Abstract

Acousto-optic imaging in diffuse media is a dual wave-sensing technique in which an acoustic field interacts with multiply scattered laser light. The acoustic field causes a phase modulation in the optical field emanating from the interaction region, and this phase-modulated optical field carries with it information about the local optomechanical properties of the media. We report on the use of a pulsed ultrasound transducer to modulate the optical field and the use of a photorefractive-crystal-based interferometry system to detect ultrasound-modulated light. The use of short pulses of focused ultrasound allows for a one-dimensional acousto-optic image to be obtained along the transducer axis from a single, time-averaged acousto-optic signal. The axial and lateral resolutions of the system are controlled by the spatial pulse length and width of the ultrasound beam, respectively. In addition, scanning the ultrasound transducer in one dimension yields two-dimensional images of optical inhomogeneities buried in turbid media.

© 2005 Optical Society of America

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References

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  1. V. V. Tuchin, ed., Handbook of Optical Biomedical Diagnostics (SPIE, Bellingham, Wash., 2002).
  2. L.-H. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. 87,043903 (2001).
    [CrossRef] [PubMed]
  3. F. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 500–510 (1993).
    [CrossRef]
  4. L.-H. Wang, S. L. Jacques, X.-M. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
    [CrossRef] [PubMed]
  5. M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
    [CrossRef]
  6. S. Leveque, A. C. Boccara, M. Lebec, H. Saint-Jalmes, “Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing,” Opt. Lett. 24, 181–183 (1999).
    [CrossRef]
  7. M. Gross, P. Goy, M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. 28, 2482–2484 (2003).
    [CrossRef] [PubMed]
  8. L.-H. Wang, G. Ku, “Frequency-swept ultrasound-modulated optical tomography of scattering media,” Opt. Lett. 23, 975–977 (1998).
    [CrossRef]
  9. G. Yao, S. Jiao, L. V. Wang, “Frequency-swept ultrasound-modulated optical tomography in biological tissue by use of parallel detection,” Opt. Lett. 25, 734–736 (2000).
    [CrossRef]
  10. B. C. Forget, F. Ramaz, M. Atlan, J. Selb, A. C. Boccara, “High-contrast fast Fourier transform acousto-optical tomography of phantom tissues with a frequency-chirp modulation of the ultrasound,” Appl. Opt. 42, 1379–1383 (2003).
    [CrossRef] [PubMed]
  11. A. Lev, B. G. Sfez, “Pulsed ultrasound-modulated light tomography,” Opt. Lett. 28, 1549–1551 (2003).
    [CrossRef] [PubMed]
  12. L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
    [CrossRef]
  13. T. W. Murray, L. Sui, G. Maguluri, R. A. Roy, A. Nieva, F. Blonigen, C. A. DiMarzio, “Detection of ultrasound modulated photons in diffuse media using the photorefractive effect,” Opt. Lett. 29, 2509–2511 (2004).
    [CrossRef] [PubMed]
  14. R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
    [CrossRef]
  15. A. Blouin, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett. 65, 932–934 (1994).
    [CrossRef]
  16. T. W. Murray, H. Tuovinen, S. Krishnaswamy, “Adaptive optical array receivers for detection of surface acoustic waves,” Appl. Opt. 39, 3276–3284 (2000).
    [CrossRef]
  17. P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
    [CrossRef]
  18. J. E. Millerd, M. Ziari, A. Partovi, “Photorefractivity in semiconductors,” in Nonlinear Optics in Semiconductors I, Vol. 58 of Semiconductors and Semimetals, E. Garmire, A. Kost, eds. (Academic, San Diego, Calif., 1998), pp. 319–401.
    [CrossRef]
  19. P. Delaye, L.-A. Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
    [CrossRef]
  20. L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996).
  21. F. A. Duck, Physical Properties of Tissue (Academic, San Diego, 1990).
  22. E. Bossy, L. Sui, T. W. Murray, R. A. Roy, “Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner,” Opt. Lett. 30, 744–746 (2005).
    [CrossRef] [PubMed]

2005 (1)

2004 (1)

2003 (3)

2001 (1)

L.-H. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. 87,043903 (2001).
[CrossRef] [PubMed]

2000 (2)

1999 (1)

1998 (1)

1997 (2)

M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
[CrossRef]

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

1995 (2)

P. Delaye, L.-A. Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

L.-H. Wang, S. L. Jacques, X.-M. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
[CrossRef] [PubMed]

1994 (1)

A. Blouin, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett. 65, 932–934 (1994).
[CrossRef]

1991 (1)

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Al-Koussa, M.

