Abstract

Optical absorption contrast, large imaging depth at ultrasonic resolution, and the potential of functional/quantitative imaging are the features driving the rapid development of photoacoustic (PA) imaging. For quantitative and functional PA imaging, the fluence distribution is required to transform a PA image to a map of absorption coefficients. A suitable method to estimate the fluence for in vivo applications must not require a priori knowledge of the medium optical properties, should work for various illumination conditions, and must be applicable to different PA imaging geometries. Existing methods of estimating fluence in tissue do not meet these requirements simultaneously. Here we present a method to measure the fluence distribution in tissue using acousto-optics (AO) that meets all the above requirements. We developed a PA and AO tomography system for small-animal imaging to investigate the potential and the feasibility of fluence-corrected PA imaging using our method in a single instrument. We performed experiments on phantoms, an ex vivo tissue sample, and freshly sacrificed mice. We demonstrate that the correction for spatial and spectral fluence variations in PA images establishes the direct relation between image value and optical absorption, which in turns improves the quantitative estimation of blood oxygen saturation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]

2017 (2)

D. Cai, G. Y. Li, D. Q. Xia, Z. F. Li, Z. D. Guo, and S. L. Chen, “Synthetic aperture focusing technique for photoacoustic endoscopy,” Opt. Express 25, 20162–20171 (2017).
[Crossref]

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

2016 (3)

2015 (3)

M. Jaeger and M. Frenz, “Towards clinical computed ultrasound tomography in echo-mode: dynamic range artefact reduction,” Ultrasonics 62, 299–304 (2015).
[Crossref]

X. L. Dean-Ben, A. C. Stiel, Y. Jiang, V. Ntziachristos, G. G. Westmeyer, and D. Razansky, “Light fluence normalization in turbid tissues via temporally unmixed multispectral optoacoustic tomography,” Opt. Lett. 40, 4691–4694 (2015).
[Crossref]

P. van Es, S. K. Biswas, H. J. B. Moens, W. Steenbergen, and S. Manohar, “Photoacoustic tomography of the human finger: towards the assessment of inflammatory joint diseases,” Proc. SPIE 9323, 93234Q (2015).
[Crossref]

2014 (4)

K. Daoudi, P. J. van den Berg, O. Rabot, A. Kohl, S. Tisserand, P. Brands, and W. Steenbergen, “Handheld probe integrating laser diode and ultrasound transducer array for ultrasound/photoacoustic dual modality imaging,” Opt. Express 22, 26365–26374 (2014).
[Crossref]

P. Shao, T. J. Harrison, and R. J. Zemp, “Consecutively reconstructing absorption and scattering distributions in turbid media with multiple-illumination photoacoustic tomography,” J. Biomed. Opt. 19, 126009 (2014).
[Crossref]

A. Hussain, K. Daoudi, E. Hondebrink, and W. Steenbergen, “Mapping optical fluence variations in highly scattering media by measuring ultrasonically modulated backscattered light,” J. Biomed. Opt. 19, 066002 (2014).
[Crossref]

S. Resink, E. Hondebrink, and W. Steenbergen, “Solving the speckle decorrelation challenge in acousto-optic sensing using tandem nanosecond pulses within the ultrasound period,” Opt. Lett. 39, 6486–6489 (2014).
[Crossref]

2013 (3)

2012 (4)

K. Daoudi, A. Hussain, E. Hondebrink, and W. Steenbergen, “Correcting photoacoustic signals for fluence variations using acousto-optic modulation,” Opt. Express 20, 14117–14129 (2012).
[Crossref]

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17, 061202 (2012).
[Crossref]

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

L. Xi, X. Q. Li, L. Yao, S. Grobmyer, and H. B. Jiang, “Design and evaluation of a hybrid photoacoustic tomography and diffuse optical tomography system for breast cancer detection,” Med. Phys. 39, 2584–2594 (2012).
[Crossref]

2011 (5)

P. Shao, B. Cox, and R. J. Zemp, “Estimating optical absorption, scattering, and Grueneisen distributions with multiple-illumination photoacoustic tomography,” Appl. Opt. 50, 3145–3154 (2011).
[Crossref]

