Abstract

A novel diffused photon-pair density wave (DPPDW) composed of correlated polarized photon pairs at different temporal frequencies and orthogonal linearly polarized states is proposed. A theory of DPPDWs is developed. A DPPDW selected by coherence gating and polarization gating that satisfies the diffusion equation has been verified experimentally. The sensitivity of amplitude and phase detection of the heterodyne signal has been improved by the properties of synchronized detection and common-path propagation of polarized pair photons in a multiple-scattering medium. Both reduced scattering coefficient μ2s′ and absorption coefficient μ2a of the scattering medium in terms of the measured phase and amplitude of the heterodyne signal have been obtained. The detection sensitivity of μ2s′ and μ2a and the properties of a DPPDW in a multiple-scattering medium are discussed and analyzed.

© 2005 Optical Society of America

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References

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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]
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    [CrossRef]
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    [CrossRef]
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2002 (1)

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (2)

1999 (1)

1998 (1)

1997 (1)

1996 (2)

1994 (2)

D. A. Boas, M. A. O’Leary, B. Chance, 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]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

1993 (2)

1991 (1)

1989 (1)

1988 (1)

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

1975 (1)

Arridge, S.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Barbieri, B.

Beyersdorf, P. T.

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 wave: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[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: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Byer, R. L.

Chan, Y. H.

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

Chance, B.

Chang, H. F.

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Chiu, M. H.

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Chou, C.

L. C. Peng, C. Chou, C. W. Lyu, J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26, 349–351 (2001).
[CrossRef]

C. Chou, L. C. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25, 1517–1519 (2000).
[CrossRef]

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

Chou, Y. H.

Cohen, S.

Constantinescu, A.

Cope, M.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Dandliker, R.

Deply, D. T.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Eggert, J. A.

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Fajardo, L. L.

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Fantini, S.

Fejer, M. M.

Fishkin, J. B.

Franceschini, M. A.

Gratton, E.

Han, C. Y.

Haskell, R. C.

Herzig, H. P.

Hsieh, J. C.

L. C. Peng, C. Chou, C. W. Lyu, J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26, 349–351 (2001).
[CrossRef]

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

Iftimia, N. V.

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Jiang, H.

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Jiang, X.

Kaschke, M.

Kempe, M.

Klove, K. L.

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Liu, H.

Lyu, C. W.

Mason, R. P.

Moes, C. J. M.

Moesta, K. T.

Nesci, A.

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density wave: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[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: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Patterson, M. S.

Peng, L. C.

Prahl, S.

S. Prahl, “Optical absorption of Methylene Blue,” http://omlc.ogi.edu/spectra/mb/ .

Prahl, S. A.

Rudolph, W.

Schlag, P. M.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 66.

Song, Y.

Su, D. C.

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

Svaasand, L. O.

Tang, Y. H.

Tromberg, B. J.

Tsay, T. T.

van der Zee, P.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

van Gemert, M. J. C.

van Marie, J.

van Staveren, H. J.

Walker, S. A.

Welch, A. J.

A. J. Welch, M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, New York, 1995).
[CrossRef]

Welsch, E.

Wilson, B. C.

Worden, K. L.

Wray, S.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Wu, J. S.

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

Wyatt, J.

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Xu, Y.

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Yau, H. F.

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

Yodh, A. G.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density wave: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[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: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Acad. Radiol. (1)

H. Jiang, N. V. Iftimia, Y. Xu, J. A. Eggert, L. L. Fajardo, K. L. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Appl. Opt. (8)

B. J. Tromberg, L. O. Svaasand, T. T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

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

S. Cohen, “Heterodyne detection: phase front alignment, beam spot size, and detector uniformity,” Appl. Opt. 14, 1953–1959 (1975).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode-based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

H. Liu, Y. Song, K. L. Worden, X. Jiang, A. Constantinescu, R. P. Mason, “Noninvasive investigation of blood oxygenation dynamics of tumors by near-infrared spectroscopy,” Appl. Opt. 39, 5231–5243 (2000).
[CrossRef]

H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

S. Fantini, S. A. Walker, M. A. Franceschini, M. Kaschke, P. M. Schlag, K. T. Moesta, “Assessment of the size, position, and optical properties of breast tumors in vivo by noninvasive optical methods,” Appl. Opt. 37, 1982–1989 (1998).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Detection and characterization of optical inhomogeneities with diffuse photon density wave: a signal-to-noise analysis,” Appl. Opt. 36, 75–92 (1997).
[CrossRef] [PubMed]

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

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

Opt. Lett. (3)

Phys. Med. Biol. (1)

D. T. Deply, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[CrossRef]

Precis. Eng. (1)

D. C. Su, M. H. Chiu, C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161–163 (1996).
[CrossRef]

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

D. A. Boas, M. A. O’Leary, B. Chance, 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]

Other (5)

Y. H. Chan, C. Chou, H. F. Chang, H. F. Yau, J. S. Wu, J. C. Hsieh, “The measurement of optical properties of a multiple scattering medium based on diffused photon pair density wave,” in Advanced Biomedical and Clinical Diagnostic System, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, G. E. Cohn, eds., Proc. SPIE4958, 259–272 (2003).
[CrossRef]

A. J. Welch, M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, New York, 1995).
[CrossRef]

Ref. 1, p. 315.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 66.

