 435-442 (1997).
    [CrossRef] [PubMed]
  5. M. A. O'Leary, "Imaging with diffuse photon density waves," Ph.D. Thesis, University of Pennsylvania (1996).
  6. M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, M. Seeber, P. Schlag, M. Kashke, "Frequency-domain techniques enhance optical mammography: Initial clinical results," Proc. Natl. Acad. Sci. USA 94, 6468-6473 (1997).
    [CrossRef] [PubMed]
  7. V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, "Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc. Natl. Acad. Sci. USA 97, 2767-2772 (2000).
    [CrossRef] [PubMed]
  8. S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems 15, R41-R93 (1999).
    [CrossRef]
  9. Y. Yang, H. Liu, X. Li, B. Chance, "Low-cost frequency-domain photon migration instrument for tissue spectroscopy, oximetry and imaging," Opt. Eng. 36, 1562-1569 (1997).
    [CrossRef]
  10. S. Madsen, E. Anderson, R. Haskell, B. Tromberg, "Portable high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy," Opt. Lett. 19, 1934-1936 (1994).
    [CrossRef] [PubMed]
  11. 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]
  12. B. Chance, K. Kang, L. He, H. Liu, S. Zhou, "Precision localization of hidden absorbers in body tissues with phased-array optical systems," Rev. Sci. Instrum. 67, 4324-4332 (1996).
    [CrossRef]
  13. 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. USA 90, 3423-3427 (1993).
    [CrossRef] [PubMed]
  14. J. M. Schmitt, A. Knuttel, J. R. Knutson, "Interference of diffuse light waves," J. Opt. Soc. Am. A 9, 1832-1843 (1992).
    [CrossRef] [PubMed]
  15. 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] [PubMed]
  16. A. Knuttel, J. M. Schmitt, R. Barnes, J. R. Knutson, "Acousto-optic scanning and interfering photon density waves for precise localization of an absorbing (or fluorescent) body in a turbid medium," Rev. Sci. Instrum. 64, 638-644 (1993).
    [CrossRef]
  17. M. G. Erickson, J. S. Reynolds, K. J. Webb, "Comparison of sensitivity for single-source and dual-interfering- source configurations in optical diffusion imaging," J. Opt. Soc. Am. A 14, 3083-3092 (1997).
    [CrossRef]
  18. 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]
  19. S. Feng, F. Zeng, B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," App. Opt. 34, 3826-3837 (1995).
    [CrossRef]
  20. Q. Zhu, D. Sullivan, B. Chance, T. Dambro, "Combined ultrasound and near infrared diffused light imaging in a test object," IEEE Trans. Ultrason. Ferroelectrics & Freq. Control 46, 665-678 (1999).
    [CrossRef]
  21. M. A. O'Leary, D. A. Boas, B. Chance, A. G. Yodh, "Reradiation and imaging of diffuse photon density waves using fluorescent inhomogeneities," J. Lumin. 60-61, 281-286 (1994).
    [CrossRef]
  22. X. Intes, B. Chance, M. J. Holboke and A. G. Yodh, "Interfering diffusive photon-density waves with an absorbing-fluorescent inhomogeneity," Opt. Express 8, 223-231 (2001). http://www.opticsexpress.org/oearchive/source/27189.htm
    [CrossRef] [PubMed]
  23. B. Chance, S. Nioka, S. Zhou, L. Hong, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, R. Thomas, "A novel method for fast imaging of brain function, non-invasively, with light," Opt. Express 2, 411-423 (1998). http://www.opticsexpress.org/oearchive/source/4445.htm
    [CrossRef] [PubMed]
  24. Y. Chen, S. Zhou, C. Xie, S. Nioka, M. Delivoria-Papadopoulos, E. Anday, B. Chance, "Preliminary evaluation of dual wavelength phased array imaging on neonatal brain function," J. Biomed. Opt. 5, 194-200 (2000).
    [CrossRef] [PubMed]
  25. S. Morgan, M. Somekh, K. Hopcraft, "Probabilistic method for phased array detection in scattering media," Opt. Eng. 37, 1618-1626 (1998).
    [CrossRef]
  26. M. S. Patterson, B. Chance, B. C. Wilson, "Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
    [CrossRef] [PubMed]
  27. D. A. Boas, M. A. O'Leary, B. Chance, A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytical solution and applications," Proc. Natl. Acad. Sci. USA 91, 4887-4891 (1994).
    [CrossRef] [PubMed]
  28. J. B. Fishkin, 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).
    [CrossRef] [PubMed]
  29. X. Intes, V. Ntziachristos, A. G. Yodh, B. Chance, "Analytical model for Phased-Array Diffuse Optical Tomography," in preparation.
  30. B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, "Phase measurement of light absorption and scatter in human tissue," Rev. Sci. Instrum. 69, 3457-3481 (1998).
    [CrossRef]
  31. R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
    [CrossRef]
  32. R. Aronson, "Boundary conditions for diffusion of light," J. Opt. Soc. Am. A 12, 2532-2539 (1995).
    [CrossRef]
  33. S. P. Morgan, K. Y. Yong, "Controlling the phase response of a diffusive wave phased array system," Opt. Express 7, 540-546 (2000). http://www.opticsexpress.org/oearchive/source/26842.htm
    [CrossRef] [PubMed]
  34. X. Li, B. Chance, A. G. Yodh, "Fluorescent heterogeneities in turbid media: limits for detection, characterization, and comparison with absorption," Appl. Opt. 37, 6833-6844 (1998).
    [CrossRef]
  35. R. Choe, Private Communication.
  36. K. Suzuki, Y. Yamashita, K. Ohta, M. Kaneko, M. Yoshida, B. Chance, "Quantitative measurement of optical parameters in normal breasts using time-resolved spectroscopy: in vivo results of 30 Japanese women," J. Biomed. Opt. 1, 330-334 (1996).
    [CrossRef] [PubMed]
  37. Y. Chen, X. Intes, S. Zhou, C. Mu, M. Holboke, A. G. Yodh, B. Chance, "Detection sensitivity and optimization of phased array system," Proc. SPIE 4250, 211-218 (2001).
    [CrossRef]
  38. Q. Zhang, T. 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," Proc. SPIE 4250, 219-238 (2001).
    [CrossRef]
  39. N. Oldham, J. Kramar, P. Hetrick, E. Teague, "Electronic limitations in phase meters for heterodyne interferometry," Precis. Eng. 15, 173-179 (1993).
    [CrossRef]
  40. D. A. Boas, T. J. Gaudette and S. R. Arridge, "Simultaneous imaging and optode calibration with diffuse optical tomography," Opt. Express 8, 263-270 (2001). http://www.opticsexpress.org/oearchive/source/30286.htm
    [CrossRef] [PubMed]