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

A. Buehler, E. Herzog, D. Razansky, and V. Ntziachristos, “Visualization of mouse kidney perfusion with multispectral optoacoustic tomography (MSOT) at video rate,” Proc. SPIE 7899, 789914 (2011).
[Crossref]

A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. H. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. 16, 096016 (2011).
[Crossref]

J. Jose, R. G. Willemink, S. Resink, D. Piras, J. C. van Hespen, C. H. Slump, W. Steenbergen, T. G. van Leeuwen, and S. Manohar, “Passive element enriched photoacoustic computed tomography (PER PACT) for simultaneous imaging of acoustic propagation properties and light absorption,” Opt. Express 19, 2093–2104 (2011).
[Crossref]

2010 (4)

J. Laufer, B. Cox, E. Zhang, and P. Beard, “Quantitative determination of chromophore concentrations from 2D photoacoustic images using a nonlinear model-based inversion scheme,” Appl. Opt. 49, 1219–1233 (2010).
[Crossref]

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Prob. 26, 085010 (2010).
[Crossref]

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[Crossref]

R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt. 49, 3566–3572 (2010).
[Crossref]

2009 (5)

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26, 443–455 (2009).
[Crossref]

L. Yao, Y. Sun, and H. B. Jiang, “Quantitative photoacoustic tomography based on the radiative transfer equation,” Opt. Lett. 34, 1765–1767 (2009).
[Crossref]

J. Gamelin, A. Maurudis, A. Aguirre, F. Huang, P. Y. Guo, L. V. Wang, and Q. Zhu, “A real-time photoacoustic tomography system for small animals,” Opt. Express 17, 10489–10498 (2009).
[Crossref]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[Crossref]

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

2008 (1)

2007 (1)

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).
[Crossref]

2006 (1)

R. Zemp, S. Sakadzic, and L. V. Wang, “Stochastic explanation of speckle contrast detection in ultrasound-modulated optical tomography,” Phys. Rev. E 73, 061920 (2006).
[Crossref]

2005 (1)

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[Crossref]

2003 (1)

2002 (1)

2001 (1)

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

2000 (1)

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

1998 (1)

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015–14019 (1998).
[Crossref]

1995 (1)

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref]

1976 (1)

P. L. Carson, “Diagnostic ultrasonics: principles and use of instruments. By W. N. McDicken, Ph.D., John Wiley and Sons, Inc. New York, New York, $28.50,” [book review] J. Clin. Ultrasound 4, 377 (1976).
[Crossref]

Aguirre, A.

Anastasio, M.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

Appledorn, C. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref]

Arridge, S. R.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17, 061202 (2012).
[Crossref]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26, 443–455 (2009).
[Crossref]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).
[Crossref]

Bal, G.

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Prob. 26, 085010 (2010).
[Crossref]

Bauer, A. Q.

A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. H. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. 16, 096016 (2011).
[Crossref]

Bayer, C.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Beard, P.

Beard, P. C.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17, 061202 (2012).
[Crossref]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26, 443–455 (2009).
[Crossref]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).
[Crossref]

Biswas, S. K.

P. van Es, S. K. Biswas, H. J. B. Moens, W. Steenbergen, and S. Manohar, “Photoacoustic tomography of the human finger: towards the assessment of inflammatory joint diseases,” Proc. SPIE 9323, 93234Q (2015).
[Crossref]

Boccara, A. C.

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

Bohndiek, S. E.

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

Brands, P.

Brochu, F. M.

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

Brunker, J.

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

Buehler, A.

A. Buehler, E. Herzog, D. Razansky, and V. Ntziachristos, “Visualization of mouse kidney perfusion with multispectral optoacoustic tomography (MSOT) at video rate,” Proc. SPIE 7899, 789914 (2011).
[Crossref]

Cai, D.

Carson, P. L.

P. L. Carson, “Diagnostic ultrasonics: principles and use of instruments. By W. N. McDicken, Ph.D., John Wiley and Sons, Inc. New York, New York, $28.50,” [book review] J. Clin. Ultrasound 4, 377 (1976).
[Crossref]

Chatni, M. R.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

Chen, S. L.

Cox, B.

Cox, B. T.

B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A 26, 443–455 (2009).
[Crossref]

B. T. Cox, S. R. Arridge, and P. C. Beard, “Gradient-based quantitative photoacoustic image reconstruction for molecular imaging,” Proc. SPIE 6437, 64371T (2007).
[Crossref]

Culver, J. P.

