Abstract

The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been obtained in the frequency domain (where the source amplitude is modulated at radio-frequencies) by making use of analytical solutions of the photon diffusion equation in an infinite slab geometry. Furthermore, solutions for the relative contrast of AC, PH and DC signals when a totally absorbing plane is placed at a fixed depth of the slab have also been obtained. The solutions have been validated by comparisons with gold standard Monte Carlo simulations. The obtained results show that the AC signal, for modulation frequencies < 200 MHz, has a depth sensitivity with similar characteristics to that of the continuous-wave (CW) domain (source modulation frequency of zero). Thus, the depth probed by such a signal can be estimated by using the formula of penetration depth for the CW domain (Sci. Rep. 6, 27057 (2016)). However, the PH signal has a different behavior compared to the CW domain, showing a larger depth sensitivity at shallow depths and a less steep relative contrast as a function of depth. These results mark a clear difference in term of depth sensitivity between AC and PH signals, and highlight the complexity of the estimation of the actual depth probed in tissue spectroscopy.

© 2017 Optical Society of America

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References

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    [Crossref]

2016 (1)

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

2014 (2)

G. Zonios, “Investigation of reflectance sampling depth in biological tissues for various common illumination/collection configurations,” J. Biomed. Opt. 19, 97001 (2014).
[Crossref] [PubMed]

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

2006 (1)

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

2004 (2)

F. Bevilacqua, J. S. You, C. K. Hayakawa, and V. Venugopalan, “Sampling tissue volumes using frequency-domain photon migration,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 051908 (2004).
[Crossref] [PubMed]

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

2003 (1)

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging,” Photochem. Photobiol. 77, 420–430 (2003).
[Crossref] [PubMed]

2002 (1)

S. Del Bianco, F. Martelli, and G. Zaccanti, “Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation,” Phys Med Biol 47, 4131–4144 (2002).
[Crossref] [PubMed]

1999 (1)

1998 (3)

G. H. Weiss, “Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis,” Appl. Opt. 37, 3558–3563 (1998).
[Crossref]

G. Weiss and J. Kiefer, “A numerical study of the statistics of penetration depth of photons re-emitted from irradiated media,” J. Mod. Opt. 45, 2327–2337 (1998).
[Crossref]

G. Weiss, J. Porra, and J. Masoliver, “Statistics of the depth probed by cw measurements of photons in a turbid medium,” Phys. Rev. E. 58, 6431–6439 (1998).
[Crossref]

1997 (3)

1995 (2)

1994 (1)

1993 (2)

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]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, R2999–R3002 (1993).
[PubMed]

1992 (2)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[Crossref]

J. M. Schmitt, A. Knuttel, and J. R. Knutson, “Interference of diffusive light waves,” J. Opt. Soc. Am. A 9, 1832–1843 (1992).
[Crossref] [PubMed]

1991 (1)

1989 (1)

G. Weiss, R. Nossal, and R. Bonner, “Statistics of Penetration Depth of Photons Re-emitted from Irradiated Tissue,” J. Mod. Opt. 36, 349–359 (1989).
[Crossref]

1988 (1)

1987 (1)

Andersson-Engels, S.

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse Optics for Tissue Monitoring and Tomography,” Rep. Prog. Phys.73 (2010).
[Crossref] [PubMed]

Bassi, A.

Bevilacqua, F.

F. Bevilacqua, J. S. You, C. K. Hayakawa, and V. Venugopalan, “Sampling tissue volumes using frequency-domain photon migration,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 051908 (2004).
[Crossref] [PubMed]

Bigio, I. J.

I. J. Bigio and S. Fantini, Quantitative Biomedical Optics: Theory, Methods, and Applications (Cambridge University Press, New York, NY, USA, 2016), 1st ed.

Binzoni, T.

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

Boas, D. 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 and wavelength transduction of diffuse photon density waves,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, R2999–R3002 (1993).
[PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[Crossref]

Bonner, R.

G. Weiss, R. Nossal, and R. Bonner, “Statistics of Penetration Depth of Photons Re-emitted from Irradiated Tissue,” J. Mod. Opt. 36, 349–359 (1989).
[Crossref]

R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, and S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
[Crossref] [PubMed]

Bonner, R. F.

