There’s plenty of light at the bottom: statistics of photon penetration depth in random media

Martelli, Fabrizio; Binzoni, Tiziano; Pifferi, Antonio; Spinelli, Lorenzo; Farina, Andrea; Torricelli, Alessandro

doi:10.1038/srep27057

Cited by 101 publications

(107 citation statements)

References 58 publications

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“…Therefore, for the slab the penetration depth for R T (r) simply coincides with the CW penetration depth calculated in [11] (see Eq. (24) in [11]). This fact implicitly means that the trajectories followed by detected photons when the FD signal, R T (r), is measured, obey to the same common rules of photon migration as those considered in the TD and CW domain.…”

Section: General Viewsupporting

confidence: 66%

“…(2) without the time derivative. Then, from Φ DC (r) the reflectance R DC (r) can be obtained as usual [11]. Thus, the reflectance, R AC0 (s 0 , ρ, μ a ), of the AC component from a diffusive slab of thickness s 0 and source-detector distance ρ can be derived as…”

Section: Depth Sensitivity Of Ac and Ph Signalsmentioning

confidence: 99%

“…Therefore, for the slab the penetration depth for R T (r) simply coincides with the CW penetration depth calculated in [11] (see Eq. (24) in [11]).…”

Section: General Viewmentioning

confidence: 99%

“…Recently, the photon penetration depth for a slab, in TD and CW domain, has been studied by means of a comprehensive statistical approach. Analytical formulae based on the diffusion equation (DE) for the mean maximum depth and the mean average depth reached by the detected photons have been obtained [11].…”

mentioning

confidence: 99%

“…The DC signal, equivalent to the CW signal and for which a statistical general theory on the penetration depth is already available, is used as a reference special case to help the reading/interpretation of the AC and PH results. We also note that from now onward the acronyms DC and CW are used with the same meaning [11].…”

mentioning

confidence: 99%

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Depth sensitivity of frequency domain optical measurements in diffusive media

Binzoni¹,

Sassaroli²,

Torricelli³

et al. 2017

Biomed. Opt. Express

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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.

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Section: General Viewsupporting

confidence: 66%

Section: Depth Sensitivity Of Ac and Ph Signalsmentioning

confidence: 99%

“…Therefore, for the slab the penetration depth for R T (r) simply coincides with the CW penetration depth calculated in [11] (see Eq. (24) in [11]).…”

Section: General Viewmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Depth sensitivity of frequency domain optical measurements in diffusive media

Binzoni¹,

Sassaroli²,

Torricelli³

et al. 2017

Biomed. Opt. Express

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Near‐infrared bone densitometry: A feasibility study on distal radius measurement

Chung

Chen

Leu

et al. 2018

Journal of Biophotonics

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Osteoporosis, defined as decreased bone mineral density (BMD), poses patients in dangers for fracture risk and has become a major public health problem worldwide because of is associated morbidity, mortality and costs. Without doubt, early detection and timely intervention are important to successfully manage osteoporosis and its associated complications. The dual-energy x-ray absorptiometry (DXA) is the most popular and standard method to measure BMD. However, limitations including radiation exposure and availability restrict its application for osteoporosis screening among general population. In this study, we developed a simple method to detect human distal radius bone density based on near infrared (NIR) image system. Among 10 volunteers (including 5 young and 5 elderly participants) receiving bone density measurement using our NIR image system at the ultradistal part of bilateral distal radius, we demonstrated a strong correlation between the optical attenuation and BMD measured with DXA, which may facilitate predicting bone density status. We hope our potential NIR image system may open a new avenue for development of osteoporosis screening facilities and help in prevention of osteoporosis related fracture and its associated complications in the near future. Pearson's correlations between BMD values from the DXA and light intensity of NIR system.

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Determination of inclusion depth in ex vivo animal tissues using surface enhanced deep Raman spectroscopy

Mosca

Dey

Tabish

et al. 2019

Journal of Biophotonics

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This work presents recent developments in spatially offset and transmission Raman spectroscopy for noninvasive detection and depth prediction of a single SERS inclusion located deep inside ex vivo biological tissues. The concept exploits the differential attenuation of Raman bands brought about by their different absorption due to tissue constituents enabling to predict the inclusion depth. Four different calibration models are tested and evaluated to predict the depth of surface enhanced Raman scattering labelled nanoparticles, within an up to 40 mm slab of porcine tissue. An external measurement carried out in transmission mode, with a noninvasively built model on the analysed sample, is shown to be insensitive to variations of the overall thickness of the tissue yielding an average root‐mean‐square error of prediction of 6.7%. The results pave the way for future noninvasive deep Raman spectroscopy in vivo enabling to localise cancer biomarkers for an early diagnosis of multiple diseases.

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There’s plenty of light at the bottom: statistics of photon penetration depth in random media

Cited by 101 publications

References 58 publications

Depth sensitivity of frequency domain optical measurements in diffusive media

Depth sensitivity of frequency domain optical measurements in diffusive media

Near‐infrared bone densitometry: A feasibility study on distal radius measurement

Determination of inclusion depth in ex vivo animal tissues using surface enhanced deep Raman spectroscopy

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