A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. H. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. 16, 096016 (2011).
[Crossref]

Daoudi, K.

Dean-Ben, X. L.

Delaye, P.

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

Engler, W. E.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015–14019 (1998).
[Crossref]

Erpelding, T. N.

A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. H. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. 16, 096016 (2011).
[Crossref]

Fang, Y. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref]

Frenz, M.

M. Jaeger and M. Frenz, “Towards clinical computed ultrasound tomography in echo-mode: dynamic range artefact reduction,” Ultrasonics 62, 299–304 (2015).
[Crossref]

Gamelin, J.

Glasl, S.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Grobmyer, S.

L. Xi, X. Q. Li, L. Yao, S. Grobmyer, and H. B. Jiang, “Design and evaluation of a hybrid photoacoustic tomography and diffuse optical tomography system for breast cancer detection,” Med. Phys. 39, 2584–2594 (2012).
[Crossref]

Gross, M.

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

Guo, P. Y.

Guo, Z. D.

Guo, Z. J.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

Harrison, T. J.

P. Shao, T. J. Harrison, and R. J. Zemp, “Consecutively reconstructing absorption and scattering distributions in turbid media with multiple-illumination photoacoustic tomography,” J. Biomed. Opt. 19, 126009 (2014).
[Crossref]

Heijblom, M.

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

Hemmer, P.

Herzog, E.

A. Buehler, E. Herzog, D. Razansky, and V. Ntziachristos, “Visualization of mouse kidney perfusion with multispectral optoacoustic tomography (MSOT) at video rate,” Proc. SPIE 7899, 789914 (2011).
[Crossref]

Hondebrink, E.

Huang, F.

Hussain, A.

Jacques, S. L.

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58, R37–R61 (2013).
[Crossref]

Jaeger, M.

M. Jaeger and M. Frenz, “Towards clinical computed ultrasound tomography in echo-mode: dynamic range artefact reduction,” Ultrasonics 62, 299–304 (2015).
[Crossref]

Jiang, H. B.

L. Xi, X. Q. Li, L. Yao, S. Grobmyer, and H. B. Jiang, “Design and evaluation of a hybrid photoacoustic tomography and diffuse optical tomography system for breast cancer detection,” Med. Phys. 39, 2584–2594 (2012).
[Crossref]

L. Yao, Y. Sun, and H. B. Jiang, “Quantitative photoacoustic tomography based on the radiative transfer equation,” Opt. Lett. 34, 1765–1767 (2009).
[Crossref]

Jiang, Y.

Jose, J.

Joseph, J.

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

Kim, C. H.

Kiser, W. L.

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

Klaase, J. M.

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

Kohl, A.

Kruger, G. A.

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

Kruger, R. A.

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref]

Ku, G.

Lai, P. X.

Laufer, J.

Laufer, J. G.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17, 061202 (2012).
[Crossref]

Lesaffre, M.

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

Lev, A.

Li, G. Y.

Li, J.

Li, X. Q.

L. Xi, X. Q. Li, L. Yao, S. Grobmyer, and H. B. Jiang, “Design and evaluation of a hybrid photoacoustic tomography and diffuse optical tomography system for breast cancer detection,” Med. Phys. 39, 2584–2594 (2012).
[Crossref]

Li, Y. Z.

Li, Z. F.

Liu, P.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref]

Mahan, G. D.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015–14019 (1998).
[Crossref]

Manohar, S.

M. Venugopal, P. van Es, S. Manohar, D. Roy, and R. M. Vasu, “Quantitative photoacoustic tomography by stochastic search: direct recovery of the optical absorption field,” Opt. Lett. 41, 4202–4205 (2016).
[Crossref]

P. van Es, S. K. Biswas, H. J. B. Moens, W. Steenbergen, and S. Manohar, “Photoacoustic tomography of the human finger: towards the assessment of inflammatory joint diseases,” Proc. SPIE 9323, 93234Q (2015).
[Crossref]

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

J. Jose, R. G. Willemink, S. Resink, D. Piras, J. C. van Hespen, C. H. Slump, W. Steenbergen, T. G. van Leeuwen, and S. Manohar, “Passive element enriched photoacoustic computed tomography (PER PACT) for simultaneous imaging of acoustic propagation properties and light absorption,” Opt. Express 19, 2093–2104 (2011).
[Crossref]

Maslov, K.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

Maurudis, A.

