This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett. 96, 163902 (2006).

[Crossref]
[PubMed]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for ultrasound-modulated multiply scattered light.,” Phys. Rev. E 74, 036618 (2006).

[Crossref]

C. U. Devi, R. M. Vasu, and A. K. Sood, “Application of ultrasound-tagged photons for measurement of amplitude of vibration of tissue caused by ultrasound: theory, simulation, and experiments,” J. Biomed. Opt. 11, 049802(2006).

[Crossref]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).

[Crossref]

L. V. Wang, “Mechanisms of ultrasonic modulation of ultiply scattered light: an analytic model,” Phys. Rev. Lett. 87, 043903 (2001).

[Crossref]
[PubMed]

J. L. Harden and V. Viasnoff, “Recent advances in DWS-based micro-rheology,” Curr. Opin. Colloid Interface Sci. 6, 438–445(2001).

[Crossref]

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

[Crossref]
[PubMed]

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffuse temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).

[Crossref]
[PubMed]

L. H. V. Wang, S. L. Jacques, and 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]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

A. Björck, Numerical Methods for Least Squares Problems (SIAM, 1989).

J. L. Lions, E. Magenes, and P. Kenneth, Non-Homogeneous Boundary Value Problems and Applications (Springer-Verlag, 1972), Vol. 2.

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

A. Björck, Numerical Methods for Least Squares Problems (SIAM, 1989).

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffuse temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).

[Crossref]
[PubMed]

C. U. Devi, R. M. Vasu, and A. K. Sood, “Application of ultrasound-tagged photons for measurement of amplitude of vibration of tissue caused by ultrasound: theory, simulation, and experiments,” J. Biomed. Opt. 11, 049802(2006).

[Crossref]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

J. L. Harden and V. Viasnoff, “Recent advances in DWS-based micro-rheology,” Curr. Opin. Colloid Interface Sci. 6, 438–445(2001).

[Crossref]

J. L. Lions, E. Magenes, and P. Kenneth, Non-Homogeneous Boundary Value Problems and Applications (Springer-Verlag, 1972), Vol. 2.

J. L. Lions, E. Magenes, and P. Kenneth, Non-Homogeneous Boundary Value Problems and Applications (Springer-Verlag, 1972), Vol. 2.

J. L. Lions, E. Magenes, and P. Kenneth, Non-Homogeneous Boundary Value Problems and Applications (Springer-Verlag, 1972), Vol. 2.

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

H. M. Varma, A. K. Nandakumaran, and R. M. Vasu, “Study of turbid media with light: recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light,” J. Opt. Soc. Am. A 26, 1472–1483(2009).

[Crossref]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for multiply scattered light modulated by an ultrasonic pulse,” J. Opt. Soc. Am. A 24, 2797–2806 (2007).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for ultrasound-modulated multiply scattered light.,” Phys. Rev. E 74, 036618 (2006).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett. 96, 163902 (2006).

[Crossref]
[PubMed]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).

[Crossref]

C. U. Devi, R. M. Vasu, and A. K. Sood, “Application of ultrasound-tagged photons for measurement of amplitude of vibration of tissue caused by ultrasound: theory, simulation, and experiments,” J. Biomed. Opt. 11, 049802(2006).

[Crossref]

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

H. M. Varma, A. K. Nandakumaran, and R. M. Vasu, “Study of turbid media with light: recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light,” J. Opt. Soc. Am. A 26, 1472–1483(2009).

[Crossref]

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

H. M. Varma, A. K. Nandakumaran, and R. M. Vasu, “Study of turbid media with light: recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light,” J. Opt. Soc. Am. A 26, 1472–1483(2009).

[Crossref]

C. U. Devi, R. M. Vasu, and A. K. Sood, “Application of ultrasound-tagged photons for measurement of amplitude of vibration of tissue caused by ultrasound: theory, simulation, and experiments,” J. Biomed. Opt. 11, 049802(2006).