Burch, C. L.

Chance, B.

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]

S. Feng, F. A. Zeng, and B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[Crossref] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, R2999–R3002 (1993).
[PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[Crossref]

Choe, R.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse Optics for Tissue Monitoring and Tomography,” Rep. Prog. Phys.73 (2010).
[Crossref] [PubMed]

Cignini, F.

Contini, D.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[Crossref] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[Crossref] [PubMed]

Cubeddu, R.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

Del Bianco, S.

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

S. Del Bianco, F. Martelli, and G. Zaccanti, “Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation,” Phys Med Biol 47, 4131–4144 (2002).
[Crossref] [PubMed]

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation Through Biological Tissue and Other Di ffusive Media: Theory, Solutions, and Software (SPIE Press, 2010).
[Crossref]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse Optics for Tissue Monitoring and Tomography,” Rep. Prog. Phys.73 (2010).
[Crossref] [PubMed]

Fantini, S.

I. J. Bigio and S. Fantini, Quantitative Biomedical Optics: Theory, Methods, and Applications (Cambridge University Press, New York, NY, USA, 2016), 1st ed.

Farina, A.

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

Feng, S.

Frisoli, J. K.

Gibson, A.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Gurfinkel, M.

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging,” Photochem. Photobiol. 77, 420–430 (2003).
[Crossref] [PubMed]

Haskell, R. C.

Havlin, S.

Hayakawa, C. K.

F. Bevilacqua, J. S. You, C. K. Hayakawa, and V. Venugopalan, “Sampling tissue volumes using frequency-domain photon migration,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 051908 (2004).
[Crossref] [PubMed]

Hebden, J. C.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Heino, J.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Houston, J. P.

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging,” Photochem. Photobiol. 77, 420–430 (2003).
[Crossref] [PubMed]

Ismaelli, A.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation Through Biological Tissue and Other Di ffusive Media: Theory, Solutions, and Software (SPIE Press, 2010).
[Crossref]

Jarvenpaa, S.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Jennions, D.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Katila, T.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Kiefer, J.

G. Weiss and J. Kiefer, “A numerical study of the statistics of penetration depth of photons re-emitted from irradiated media,” J. Mod. Opt. 45, 2327–2337 (1998).
[Crossref]

R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, and S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
[Crossref] [PubMed]

Knutson, J. R.

Knuttel, A.

Kotilahti, K.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Lakowicz, J. R.

Lipiainen, L.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Macdonald, R.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

Martelli, F.

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

S. Del Bianco, F. Martelli, and G. Zaccanti, “Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation,” Phys Med Biol 47, 4131–4144 (2002).
[Crossref] [PubMed]

F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[Crossref] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[Crossref] [PubMed]

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation Through Biological Tissue and Other Di ffusive Media: Theory, Solutions, and Software (SPIE Press, 2010).
[Crossref]

Masoliver, J.

G. Weiss, J. Porra, and J. Masoliver, “Statistics of the depth probed by cw measurements of photons in a turbid medium,” Phys. Rev. E. 58, 6431–6439 (1998).
[Crossref]

Mazurenka, M.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

Ninni, P. D.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

Nissila, I.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Noponen, T.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Nossal, R.

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 and wavelength transduction of diffuse photon density waves,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, R2999–R3002 (1993).
[PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[Crossref]

Osei, E. K.

Osterberg, U.

Patterson, M. S.

Paulsen, K.

Pifferi, A.

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

Pogue, B.

Porra, J.

G. Weiss, J. Porra, and J. Masoliver, “Statistics of the depth probed by cw measurements of photons in a turbid medium,” Phys. Rev. E. 58, 6431–6439 (1998).
[Crossref]

Ripoll, J.

J. Ripoll, Principles of Diffuse Light Propagation: Light Propagation in Tissues with Applications in Biology and Medicine (World Scientific, 2012).

Sassaroli, A.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

Schmitt, J. M.

Schweiger, M.

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

Sevick, E. M.

Sevick-Muraca, E. M.