Miller, K. D.

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

Moens, H. J. B.

P. van Es, S. K. Biswas, H. J. B. Moens, W. Steenbergen, and S. Manohar, “Photoacoustic tomography of the human finger: towards the assessment of inflammatory joint diseases,” Proc. SPIE 9323, 93234Q (2015).
[Crossref]

Morscher, S.

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

Multhoff, G.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Nothdurft, R. E.

A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. H. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. 16, 096016 (2011).
[Crossref]

Ntziachristos, V.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

X. L. Dean-Ben, A. C. Stiel, Y. Jiang, V. Ntziachristos, G. G. Westmeyer, and D. Razansky, “Light fluence normalization in turbid tissues via temporally unmixed multispectral optoacoustic tomography,” Opt. Lett. 40, 4691–4694 (2015).
[Crossref]

A. Buehler, E. Herzog, D. Razansky, and V. Ntziachristos, “Visualization of mouse kidney perfusion with multispectral optoacoustic tomography (MSOT) at video rate,” Proc. SPIE 7899, 789914 (2011).
[Crossref]

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[Crossref]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[Crossref]

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[Crossref]

Nunes, A.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Olefir, I.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Petersen, W.

Peterson, W.

Piras, D.

Rabot, O.

Ramaz, F.

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

Razansky, D.

X. L. Dean-Ben, A. C. Stiel, Y. Jiang, V. Ntziachristos, G. G. Westmeyer, and D. Razansky, “Light fluence normalization in turbid tissues via temporally unmixed multispectral optoacoustic tomography,” Opt. Lett. 40, 4691–4694 (2015).
[Crossref]

A. Buehler, E. Herzog, D. Razansky, and V. Ntziachristos, “Visualization of mouse kidney perfusion with multispectral optoacoustic tomography (MSOT) at video rate,” Proc. SPIE 7899, 789914 (2011).
[Crossref]

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[Crossref]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[Crossref]

Reinecke, D. R.

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

Resink, S.

Reynolds, H. E.

R. A. Kruger, K. D. Miller, H. E. Reynolds, W. L. Kiser, D. R. Reinecke, and G. A. Kruger, “Breast cancer in vivo: contrast enhancement with thermoacoustic CT at 434  MHz—feasibility study,” Radiology 216, 279–283 (2000).
[Crossref]

Ripoll, J.

J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E 71, 031912 (2005).
[Crossref]

Roosen, G.

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

Rosenthal, A.

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[Crossref]

Roy, D.

Sakadzic, S.

R. Zemp, S. Sakadzic, and L. V. Wang, “Stochastic explanation of speckle contrast detection in ultrasound-modulated optical tomography,” Phys. Rev. E 73, 061920 (2006).
[Crossref]

Sfez, B. G.

Shao, P.

P. Shao, T. J. Harrison, and R. J. Zemp, “Consecutively reconstructing absorption and scattering distributions in turbid media with multiple-illumination photoacoustic tomography,” J. Biomed. Opt. 19, 126009 (2014).
[Crossref]

P. Shao, B. Cox, and R. J. Zemp, “Estimating optical absorption, scattering, and Grueneisen distributions with multiple-illumination photoacoustic tomography,” Appl. Opt. 50, 3145–3154 (2011).
[Crossref]

Slump, C. H.

Staley, J.

Stangl, S.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Steenbergen, W.

A. Hussain, W. Petersen, J. Staley, E. Hondebrink, and W. Steenbergen, “Quantitative blood oxygen saturation imaging using combined photoacoustics and acousto-optics,” Opt. Lett. 41, 1720–1723 (2016).
[Crossref]

P. van Es, S. K. Biswas, H. J. B. Moens, W. Steenbergen, and S. Manohar, “Photoacoustic tomography of the human finger: towards the assessment of inflammatory joint diseases,” Proc. SPIE 9323, 93234Q (2015).
[Crossref]

