Abstract

As a continuation of the previously developed theory of a diffuse photon-pairs density wave (DPPDW) [Appl. Opt. 44, 1416–1425 (2005)], this research experimentally studies and verifies the DPPDW theory in a heterogeneous multiple-scattering medium. The DPPDW is generated by collecting the scattered linear polarized photon pairs (LPPPs) in the multiple-scattering medium. Theoretically, the common-path propagation of LPPPs not only provides common phase noise rejection mode but also performs coherence technique via heterodyne detection. In addition, the polarization gating and spatial coherence gating of LPPPs would suppress the severe scattered photon in the multiple-scattering medium. In the experiment, the amplitude and phase wavefronts of DPPDWs, which are distorted by a small object embedded in a homogeneous multiple-scattering medium, are measured in one dimension or two dimensions by scanning the source detector pair. The measured distortion of DPPDW wavefronts are detected precisely and are consistent with the theoretical calculation of DPPDW. It implies an improvement on the detection sensitivity of a small object compared with the conventional diffuse photon density wave (DPDW).

© 2008 Optical Society of America

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References

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  1. T. Vo-Dinh, Biomedical Photonics Handbook (SPIE, 2003).
    [CrossRef]
  2. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE, 2007).
  3. A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue, (Springer, 1995).
  4. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
    [CrossRef]
  5. V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41-46 (2001).
    [CrossRef] [PubMed]
  6. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41-93 (1999).
    [CrossRef]
  7. B. J. Tromberg, L. O. Svaasand, T. T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607-616 (1993).
    [CrossRef] [PubMed]
  8. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” in Proc. Natl. Acad. Sci. USA 91, 4887-4891(1994).
    [CrossRef] [PubMed]
  9. D. A. Boas, M. A. O'Leary, B. Chance, and 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]
  10. S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935-1944 (1998).
    [CrossRef]
  11. Y. Chen, C. Mu, X. Intes, and B. Chance, “Signal-to-noise analysis for detection sensitivity of small absorbing heterogeneity in turbid media with single-source and dual-interfering-source,” Opt. Express 9, 212-224 (2001).
    [CrossRef] [PubMed]
  12. Y. H. Chan, C. Chou, J. S. Wu, H. F. Chang, and H. F. Yau, “Properties of a diffused photon-pair density wave in a multiple-scattering medium,” Appl. Opt. 44, 1416-1425 (2005).
    [CrossRef] [PubMed]
  13. L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26, 349-351 (2001).
    [CrossRef]
  14. C. Chou, L. C. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, and C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25, 1517-1519 (2000).
    [CrossRef]
  15. H. J. van Staveren, C. J. M. Moes, J. van Marie, S. A. Prahl, and 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]
  16. T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
    [CrossRef]
  17. Y. Chen, C. Mu, X. Intes, and B. Chance, “Signal-to-noise analysis for detection sensitivity of small absorbing heterogeneity in turbid media with single-source and dual-interfering-source,” Opt. Express 9, 212-224 (2001).
    [CrossRef] [PubMed]
  18. D. A. Boas, “diffuse photon density waves,” http://omlc.ogi.edu/software/density/index.html.
  19. X. Li, B. Chance, and A. G. Yodh, “Fluorescent heterogeneities in turbid media: limits for detection, characterization, and comparison with absorption,” Appl. Opt. 37, 6833-6844 (1998)
    [CrossRef]
  20. K. C. Hadley and I. A. Vitkin, “Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media,” J. Biomed. Opt. 7, 291-299 (2002).
    [CrossRef] [PubMed]

2005

2002

K. C. Hadley and I. A. Vitkin, “Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media,” J. Biomed. Opt. 7, 291-299 (2002).
[CrossRef] [PubMed]

2001

2000

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

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

1999

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41-93 (1999).
[CrossRef]

1998

1997

1994

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

1993

1991

Anderson, E.

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41-93 (1999).
[CrossRef]

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935-1944 (1998).
[CrossRef]

D. A. Boas, M. A. O'Leary, B. Chance, and 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]

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

D. A. Boas, “diffuse photon density waves,” http://omlc.ogi.edu/software/density/index.html.

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Chan, Y. H.

Chance, B.

Chang, H. F.

Chen, Y.

Chou, C.

Chou, Y. H.

Coquz, O.

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Fishkin, J. B.

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Gratton, E.

Hadley, K. C.

K. C. Hadley and I. A. Vitkin, “Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media,” J. Biomed. Opt. 7, 291-299 (2002).
[CrossRef] [PubMed]

Han, C. Y.

Haskell, R. C.

Hsieh, J. C.

Intes, X.

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Li, X.

Lyu, C. W.

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Moes, C. J. M.

Mu, C.

Ntziachristos, V.

V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41-46 (2001).
[CrossRef] [PubMed]

O'Leary, M. A.

D. A. Boas, M. A. O'Leary, B. Chance, and 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]

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

Peng, L. C.

Pharm, T. H.

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

Prahl, S. A.

Svaasand, L. O.

Tang, Y. H.

Tromberg, B. J.

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

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

Tsay, T. T.

Tuchin, V. V.

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE, 2007).

van Gemert, M. J. C.

van Marie, J.

van Staveren, H. J.

Vitkin, I. A.

K. C. Hadley and I. A. Vitkin, “Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media,” J. Biomed. Opt. 7, 291-299 (2002).
[CrossRef] [PubMed]

Vo-Dinh, T.

T. Vo-Dinh, Biomedical Photonics Handbook (SPIE, 2003).
[CrossRef]

Walker, S. A.

Welch, A. J.