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging,” Photochem. Photobiol. 77, 420–430 (2003).
[Crossref] [PubMed]

Spinelli, L.

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

Svaasand, L. O.

Taddeucci, A.

Taitelbaum, H.

Taroni, P.

Testorf, M.

Thompson, A. B.

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging,” Photochem. Photobiol. 77, 420–430 (2003).
[Crossref] [PubMed]

Torricelli, A.

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

Tromberg, B. J.

Tsay, T. T.

Venugopalan, V.

F. Bevilacqua, J. S. You, C. K. Hayakawa, and V. Venugopalan, “Sampling tissue volumes using frequency-domain photon migration,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 051908 (2004).
[Crossref] [PubMed]

Wabnitz, H.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

Weiss, G.

G. Weiss and J. Kiefer, “A numerical study of the statistics of penetration depth of photons re-emitted from irradiated media,” J. Mod. Opt. 45, 2327–2337 (1998).
[Crossref]

G. Weiss, J. Porra, and J. Masoliver, “Statistics of the depth probed by cw measurements of photons in a turbid medium,” Phys. Rev. E. 58, 6431–6439 (1998).
[Crossref]

G. Weiss, R. Nossal, and R. Bonner, “Statistics of Penetration Depth of Photons Re-emitted from Irradiated Tissue,” J. Mod. Opt. 36, 349–359 (1989).
[Crossref]

Weiss, G. H.

Wilson, B. C.

Yodh, A. G.

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 and wavelength transduction of diffuse photon density waves,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, R2999–R3002 (1993).
[PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[Crossref]

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse Optics for Tissue Monitoring and Tomography,” Rep. Prog. Phys.73 (2010).
[Crossref] [PubMed]

You, J. S.

F. Bevilacqua, J. S. You, C. K. Hayakawa, and V. Venugopalan, “Sampling tissue volumes using frequency-domain photon migration,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 051908 (2004).
[Crossref] [PubMed]

Zaccanti, G.

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

S. Del Bianco, F. Martelli, F. Cignini, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Liquid phantom for investigating light propagation through layered diffusive media,” Opt. Express 12, 2102–2111 (2004).
[Crossref] [PubMed]

S. Del Bianco, F. Martelli, and G. Zaccanti, “Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation,” Phys Med Biol 47, 4131–4144 (2002).
[Crossref] [PubMed]

F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[Crossref] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[Crossref] [PubMed]

G. Zaccanti, “Monte Carlo study of light propagation in optically thick media: point source case,” Appl. Opt. 30, 2031–2041 (1991).
[Crossref] [PubMed]

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation Through Biological Tissue and Other Di ffusive Media: Theory, Solutions, and Software (SPIE Press, 2010).
[Crossref]

Zeng, F. A.

Zonios, G.

G. Zonios, “Investigation of reflectance sampling depth in biological tissues for various common illumination/collection configurations,” J. Biomed. Opt. 19, 97001 (2014).
[Crossref] [PubMed]

Appl. Opt. (11)

R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, and S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
[Crossref] [PubMed]

G. Zaccanti, “Monte Carlo study of light propagation in optically thick media: point source case,” Appl. Opt. 30, 2031–2041 (1991).
[Crossref] [PubMed]

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]

E. M. Sevick, J. K. Frisoli, C. L. Burch, and J. R. Lakowicz, “Localization of absorbers in scattering media by use of frequency-domain measurements of time-dependent photon migration,” Appl. Opt. 33, 3562–3570 (1994).
[Crossref] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[Crossref] [PubMed]

F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[Crossref] [PubMed]

G. H. Weiss, “Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis,” Appl. Opt. 37, 3558–3563 (1998).
[Crossref]

M. S. Patterson, S. Andersson-Engels, B. C. Wilson, and E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
[Crossref] [PubMed]

S. Feng, F. A. Zeng, and B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[Crossref] [PubMed]

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]

M. Testorf, U. Osterberg, B. Pogue, and K. Paulsen, “Sampling of time- and frequency-domain signals in monte carlo simulations of photon migration,” Appl. Opt. 38, 236–245 (1999).
[Crossref]

J Biomed. Opt. (1)