K. Daoudi, P. J. van den Berg, O. Rabot, A. Kohl, S. Tisserand, P. Brands, and W. Steenbergen, “Handheld probe integrating laser diode and ultrasound transducer array for ultrasound/photoacoustic dual modality imaging,” Opt. Express 22, 26365–26374 (2014).
[Crossref]

A. Hussain, K. Daoudi, E. Hondebrink, and W. Steenbergen, “Mapping optical fluence variations in highly scattering media by measuring ultrasonically modulated backscattered light,” J. Biomed. Opt. 19, 066002 (2014).
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S. Resink, E. Hondebrink, and W. Steenbergen, “Solving the speckle decorrelation challenge in acousto-optic sensing using tandem nanosecond pulses within the ultrasound period,” Opt. Lett. 39, 6486–6489 (2014).
[Crossref]

J. Staley, E. Hondebrink, W. Peterson, and W. Steenbergen, “Photoacoustic guided ultrasound wavefront shaping for targeted acousto-optic imaging,” Opt. Express 21, 30553–30562 (2013).
[Crossref]

K. Daoudi, A. Hussain, E. Hondebrink, and W. Steenbergen, “Correcting photoacoustic signals for fluence variations using acousto-optic modulation,” Opt. Express 20, 14117–14129 (2012).
[Crossref]

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

J. Jose, R. G. Willemink, S. Resink, D. Piras, J. C. van Hespen, C. H. Slump, W. Steenbergen, T. G. van Leeuwen, and S. Manohar, “Passive element enriched photoacoustic computed tomography (PER PACT) for simultaneous imaging of acoustic propagation properties and light absorption,” Opt. Express 19, 2093–2104 (2011).
[Crossref]

Stiel, A. C.

Sun, Y.

Suzuki, Y.

Symvoulidis, P.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Tiemann, J. J.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015–14019 (1998).
[Crossref]

Tisserand, S.

Tomaszewski, M. R.

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

Tzoumas, S.

S. Tzoumas, A. Nunes, I. Olefir, S. Stangl, P. Symvoulidis, S. Glasl, C. Bayer, G. Multhoff, and V. Ntziachristos, “Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues,” Nat. Commun. 7, 12121 (2016).
[Crossref]

Uhlmann, G.

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Prob. 26, 085010 (2010).
[Crossref]

Uzgiris, E.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015–14019 (1998).
[Crossref]

van den Berg, P. J.

van den Engh, F. M.

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

van Es, P.

M. Venugopal, P. van Es, S. Manohar, D. Roy, and R. M. Vasu, “Quantitative photoacoustic tomography by stochastic search: direct recovery of the optical absorption field,” Opt. Lett. 41, 4202–4205 (2016).
[Crossref]

P. van Es, S. K. Biswas, H. J. B. Moens, W. Steenbergen, and S. Manohar, “Photoacoustic tomography of the human finger: towards the assessment of inflammatory joint diseases,” Proc. SPIE 9323, 93234Q (2015).
[Crossref]

van Hespen, J. C.

van Leeuwen, T. G.

J. Jose, R. G. Willemink, S. Resink, D. Piras, J. C. van Hespen, C. H. Slump, W. Steenbergen, T. G. van Leeuwen, and S. Manohar, “Passive element enriched photoacoustic computed tomography (PER PACT) for simultaneous imaging of acoustic propagation properties and light absorption,” Opt. Express 19, 2093–2104 (2011).
[Crossref]

M. Heijblom, J. M. Klaase, F. M. van den Engh, T. G. van Leeuwen, W. Steenbergen, and S. Manohar, “Imaging tumor vascularization for detection and diagnosis of breast cancer,” Technol. Cancer Res. Treat. 10, 607–623 (2011).
[Crossref]

Vasu, R. M.

Venugopal, M.

Wang, K.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

Wang, L. H.

Wang, L. H. V.