S. Prahl, “Optical absorption of Methylene Blue,” http://omlc.ogi.edu/spectra/mb/ .

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Figures (11)

Fig. 1
Fig. 1

Pair of parallel-polarized states (Lp, Ls) generated when P- and S-polarized waves are transmitted through an analyzer.

Fig. 2
Fig. 2

Dispersion relation of angular wave numbers k2r and k2i of a DPPDW in a 15% Intralipid-10% solution. Filled squares and filled triangles are measured k2i and k2r, respectively; solid lines are theoretical calculations.

Fig. 3
Fig. 3

Optical setup: ZL, Zeeman laser; An, Glan–Thompson polarizer; BS, beam splitter; Obj, Objective (20×); PMT, photomultiplier tube; LA, linear amplifier; M, mirror; L1, lens; Dr, photodetector; BPFs, bandpass filters; LIA, lock-in amplifier.

Fig. 4
Fig. 4

(a) Spherical wave front of the attenuated amplitude and (b) phase delay of a DPPDW in a homogeneous solution of 15% Intralipid-10%.

Fig. 5
Fig. 5

Linear dependence of (a) the attenuated amplitude and (b) the phase delay on r of a DPPDW at three volumes of concentration of an Intralipid-10% solution. The error bar of each measurement is less than the size of the data point.

Fig. 6
Fig. 6

Response of (a) the attenuated amplitude and (b) the phase delay of a DPPDW with and without 5 μL of India Ink as the absorber in a 15% Intralipid-10% solution. The error bar of each measurement is less than the size of the data point.

Fig. 7
Fig. 7

Linear dependence of (a) the attenuated amplitude and (b) the phase delay on Δr of a 15% solution of Intralipid-10% at three beat frequencies. The error bar of each measurement is less than the size of the data point.

Fig. 8
Fig. 8

Linear relationship of μ2s′ to the concentration of Intralipid-10% solution at 20-MHz beat frequency. The error bar of each measurement is less than the size of the data point.

Fig. 9
Fig. 9

Linear relationship of μ2a to the concentration of MB absorber added to a 15% solution of Intralipid-10% at a beat frequency of 20 MHz. The error bar of each measurement is less than the size of the data point.

Fig. 10
Fig. 10

Phase velocities of (a) a DPPDW in an Intralipid-10% solution (Fig. 8) and (b) MB in a 15% solution of Intralipid-10% (Fig. 9).

Fig. 11
Fig. 11

Independence of the phase velocities to the beat frequency of a DPPDW in a 15% solution of Intralipid-10%. The solid lines are related theoretical calculations of V2p.

Tables (3)

Tables Icon

Table 1 Absorption and Reduced Scattering Coefficients of an Intralipid Solution Obtained from a DPPDW at Several Beat Frequencies

Tables Icon

Table 2 Absorption and Reduced Scattering Coefficients for Three Concentrations of Intralipid-10% Solution at a Beat Frequency of 20 MHz as Shown in Fig. 8

Tables Icon

Table 3 Absorption and Reduced Scattering Coefficients at Several Concentrations of MB in a 15% Intralipid-10% Solution at a Beat Frequency of 20 MHz as Shown in Fig. 9

Equations (13)

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

I a c ( Δ ω t ) = A p A s γ sin 2 θ cos ( Δ ω t + Δ Φ ) ,
φ ˜ j ( r , t ) = φ 0 [ exp ( - k r j r ) r ] 1 / 2 exp [ i ( k i j r - ω j t ) ] ( j = 1 , 2 ) ,
I ( Δ ω t ) = φ ˜ 1 ( r , t ) + φ ˜ 2 ( r , t ) 2 = φ 0 2 exp ( - k 2 r r ) r cos ( Δ ω t - Δ Φ ) = φ 0 2 exp ( - k 2 r r ) r Re { exp [ i ( Δ ω t - Δ Φ ) ] } ,
Δ Φ = [ k i 1 ( ω 1 ) - k i 2 ( ω 2 ) ] × r ,
k r 1 k r 2 = k 2 r = [ 3 μ 2 a ( μ 2 s + μ 2 a ) ] 1 / 2
r ˜ = ( 3 μ 2 s 4 μ 2 a ) 1 / 2 × r .
Δ Φ [ k i 1 ( ω 1 ) - k i 2 ( ω 2 ) ] × r ˜ = n Δ ω c ( 3 μ 2 s 4 μ 2 a ) 1 / 2 × r = k 2 i r ,
k 2 i = n Δ ω c ( 3 μ 2 s 4 μ 2 a ) 1 / 2 ,
λ 2 = 2 π k 2 i = 2 π c n Δ ω ( 4 μ 2 a 3 μ 2 s ) 1 / 2 ,
V 2 p = Δ ω k 2 i = c n ( 4 μ 2 a 3 μ 2 s ) 1 / 2 .
ln ( I I 0 ) = [ ln ( r 0 r ) - k 2 r Δ r ] ,
μ 2 s = 2 c k 2 r k 2 i 3 n Δ ω ,
μ 2 a = n Δ ω 2 c ( k 2 r k 2 i ) .

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