[Crossref]

J. L. Harden and V. Viasnoff, “Recent advances in DWS-based micro-rheology,” Curr. Opin. Colloid Interface Sci. 6, 438–445(2001).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for multiply scattered light modulated by an ultrasonic pulse,” J. Opt. Soc. Am. A 24, 2797–2806 (2007).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for ultrasound-modulated multiply scattered light.,” Phys. Rev. E 74, 036618 (2006).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett. 96, 163902 (2006).

[Crossref]
[PubMed]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).

[Crossref]

L. V. Wang, “Mechanisms of ultrasonic modulation of ultiply scattered light: an analytic model,” Phys. Rev. Lett. 87, 043903 (2001).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

G. Yao and L. V. Wang, “Theoretical and experimental studies of ultrasound-modulated optical tomography in biological tissue,” Appl. Opt. 39, 659–664 (2000).

[Crossref]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

J. L. Harden and V. Viasnoff, “Recent advances in DWS-based micro-rheology,” Curr. Opin. Colloid Interface Sci. 6, 438–445(2001).

[Crossref]

C. U. Devi, R. M. Vasu, and A. K. Sood, “Application of ultrasound-tagged photons for measurement of amplitude of vibration of tissue caused by ultrasound: theory, simulation, and experiments,” J. Biomed. Opt. 11, 049802(2006).

[Crossref]

This perturbation approach is commonly used to solve the inverse paramater recovery problem. See, for example, H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267 (2010).

[Crossref]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for multiply scattered light modulated by an ultrasonic pulse,” J. Opt. Soc. Am. A 24, 2797–2806 (2007).

[Crossref]

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

[Crossref]

D. A. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A 14, 192–215 (1997).

[Crossref]

H. M. Varma, A. K. Nandakumaran, and R. M. Vasu, “Study of turbid media with light: recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light,” J. Opt. Soc. Am. A 26, 1472–1483(2009).

[Crossref]

H. M. Varma, B. Banerjee, D. Roy, A. K. Nandakumaran, and R. M. Vasu, “Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography,” J. Opt. Soc. Am. A 27, 259–267(2010).

[Crossref]

S. Leveque, A. C. Boccara, M. Lebec, and H. Saint-Jalmes, “Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing,” Opt. Lett. 24, 181–183 (1999).

[Crossref]

L. H. V. Wang, S. L. Jacques, and 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]

S. Sakadzic and L. V. Wang, “Correlation transfer equation for ultrasound-modulated multiply scattered light.,” Phys. Rev. E 74, 036618 (2006).

[Crossref]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: An analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).

[Crossref]

L. V. Wang, “Mechanisms of ultrasonic modulation of ultiply scattered light: an analytic model,” Phys. Rev. Lett. 87, 043903 (2001).

[Crossref]
[PubMed]

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffuse temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).

[Crossref]
[PubMed]

S. Sakadzic and L. V. Wang, “Correlation transfer and diffusion of ultrasound-modulated multiply scattered light,” Phys. Rev. Lett. 96, 163902 (2006).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

D. A. Weitz, J. X. Zhu, D. J. Durian, H. Gang, and D. J. Pine, “Diffusing-wave spectroscopy: the technique and some applications,” Phys. Scr. T49, 610–621 (1993).

[Crossref]

In general the measurement F(p,r,ωa)=|F˜(p,r,ωa)|. However, from the numerical simulations, for the objects we have chosen, we have noticed that the imaginary part of F˜(p,r,ωa) is negligible compared to its real part. Therefore, we have taken the measurement as F(p,r,ωa)≈F˜(p,r,ωa).

J. L. Lions, E. Magenes, and P. Kenneth, Non-Homogeneous Boundary Value Problems and Applications (Springer-Verlag, 1972), Vol. 2.

A. Björck, Numerical Methods for Least Squares Problems (SIAM, 1989).