A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. H. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. 16, 096016 (2011).
[Crossref]

Y. Z. Li, P. Hemmer, C. H. Kim, H. L. Zhang, and L. H. V. Wang, “Detection of ultrasound-modulated diffuse photons using spectral-hole burning,” Opt. Express 16, 14862–14874 (2008).
[Crossref]

J. Li, G. Ku, and L. H. V. Wang, “Ultrasound-modulated optical tomography of biological tissue by use of contrast of laser speckles,” Appl. Opt. 41, 6030–6035 (2002).
[Crossref]

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

Wang, L. V.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

J. Gamelin, A. Maurudis, A. Aguirre, F. Huang, P. Y. Guo, L. V. Wang, and Q. Zhu, “A real-time photoacoustic tomography system for small animals,” Opt. Express 17, 10489–10498 (2009).
[Crossref]

R. Zemp, S. Sakadzic, and L. V. Wang, “Stochastic explanation of speckle contrast detection in ultrasound-modulated optical tomography,” Phys. Rev. E 73, 061920 (2006).
[Crossref]

Westmeyer, G. G.

Willemink, R. G.

Xi, L.

L. Xi, X. Q. Li, L. Yao, S. Grobmyer, and H. B. Jiang, “Design and evaluation of a hybrid photoacoustic tomography and diffuse optical tomography system for breast cancer detection,” Med. Phys. 39, 2584–2594 (2012).
[Crossref]

Xia, D. Q.

Xia, J.

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

Xu, X.

Yao, L.

L. Xi, X. Q. Li, L. Yao, S. Grobmyer, and H. B. Jiang, “Design and evaluation of a hybrid photoacoustic tomography and diffuse optical tomography system for breast cancer detection,” Med. Phys. 39, 2584–2594 (2012).
[Crossref]

L. Yao, Y. Sun, and H. B. Jiang, “Quantitative photoacoustic tomography based on the radiative transfer equation,” Opt. Lett. 34, 1765–1767 (2009).
[Crossref]

Zemp, R.

R. Zemp, S. Sakadzic, and L. V. Wang, “Stochastic explanation of speckle contrast detection in ultrasound-modulated optical tomography,” Phys. Rev. E 73, 061920 (2006).
[Crossref]

Zemp, R. J.

Zhang, E.

Zhang, H. L.

Zhu, Q.

Appl. Opt. (4)

Chem. Rev. (1)

V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography (MSOT),” Chem. Rev. 110, 2783–2794 (2010).
[Crossref]

Eur. Phys. J. E (1)

M. Gross, M. Lesaffre, F. Ramaz, P. Delaye, G. Roosen, and A. C. Boccara, “Detection of the tagged or untagged photons in acousto-optic imaging of thick highly scattering media by photorefractive adaptive holography,” Eur. Phys. J. E 28, 173–182 (2009).
[Crossref]

IEEE Trans. Med. Imaging (2)

F. M. Brochu, J. Brunker, J. Joseph, M. R. Tomaszewski, S. Morscher, and S. E. Bohndiek, “Towards quantitative evaluation of tissue absorption coefficients using light fluence correction in optoacoustic tomography,” IEEE Trans. Med. Imaging 36, 322–331 (2017).
[Crossref]

A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging 28, 1997–2006 (2009).
[Crossref]

Inverse Prob. (1)

G. Bal and G. Uhlmann, “Inverse diffusion theory of photoacoustics,” Inverse Prob. 26, 085010 (2010).
[Crossref]

J. Biomed. Opt. (5)

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17, 061202 (2012).
[Crossref]

J. Xia, M. R. Chatni, K. Maslov, Z. J. Guo, K. Wang, M. Anastasio, and L. V. Wang, “Whole-body ring-shaped confocal photoacoustic computed tomography of small animals in vivo,” J. Biomed. Opt. 17, 050506 (2012).
[Crossref]