Other

D. Watmough, "Transillumination of breast tissues: factors governing optimal imaging of lesions," Radiology 147, 89-92 (1983).
[PubMed]

F. F. Jobsis, "Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameter," Science 198, 1264-1267 (1977).
[CrossRef] [PubMed]

A. G. Yodh, B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48, 34-40 (1995).
[CrossRef]

A. Villringer, B. Chance, "Noninvasive optical spectroscopy and imaging of human brain function," Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

M. A. O'Leary, "Imaging with diffuse photon density waves," Ph.D. Thesis, University of Pennsylvania (1996).

M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, M. Seeber, P. Schlag, M. Kashke, "Frequency-domain techniques enhance optical mammography: Initial clinical results," Proc. Natl. Acad. Sci. USA 94, 6468-6473 (1997).
[CrossRef] [PubMed]

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, "Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc. Natl. Acad. Sci. USA 97, 2767-2772 (2000).
[CrossRef] [PubMed]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems 15, R41-R93 (1999).
[CrossRef]

Y. Yang, H. Liu, X. Li, B. Chance, "Low-cost frequency-domain photon migration instrument for tissue spectroscopy, oximetry and imaging," Opt. Eng. 36, 1562-1569 (1997).
[CrossRef]

S. Madsen, E. Anderson, R. Haskell, B. Tromberg, "Portable high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy," Opt. Lett. 19, 1934-1936 (1994).
[CrossRef] [PubMed]

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]

B. Chance, K. Kang, L. He, H. Liu, S. Zhou, "Precision localization of hidden absorbers in body tissues with phased-array optical systems," Rev. Sci. Instrum. 67, 4324-4332 (1996).
[CrossRef]

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. USA 90, 3423-3427 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knuttel, J. R. Knutson, "Interference of diffuse light waves," J. Opt. Soc. Am. A 9, 1832-1843 (1992).
[CrossRef] [PubMed]

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] [PubMed]

A. Knuttel, J. M. Schmitt, R. Barnes, J. R. Knutson, "Acousto-optic scanning and interfering photon density waves for precise localization of an absorbing (or fluorescent) body in a turbid medium," Rev. Sci. Instrum. 64, 638-644 (1993).
[CrossRef]