Atlan, M.

Blonigen, F.

T. W. Murray, L. Sui, G. Maguluri, R. A. Roy, A. Nieva, F. Blonigen, C. A. DiMarzio, “Detection of ultrasound modulated photons in diffuse media using the photorefractive effect,” Opt. Lett. 29, 2509–2511 (2004).
[CrossRef] [PubMed]

L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
[CrossRef]

Blouin, A.

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

A. Blouin, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett. 65, 932–934 (1994).
[CrossRef]

Boccara, A. C.

Bossy, E.

Brooksby, G. W.

F. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

Delaye, P.

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

P. Delaye, L.-A. Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

DiMarzio, C.

L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
[CrossRef]

DiMarzio, C. A.

Drolet, D.

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

Duck, F. A.

F. A. Duck, Physical Properties of Tissue (Academic, San Diego, 1990).

Forget, B. C.

Genack, A. Z.

M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
[CrossRef]

Goy, P.

Gross, M.

Grunnet-Jepsen, A.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996).

Ing, R. K.

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Jacques, S. L.

Jiao, S.

Kempe, M.

M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
[CrossRef]

Krishnaswamy, S.

Ku, G.

Larionov, M.

M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
[CrossRef]

Lebec, M.

Lev, A.

Leveque, S.

Maguluri, G.

T. W. Murray, L. Sui, G. Maguluri, R. A. Roy, A. Nieva, F. Blonigen, C. A. DiMarzio, “Detection of ultrasound modulated photons in diffuse media using the photorefractive effect,” Opt. Lett. 29, 2509–2511 (2004).
[CrossRef] [PubMed]

L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
[CrossRef]

Marks, F. A.

F. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

Millerd, J. E.

J. E. Millerd, M. Ziari, A. Partovi, “Photorefractivity in semiconductors,” in Nonlinear Optics in Semiconductors I, Vol. 58 of Semiconductors and Semimetals, E. Garmire, A. Kost, eds. (Academic, San Diego, Calif., 1998), pp. 319–401.
[CrossRef]

Monchalin, J.-P.

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

A. Blouin, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett. 65, 932–934 (1994).
[CrossRef]

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Montmorillon, L.-A.

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

P. Delaye, L.-A. Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Murray, T.

L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
[CrossRef]

Murray, T. W.

Nieva, A.

T. W. Murray, L. Sui, G. Maguluri, R. A. Roy, A. Nieva, F. Blonigen, C. A. DiMarzio, “Detection of ultrasound modulated photons in diffuse media using the photorefractive effect,” Opt. Lett. 29, 2509–2511 (2004).
[CrossRef] [PubMed]

L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
[CrossRef]

Partovi, A.

J. E. Millerd, M. Ziari, A. Partovi, “Photorefractivity in semiconductors,” in Nonlinear Optics in Semiconductors I, Vol. 58 of Semiconductors and Semimetals, E. Garmire, A. Kost, eds. (Academic, San Diego, Calif., 1998), pp. 319–401.
[CrossRef]

Ramaz, F.

Roosen, G.

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

P. Delaye, L.-A. Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Roy, R. A.

Saint-Jalmes, H.

Selb, J.

Sfez, B. G.

Solymar, L.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996).

Sui, L.

Tomlinson, H. W.

F. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

Tuchin, V. V.

V. V. Tuchin, ed., Handbook of Optical Biomedical Diagnostics (SPIE, Bellingham, Wash., 2002).

Tuovinen, H.

Wang, L. V.

Wang, L.-H.

Webb, D. J.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996).

Yao, G.

Zaslavsky, D.

M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
[CrossRef]

Zhao, X.-M.

Ziari, M.