A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue, (Springer, 1995).

Wu, J. S.

Yau, H. F.

Yodh, A. G.

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Appl. Opt.

Breast Cancer Res.

V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41-46 (2001).
[CrossRef] [PubMed]

IEEE Signal Process Mag.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process Mag. 18, 57-75(2001).
[CrossRef]

Inverse Probl.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, 41-93 (1999).
[CrossRef]

J. Biomed. Opt.

K. C. Hadley and I. A. Vitkin, “Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media,” J. Biomed. Opt. 7, 291-299 (2002).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Proc. Natl. Acad. Sci. USA

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

Rev. Sci. Instrum.

T. H. Pharm, O. Coquz, J. B. Fishkin, E. Anderson, and B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500-2513 (2000).
[CrossRef]

Other

D. A. Boas, “diffuse photon density waves,” http://omlc.ogi.edu/software/density/index.html.

T. Vo-Dinh, Biomedical Photonics Handbook (SPIE, 2003).
[CrossRef]

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE, 2007).

A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue, (Springer, 1995).

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Figures (11)

Fig. 1
Fig. 1

Dispersion relation of DPPDW and DPDW. The real part ( k 2 r ) and imaginary part ( k 2 i ) of the wave number of DPPDW are presented by dots and crosses, respectively; the real part ( k r ) of and the imaginary part ( k i ) of the wave number of DPDW are plotted with solid line and open circle, respectively. For DPPDW, k 2 i is linearly proportional to the beat frequency δ ω of the LPPPs, and k 2 r is independent of δ ω . However, both k r and k i of DPDW are proportional to ω in the regime of high modulation frequency.

Fig. 2
Fig. 2

Experimental setup of the DPPDW system. TL: two-frequency laser; An: Glan-Thompson analyzer; BS: beam splitter, Obj: Objective lens; PMT: photomultiplier tube; M: mMirror; Det: photodetector; BPF: bandpass filter; LIA: lock-in amplifier.

Fig. 3
Fig. 3

Stability of the DPPDW system on (a) the amplitude and (b) the phase in a 1% Intralipid solution. The long-term stability of the amplitude and the phase are less than 0.2% and 0.05 ° , respectively.

Fig. 4
Fig. 4

DPPDW propagates from a 1% Intralipid solution to a 0.25% Intralipid solution. The phase contours are drawn every 2 ° . An interface, which is a transparent acrylic wall in 3 mm thickness, is used to separate the two different media.

Fig. 5
Fig. 5

Derivative of the imaginary part of the wavenumber of the DPPDW and the DPDW ( k 2 i / μ s and k i / μ s ) plotted as a function of the reduced scattering coefficient μ s ' . The k 2 i / μ s (solid curve) and k i / μ s (dotted curve) represent the sensitivity of phase signal to the change of μ s . As a result, k 2 i / μ s > k i / μ s explains that the phase signal change of the DPPDW in detecting μ s is more sensitive than one of the DPDW.

Fig. 6
Fig. 6

Experimental geometry of 1D scan of an absorber in 13 l of a 1% Intralipid solution ( μ s = 13 cm 1 and μ a = 0.01 cm 1 ); (a) shows the case of detecting a spherical absorber and (b) shows the case of detecting a cylindrical absorber. A source–detector pair is separated by 5 cm in distance and scans in parallel.

Fig. 7
Fig. 7

Fits to the 1D measurement of DPPDW scattered by a 3 mm diameter spherical perfect absorber; (a) is the amplitude attenuation and (b) is the phase change. The experimental data (dots) are compared to the best fit (solid curve). The scanning geometry is shown in Fig. 6a.

Fig. 8
Fig. 8

Fits to the 1D measurement of the DPPDW scattered by a 3 mm diameter cylindrical perfect absorber; (a) is the amplitude attenuation and (b) is the phase change. The experimental data (dots) are compared to the best fit (solid curve). The scanning geometry is shown in Fig. 6b.

Fig. 9
Fig. 9

Fits to the 1D measurement of the DPPDW scattered by a 7.4 mm diameter cylindrical perfect absorber; (a) is the amplitude attenuation and (b) is the phase change. The experimental data (dots) are compared to the best fit (solid curve). The scanning geometry is shown in Fig. 6b.

Fig. 10
Fig. 10

Schematic geometry of measuring the DPPDW contours in a 2D plane. A 3 mm diameter spherical perfect absorber is located at the center position ( 0 , 0 ) mm and the source fiber is placed at ( 60 , 0 ) mm . The measurements of the DPPDW were conducted by scanning the detector on a grid pattern with 3 mm for each interval. For this experiment, the optical properties of the surrounding medium are μ s = 13 cm 1 and μ a = 0.01 cm 1 .

Fig. 11
Fig. 11

2D measurement (solid curves) of a DPPDW scattered by a 3 mm diameter spherical perfect absorber are compared to the theoretical calculation (dashed curves) for the given parameters described in Fig. 10; (a) shows the amplitude contours and (b) shows the phase contours. The amplitude contours are drawn every 1 dB and the phase contours are drawn every 3 ° .

Equations (3)

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

I AC = | A 1 e i ω 1 t + A 2 e i ω 2 t + ϕ 0 | AC 2 2 γ | A 1 | | A 2 | cos ( δ ω t + ϕ 0 ) ,
Φ AC = γ | A 1 | | A 2 | 3 μ s 4 π r exp ( k 2 r r ) cos ( δ ω t δ ϕ ) ,
δ ϕ = n δ ω c r ˜ = n δ ω c 3 μ s 4 μ a r k 2 i r ,

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