I. Nissila, J. C. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Jarvenpaa, L. Lipiainen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J Biomed. Opt. 11, 064015 (2006).
[Crossref]

J. Biomed. Opt. (2)

F. Martelli, P. D. Ninni, G. Zaccanti, D. Contini, L. Spinelli, A. Torricelli, R. Cubeddu, H. Wabnitz, M. Mazurenka, R. Macdonald, A. Sassaroli, and A. Pifferi, “Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation,” J. Biomed. Opt. 19, 076011 (2014).
[Crossref]

G. Zonios, “Investigation of reflectance sampling depth in biological tissues for various common illumination/collection configurations,” J. Biomed. Opt. 19, 97001 (2014).
[Crossref] [PubMed]

J. Mod. Opt. (2)

G. Weiss, R. Nossal, and R. Bonner, “Statistics of Penetration Depth of Photons Re-emitted from Irradiated Tissue,” J. Mod. Opt. 36, 349–359 (1989).
[Crossref]

G. Weiss and J. Kiefer, “A numerical study of the statistics of penetration depth of photons re-emitted from irradiated media,” J. Mod. Opt. 45, 2327–2337 (1998).
[Crossref]

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

Opt. Express (1)

Photochem. Photobiol. (1)

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging,” Photochem. Photobiol. 77, 420–430 (2003).
[Crossref] [PubMed]

Phys Med Biol (1)

S. Del Bianco, F. Martelli, and G. Zaccanti, “Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation,” Phys Med Biol 47, 4131–4144 (2002).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

F. Bevilacqua, J. S. You, C. K. Hayakawa, and V. Venugopalan, “Sampling tissue volumes using frequency-domain photon migration,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69, 051908 (2004).
[Crossref] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 47, R2999–R3002 (1993).
[PubMed]

Phys. Rev. E. (1)

G. Weiss, J. Porra, and J. Masoliver, “Statistics of the depth probed by cw measurements of photons in a turbid medium,” Phys. Rev. E. 58, 6431–6439 (1998).
[Crossref]

Phys. Rev. Lett. (1)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[Crossref]

Sci. Rep. (1)

F. Martelli, T. Binzoni, A. Pifferi, L. Spinelli, A. Farina, and A. Torricelli, “There’s plenty of light at the bottom: statistics of photon penetration depth in random media,” Sci. Rep. 6, 27057 (2016).
[Crossref]

Other (4)

J. Ripoll, Principles of Diffuse Light Propagation: Light Propagation in Tissues with Applications in Biology and Medicine (World Scientific, 2012).

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation Through Biological Tissue and Other Di ffusive Media: Theory, Solutions, and Software (SPIE Press, 2010).
[Crossref]

I. J. Bigio and S. Fantini, Quantitative Biomedical Optics: Theory, Methods, and Applications (Cambridge University Press, New York, NY, USA, 2016), 1st ed.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse Optics for Tissue Monitoring and Tomography,” Rep. Prog. Phys.73 (2010).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Comparison between DE and MC results for the depth sensitivity of AC and PH signals, sAC (z, ρ, ω) and sPH (z, ρ, ω), plotted versus the maximum depth z for a slab 100 mm thick, with ρ =20 mm, μ s = 1 mm 1, μa =0.005 mm−1, ν =100 MHz (data plotted in black) and ν =0 (data plotted in red), and refractive indexes of slab and external, 1.4 and 1, respectively. We stress that the data in red (ν =0) represent the DC sensitivity sDC (z, ρ).

Fig. 2
Fig. 2

Depth sensitivity obtained with the DE for AC and PH signals, sAC and sPH, versus the maximum depth z for a slab 100 mm thick, ρ =20 mm, μ s = 1 mm 1, μa =0.001, 0.005 and 0.01 mm−1, ν = {10−6, 100, 200, 400} MHz and refractive indexes of slab and external, 1.4 and 1, respectively.

Fig. 3
Fig. 3

Comparison of the depth sensitivity functions sAC (z, ρ, ω), sPH (z, ρ, ω), and sDC (z, ρ) obtained with the DE. The results pertain to a slab 100 mm thick, ρ =20 mm, μ s = 1 mm 1, μa =0.005 mm−1, ν = {100, 200, 400} MHz and refractive indexes of slab and external, 1.4 and 1, respectively.

