Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator VI Time-domain analysis

Abstract

Part VI analytically examines time-domain (TD) photon diffusion in a homogeneous medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to assess characteristics of TD photon diffusion, in response to a spatially and temporally impulsive source, versus the line-of-sight source-detector distance along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts evaluated along a straight line on a semi-infinite medium-applicator interface versus the same source-detector distance, the following patterns are indicated: (1) the peak photon fluence rate is always reached sooner in concave and later in convex geometry; (2) the peak photon fluence rate decreases slower along the azimuthal and faster along the longitudinal direction on the concave interface, and conversely on the convex interface; (3) the total photon fluence decreases slower along the azimuthal and faster along the longitudinal direction on the concave interface, and conversely on the convex interface; (4) the ratio between the peak photon fluence rate and the total fluence is always greater in concave geometry and smaller in convex geometry. The total fluence is equivalent to the steady-state photon fluence analyzed in Part I [J. Opt. Soc. Am. A27, 648 (2010)10.1364/JOSAA.27.000648JOAOD61084-7529]. The patterns of peak fluence rate, time to reaching peak fluence rate, and the ratio of these two, correspond to those of AC amplitude, phase, and modulation depth of frequency-domain results demonstrated in Part IV [J. Opt. Soc. Am. A29, 1445 (2012)10.1364/JOSAA.29.001445JOAOD61084-7529].

On the stress-induced photon emission from organism: I, will the scattering-limited delay affect the temporal course?

“…the frequency-shifting property of LT and the time delay or phase-shifting properties of LT. Thus, the time-resolved photon fluence rate in a homogeneous boundless medium which is the inverse LT of � Ψ inf ⃗ � , 0| ⃗, s is obtained as [56] Based on Eq. (8), the LT of the photon fluence rate associated with the photogenic source q ⃗ ′ , 0 and evaluated on the extrapolated boundary, for which the source locates at r < = R phot and the field point locates at…”

“…where the q * l terms are dependent upon the order (or moment) l . Based on the essence of "image-source" [55,56], the two unknown terms q * l and r > associated with the lth-order (or moment) "image" source (the k l component) can be expressed by a single unknown term q l associated with the same order (or moment) of the actual photogenic source q ⃗ ′ , 0 located within the tissue at R phot , ′ , ′ (the i l component), as the following:…”

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

“…In our recent approach to a new routine of solutions of DE for an infinite-length cylinder domain as demonstrated in a series of work applicable to CW, 25 frequency domain 26 and time domain, 27 the solutions for DE were presented using a pair of the modified Bessel functions of the first and the second kinds. The basic form of the DE solution for the unbounded homogeneous medium geometry shown in Refs.…”