J. E. Millerd, M. Ziari, A. Partovi, “Photorefractivity in semiconductors,” in Nonlinear Optics in Semiconductors I, Vol. 58 of Semiconductors and Semimetals, E. Garmire, A. Kost, eds. (Academic, San Diego, Calif., 1998), pp. 319–401.
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

A. Blouin, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by two-wave mixing in a photorefractive GaAs crystal,” Appl. Phys. Lett. 65, 932–934 (1994).
[CrossRef]

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

M. Kempe, M. Larionov, D. Zaslavsky, A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A. 14, 1151–1158 (1997).
[CrossRef]

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

P. Delaye, A. Blouin, D. Drolet, L.-A. Montmorillon, G. Roosen, J.-P. Monchalin, “Detection of ultrasonic motion of a scattering surface by photorefractive InP:Fe under an applied dc field,” J. Opt. Soc. Am. B. 14, 1723–1734 (1997).
[CrossRef]

Opt. Commun. (1)

P. Delaye, L.-A. Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. Lett. (1)

L.-H. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. 87,043903 (2001).
[CrossRef] [PubMed]

Other (6)

F. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

V. V. Tuchin, ed., Handbook of Optical Biomedical Diagnostics (SPIE, Bellingham, Wash., 2002).

L. Sui, T. Murray, G. Maguluri, A. Nieva, F. Blonigen, C. DiMarzio, R. A. Roy, “Enhanced detection of acousto-photonic scattering using a photorefractive crystal,” in Photons Plus Ultrasound: Imaging and Sensing, A. A. Oraevsky, L. V. Wang, eds. Proc. SPIE5320, 164–171 (2004).
[CrossRef]

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford, New York, 1996).

F. A. Duck, Physical Properties of Tissue (Academic, San Diego, 1990).

J. E. Millerd, M. Ziari, A. Partovi, “Photorefractivity in semiconductors,” in Nonlinear Optics in Semiconductors I, Vol. 58 of Semiconductors and Semimetals, E. Garmire, A. Kost, eds. (Academic, San Diego, Calif., 1998), pp. 319–401.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

TWM configuration of a PRC with length L. The signal beam before the PRC is given by ISO; the intensity after the TWM process is given by ISE.

Fig. 2
Fig. 2

Experimental setup for PRC-based detection of ultrasound-modulated optical signals. FG, function generator; A, power amplifier; M, impedance matching box; TS, translation stage; UT, ultrasound transducer; VBS, variable beam splitter; R, reference beam; SB, signal beam; BE, beam expander; BP, optical bandpass filter; APD, avalanche photodiode; PA, preamplifier; LP, low-pass filter.

Fig. 3
Fig. 3

Photograph of a phantom (4 cm × 4 cm) with an optical absorber (5 mm × 5 mm) embedded in the middle. The reduced scattering coefficient of the phantom is approximately 2 cm−1, and the absorption coefficient of the absorber is approximately 3 cm−1.

Fig. 4
Fig. 4

Normalized focal pressure responses generated when the ultrasound transducer is driven with (a) 1-, (b) 2-, (c) 4-cycle electrical pulses at a 1-MHz center frequency.

Fig. 5
Fig. 5

Experimental results showing the detected optical signals sensed without the PRC-based system (top) and with the PRC-based system (bottom).

Fig. 6
Fig. 6

Normalized dc offset signals (a) detected when the transducer is scanned along the x axis at three different locations corresponding to positions 1, 2, and 3 in (b). There is a 4.5-mm spacing between these three locations with position 2 passing through the middle of the absorber.

Fig. 7
Fig. 7

Effect of changing the ultrasound pulse length on the dc offset component of the ultrasound-modulated optical signal.

Fig. 8
Fig. 8

Two-dimensional image (XZ plane) obtained by scanning the transducer across a 5 mm × 5 mm optical absorber: (a) global view; (b) zoomed-in view centered on the absorber.

Fig. 9
Fig. 9

Normalized 1-D acousto-optic image contrast obtained along orthogonal lines intersecting at the center of the optical absorber. Acousto-optic contrast for paths in the X (“scanning”) and the Z (“axial”) directions are given in plots (a) and (b), respectively.

Equations (4)

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

ϕ = ϕ a f ( t ) sin ( ω a t + χ r ) ,
I SE = exp ( α L ) I SO ( | e γ L 1 | 2 + 1 + 2 Re { ( e γ L 1 ) * exp [ i ϕ a f ( t ) sin ( ω a t + χ r ) ] } ) ,
I SE AC = 4 exp ( α L ) I SO e γ L × sin ( γ L ) J 1 [ ϕ a f ( t ) ] sin ( ω a t + χ r ) ,
I SE DC = exp ( α L ) I SO { | e γ L 1 | 2 + 2 [ e γ L cos ( γ L ) 1 ] J 0 [ ϕ a f ( t ) ] } .

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