M. G. Erickson, J. S. Reynolds, K. J. Webb, "Comparison of sensitivity for single-source and dual-interfering- source configurations in optical diffusion imaging," J. Opt. Soc. Am. A 14, 3083-3092 (1997).
[CrossRef]

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]

S. Feng, F. Zeng, B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," App. Opt. 34, 3826-3837 (1995).
[CrossRef]

Q. Zhu, D. Sullivan, B. Chance, T. Dambro, "Combined ultrasound and near infrared diffused light imaging in a test object," IEEE Trans. Ultrason. Ferroelectrics & Freq. Control 46, 665-678 (1999).
[CrossRef]

M. A. O'Leary, D. A. Boas, B. Chance, A. G. Yodh, "Reradiation and imaging of diffuse photon density waves using fluorescent inhomogeneities," J. Lumin. 60-61, 281-286 (1994).
[CrossRef]

X. Intes, B. Chance, M. J. Holboke and A. G. Yodh, "Interfering diffusive photon-density waves with an absorbing-fluorescent inhomogeneity," Opt. Express 8, 223-231 (2001). http://www.opticsexpress.org/oearchive/source/27189.htm
[CrossRef] [PubMed]

B. Chance, S. Nioka, S. Zhou, L. Hong, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, R. Thomas, "A novel method for fast imaging of brain function, non-invasively, with light," Opt. Express 2, 411-423 (1998). http://www.opticsexpress.org/oearchive/source/4445.htm
[CrossRef] [PubMed]

Y. Chen, S. Zhou, C. Xie, S. Nioka, M. Delivoria-Papadopoulos, E. Anday, B. Chance, "Preliminary evaluation of dual wavelength phased array imaging on neonatal brain function," J. Biomed. Opt. 5, 194-200 (2000).
[CrossRef] [PubMed]

S. Morgan, M. Somekh, K. Hopcraft, "Probabilistic method for phased array detection in scattering media," Opt. Eng. 37, 1618-1626 (1998).
[CrossRef]

M. S. Patterson, B. Chance, B. C. Wilson, "Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef] [PubMed]

D. A. Boas, M. A. O'Leary, B. Chance, A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytical solution and applications," Proc. Natl. Acad. Sci. USA 91, 4887-4891 (1994).
[CrossRef] [PubMed]

J. B. Fishkin, 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).
[CrossRef] [PubMed]

X. Intes, V. Ntziachristos, A. G. Yodh, B. Chance, "Analytical model for Phased-Array Diffuse Optical Tomography," in preparation.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, B. Tromberg, "Phase measurement of light absorption and scatter in human tissue," Rev. Sci. Instrum. 69, 3457-3481 (1998).
[CrossRef]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
[CrossRef]

R. Aronson, "Boundary conditions for diffusion of light," J. Opt. Soc. Am. A 12, 2532-2539 (1995).
[CrossRef]

S. P. Morgan, K. Y. Yong, "Controlling the phase response of a diffusive wave phased array system," Opt. Express 7, 540-546 (2000). http://www.opticsexpress.org/oearchive/source/26842.htm
[CrossRef] [PubMed]

X. Li, B. Chance, A. G. Yodh, "Fluorescent heterogeneities in turbid media: limits for detection, characterization, and comparison with absorption," Appl. Opt. 37, 6833-6844 (1998).
[CrossRef]

R. Choe, Private Communication.

K. Suzuki, Y. Yamashita, K. Ohta, M. Kaneko, M. Yoshida, B. Chance, "Quantitative measurement of optical parameters in normal breasts using time-resolved spectroscopy: in vivo results of 30 Japanese women," J. Biomed. Opt. 1, 330-334 (1996).
[CrossRef] [PubMed]

Y. Chen, X. Intes, S. Zhou, C. Mu, M. Holboke, A. G. Yodh, B. Chance, "Detection sensitivity and optimization of phased array system," Proc. SPIE 4250, 211-218 (2001).
[CrossRef]

Q. Zhang, T. 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," Proc. SPIE 4250, 219-238 (2001).
[CrossRef]

N. Oldham, J. Kramar, P. Hetrick, E. Teague, "Electronic limitations in phase meters for heterodyne interferometry," Precis. Eng. 15, 173-179 (1993).
[CrossRef]

D. A. Boas, T. J. Gaudette and S. R. Arridge, "Simultaneous imaging and optode calibration with diffuse optical tomography," Opt. Express 8, 263-270 (2001). http://www.opticsexpress.org/oearchive/source/30286.htm
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

(a) Vector diagram for summing up two single-source signals, AB and BC, and resulting in the dual-source signal, AC. When the DPDW from single-source has been perturbed, i.e., BC changes to BC’, then the result of dual-source also changes to AC’ (b) Phase shift (absolute value) and (c) Amplitude variation ratio (absolute value) for dual-source signal vs. the perturbation in single-source signal, with different phase offset (180°-α).