Fig. 4
Fig. 4

It pertains to the same optical properties and geometry as Fig. 1 but for the relative contrast of a totally absorbing plane placed at z inside the slab. The DE and the MC results for AC, PH and DC have been plotted versus the maximum depth z.

Fig. 5
Fig. 5

Relative DE contrast of a totally absorbing plane in a slab: comparison of CAC (z, ρ, ω), CPH (z, ρ, ω), and CDC (z, ρ) versus the z position of the plane. The results pertain to a slab 100 mm thick, ρ =20 mm, μ s = 1 mm 1, μa = {0.001, 0.01} mm−1, ν =100 MHz and refractive indexes of slab and external, 1.4 and 1, respectively.

Fig. 6
Fig. 6

Relative DE contrast of a totally absorbing plane in a slab for AC and PH versus the position of the plane z, for ν = {10−6, 100, 200, 400} MHz. The results pertain to a slab 100 mm thick, ρ =20 mm, μ s = 1 mm 1, μa =0.005 mm−1, and refractive indexes of slab and external, 1.4 and 1, respectively.

Equations (16)

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q ˜ ( r , ω , t ) = q D C 0 ( r ) + q A C 0 ( r ) exp ( i ω t ) ,
[ 1 c n t + μ a D 2 ] Φ ˜ ( r , t ) = q ˜ ( r , ω , t ) ,
Φ ˜ ( r , t ) = Φ D C ( r ) + Φ ˜ A C ( r , t ) .
Φ ˜ A C ( r , t ) = Φ ˜ A C 0 exp ( i ω t ) .
R ˜ ( r , t ) = R D C ( r ) + R ˜ A C 0 exp ( i ω t ) .
R T ( r ) = 1 T 0 T R ˜ ( r , t ) d t = R D C ( r ) ,
[ i ω c n + μ a D 2 ] Φ ˜ A C 0 ( r ) = q A C 0 ( r ) .
R ˜ A C 0 ( s 0 , ρ , μ a ) = | R ˜ A C 0 ( s 0 , ρ , μ a ) | exp ( i φ ˜ ( s 0 , ρ , μ a ) ) = R D C ( s 0 , ρ , μ a ( i ω ) / c n ) ,
| R ˜ A C 0 ( s 0 , ρ , μ a ) | = { [ R D C ( s 0 , ρ , μ a ( i ω ) / c n ) ] 2 + J [ R D C ( s 0 , ρ , μ a ( i ω ) / c n ) ] 2 } 1 / 2 ,
φ ˜ ( s 0 , ρ , μ a ) = arctan ( J [ R D C ( s 0 , ρ , μ a ( i ω ) / c n ) ] [ R D C ( s 0 , ρ , μ a ( i ω ) / c n ) ] ) .
s A C ( z , ρ , ω ) = 1 | R ˜ A C 0 ( s 0 , ρ , μ a ) | | R ˜ A C 0 ( z , ρ , μ a ) | z ,
s P H ( z , ρ , ω ) = 1 φ ˜ ( s 0 , ρ , μ a ) φ ˜ ( z , ρ , μ a ) z .
s D C ( z , ρ ) = 1 R D C ( s 0 , ρ ) R D C ( z , ρ ) z .
C A C ( z , ρ , ω ) = | R ˜ A C 0 ( s 0 , ρ , μ a ) | | R ˜ A C 0 ( z , ρ , μ a ) | | R ˜ A C 0 ( s 0 , ρ , μ a ) | = z s 0 s A C ( z , ρ , ω ) d z ,
C P H ( z , ρ , ω ) = φ ˜ ( s 0 , ρ , μ a ) φ ˜ ( z , ρ , μ a ) φ ˜ ( s 0 , ρ , μ a ) = z s 0 s P H ( z , ρ , ω ) d z .
C C D ( z , ρ ) = R D C ( s 0 , ρ ) R D C ( z , ρ ) R D C ( s 0 , ρ ) = z s 0 s D C ( z , ρ , ω = 0 ) d z .

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