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• W2008130588 abstract "The predictions of the frequency-domain standard diffusion equation (SDE) model for light propagation in an infinite turbid medium diverge from the more complete ${mathit{P}}_{1}$ approximation to the linear Boltzmann transport equation at intensity modulation frequencies greater than several hundred MHz. The ${mathit{P}}_{1}$ approximation is based on keeping only the terms l=0 and l=1 in the expansion of the angular photon density in spherical harmonics, and the nomenclature ${mathit{P}}_{1}$ approximation is used since the spherical harmonics of order l=1 can be written in terms of the first order Legendre polynomial, which is traditionally represented by the symbol ${mathit{P}}_{1}$. Frequency-domain data acquired in a quasi-infinite turbid medium at modulation frequencies ranging from 0.38 to 3.2 GHz using a superheterodyning microwave detection system were analyzed using expressions derived from both the ${mathit{P}}_{1}$ aproximation equation and the SDE. This analysis shows that the ${mathit{P}}_{1}$ approximation provides a more accurate description of the data over this range of modulation frequencies. Some researchers have claimed that the ${mathit{P}}_{1}$ approximation predicts that a light pulse should propagate with an average speed of c/ ensuremath{surd}3 in a thick turbid medium. However, an examination of the Green's function that we obtained from the frequency-domain ${mathit{P}}_{1}$ approximation model indicates that a photon density wave phase velocity of c/ ensuremath{surd}3 is only asymptotically approached in a regime where the light intensity modulation frequency aproaches infinity. The Fourier transform of this frequency-domain result shows that in the time domain, the ${mathit{P}}_{1}$ approximation predicts that only the leading edge of the pulse (i.e., the photons arriving at the detector at the earliest time) approaches a speed of c/ensuremath{surd}3. textcopyright{} 1996 The American Physical Society." @default.
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• W2008130588 date "1996-03-01" @default.
• W2008130588 modified "2023-10-18" @default.
• W2008130588 title "Gigahertz photon density waves in a turbid medium: Theory and experiments" @default.
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• W2008130588 doi "https://doi.org/10.1103/physreve.53.2307" @default.
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