P. Shao, T. J. Harrison, and R. J. Zemp, “Consecutively reconstructing absorption and scattering distributions in turbid media with multiple-illumination photoacoustic tomography,” J. Biomed. Opt. 19, 126009 (2014).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Illustration of the experimental setup. AOM, acousto-optic modulator; PBS, polarization beam splitter; CCD, charged-coupled device (camera); rotation (360°); translation (200 mm). The inset marked with dotted rectangle shows the illustration of the method for AO scanning in transverse direction of US focus propagation.
Fig. 2.
Fig. 2. Measured pressure distribution in the imaging plane of the US array; (b) Schlieren images of the US focus after 2.6 cm propagation through water (top), agar plus Intralipid phantom (middle) and chicken breast tissue (bottom); (c) measured change in contrast as a function of acoustic pressure; solid line is the quadratic fit, and squares are measured data. The error bars on measured data are standard deviations after 10 measurements. Trans.axis, transverse axis; P, pressure in MPa; a, constant; b, constant.
Fig. 3.
Fig. 3. Demonstration of 2D fluence compensation in PA images. (a) Photograph of the phantom with three identical absorbing inclusions at different locations; (b) PA image acquired using six projections; (c) measured fluence distribution using ultrasonically modulated light; (d) fluence-normalized PA image; (e) line profile through the absorbers (1, 2 and 3) before (broken line) and after (solid line) fluence correction.
Fig. 4.
Fig. 4. Comparison of absolute blood oxygen saturation (sO2) estimation using PA without and with fluence correction in an optically heterogeneous phantom; (a) illustration of the phantom cross section with two blood-filled nylon tubes; (b) and (c) uncorrected PA images at 750 and 800 nm wavelengths; (d) measured fluence variations for 750 and 800 nm wavelengths along the lines marked by solid lines in (a), where the error bars represent the standard deviation of the 10 measurements; (e) and (f) corresponding fluence-corrected PA images; (g) estimated blood sO2 using PA measurements before and after fluence correction plotted against the ground truth sO2 measured using an oximeter (Avoximeter 1000E), where vertical error bars are based on the error propagated from fluence measurement (d) and horizontal errors bars are based on the specification of (Avoximeter 1000E).
Fig. 5.
Fig. 5. Comparison of absolute blood oxygen saturation (sO2) estimation using PA without and with fluence correction in porcine tissue sample. (a) Photograph of the sample; (b) US image of the sample with two blood-filled tubes embedded; (c) example of fluence-corrected PA image at 750 nm; (d) measured fluence variation along the radial line through the tubes, where the error bars represent the standard deviation of the five measurements; (e) estimated blood sO2 using PA measurements before and after fluence correction plotted against the ground truth sO2 measured using an oximeter (Avoximeter 1000E), where vertical error bars are based on the error propagated from fluence measurement (d) and horizontal errors bars are based on the specification of (Avoximeter 1000E).
Fig. 6.
Fig. 6. (a) Photograph of the xenografted nude mouse with two nylon tubes (T1 and T2) embedded in the tumor; (b) PA image of the mouse cross section in the proximity of the dotted line in (a); (c) measured fluence variation map in the region marked by dotted polygon in (b); (d) fluence-normalized PA image; (e) line profile of the uncorrected (b) and corrected (d) PA images along the line marked though the tubes.
Fig. 7.
Fig. 7. Two-dimensional fluence compensation in a sacrificed mouse. (a) Cross-sectional US tomographic images at two locations 9 mm apart from each other; (b) uncorrected PA images; (c) acousto-optically measured fluence variation maps; (d) fluence-normalized PA images; (e) line profiles of the uncorrected and fluence-corrected PA images for quantitative comparison. Description of markers in (a) and (b): T, tumor; Sp, spine; B, bladder; A/VC, aorta and inferior vena cava (the two are not distinguishable in the images); K, kidney; and S, spleen.
Fig. 8.
Fig. 8. Zoomed in on a region marked by the dotted rectangle in Fig. 7(d) for the visual comparison of the fluence compensation effect on PA image. (a) Before fluence compensation and (b) after fluence compensation.

Equations (11)

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σo(r,λ)=ΓEa(λ,r)=Γφ(λ,r)μa(r,λ),
φxT=4πnPini=1nPr(xi,xT),
PL,T=ηφxTAT=4πnPinATηi=1nPr(xi,xT),
PL,xD=AΩ4πnPinATη(i=1nPr(xi,xT)Pr(xT,xi)+ijnPr(xi,xT)Pr(xT,xj)).
Pr(xi,xT)=Pr(xT,xi).
PL,D=AΩ4πnPinATη(i=1nPr(xi,xT)2+ijnPr(xi,xT)Pr(xj,xT)).
φxT2=(4πnPin)2(i=1nPr(xi,xT)2+ijnPr(xi,xT)Pr(xj,xT)).
φxT=4πATAΩηPL,D*,
φxT=κ1PL,D*;κ1=4πATAΩη.
φT=κ1κΔC.
sO2=Mλ1ϵHb,λ2Mλ2ϵHb,λ1Mλ2Δϵλ1Mλ1Δϵλ2,