Fig. 2.
Fig. 2.

Phase measurement through zero-crossing time interval

Fig. 3.
Fig. 3.

Transmission and remission geometry for single- and dual-source configurations

Fig. 4.
Fig. 4.

Noise model for summation of two vectors. The vectors are the average signals and the dotted circles are the distribution of sampling values. The standard deviation of the green spots is the noise distribution for single-source. The standard deviation of the red spots gives the amplitude and phase noise of the dual-source measurement.

Fig. 5.
Fig. 5.

Contour plot of the signal-to-noise ratio equals to one for amplitude and phase signals in single- and dual-source configurations. To the right side of the curve indicates a signal-to-noise ratio larger than 1 and the object with those parameters will be detected

Fig. 6.
Fig. 6.

Diameter of the smallest detectable absorber plotted as a function of µaout and µain for single- and dual-source systems in transmission mode. The background and object scattering coefficients are kept same (10 cm-1) and the modulation frequency is 50 MHz. (Bandwidth=1 Hz)

Fig. 7.
Fig. 7.

Diameter of the smallest detectable absorber plotted as a function of µaout and µain for single- and dual-source systems in remission mode. The background and object scattering coefficients are kept same (10 cm-1) and the modulation frequency is 50 MHz. (Bandwidth=1 Hz)

Fig. 8.
Fig. 8.

Dual-source detection on homogenous medium (a) and heterogeneous medium (b). The background optical coefficients are µa=0.08 cm-1, µ’s=12.0 cm-1. For the homogeneous case, the small scanning absorber has µa=0.5 cm-1and r=0.1 cm. The two sources are balanced (S1=S2=1.0). For the heterogeneous case, we introduce another larger fixed absorber (µa=0.5 cm-1and r=0.5 cm) to simulate the inhomogeneous background, and the balanced is disturbed. If we increase the strength of S2, the two sources will cancel with each other again (S1=1.0, S2=1.12). The phase transition for the above three cases are plotted in (c). (Blue is for case (a); Black is for case (b) with S1=S2; Red is for case (b) with S2=1.12*S1).

Tables (1)

Tables Icon

Table 1: Noise Level for Single- and Dual-Source Systems

Equations (20)

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1 v t U ( r , t ) · [ D ( r ) U ( r , t ) ] + μ a ( r ) U ( r , t ) = S ( r , t )
( 2 + k 2 ) U ac ( r ) = A δ ( r s ) / D
tan ϕ = C D A D = δ M cos ( α / 2 ) 2 M sin ( α / 2 ) δ M sin ( α / 2 ) = δ M / M 2 ( δ M / M ) cot ( α 2 ) ,
ϕ = tan 1 [ Δ 2 Δ cot ( α 2 ) ]
δ I = A C A C = δ M cos ( α / 2 ) sin ϕ 2 M sin ( α 2 ) = δ M ( M δ M ) · [ δ M cos ( α / 2 ) sin ϕ 2 sin ( α 2 ) ] ,
so that : δ I δ M = 1 Δ [ Δ sin ϕ cos ( α 2 ) 2 sin ( α 2 ) ] .
i sig = η q h v ( R U ) · G
i shot = 2 q ( i sig / A ) B ,
i NEP = NEP · B 1 / 2 K ,
N 1 = i shot 2 + i NEP 2 / i sig .
ϕ = ( T T / T R ) × 2 π
σ 1 ( N s ) = sin 1 ( N s ) .
σ ϕ ( N s ) = σ 1 ( N s ) + σ 0 ,
N s s = N 1 2 + N 2 2 ,
σ s s = σ ϕ ( N s s ) .
A 1 N ( A 1 , N s s a , σ s s a ) ,
A 2 N ( A 2 , N s s b , σ s s b ) .
A 3 = A 1 + A 2 N ( A 3 , N d s , σ d s )
0 = S · sin ( ω T T + ϕ ) ,
Δ S = S · sin ( ω T T + ϕ + σ 1 ) .

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