On the “Bi-Phase” of Fluorescence to Scattering with Single-Fiber Illumination and Detection: A Quasi-Analytical Photon-Transport Approach Operated with Center-Illuminated Area Detection

Bi-phasic (with a local minimum) response of fluorescence to scattering when probed by a single fiber (SF) was first observed in 2003. Subsequent experiments and Monte Carlo studies have shown the bi-phasic turning of SF fluorescence to occur at a dimensionless reduced scattering of ~1 and vary with absorption. The bi-phase of SF fluorescence received semi-empirical explanations; however, better understandings of the bi-phase and its dependence on absorption are necessary. This work demonstrates a quasi-analytical projection of a bi-phasic pattern comparable to that of SF fluorescence via photon-transport analyses of fluorescence in a center-illuminated-area-detection (CIAD) geometry. This model-approach is principled upon scaling of the diffuse fluorescence between CIAD and a SF of the same size of collection, which expands the scaling of diffuse reflectance between CIAD and a SF discovered for steady-state and time-domain cases. Analytical fluorescence for CIAD is then developed via radial-integration of radially resolved fluorescence. The radiance of excitation is decomposed to surface, collimated, and diffusive portions to account for the surface, near the point-of-entry, and diffuse portion of fluorescence associated with a centered illumination. Radiative or diffuse transport methods are then used to quasi-analytically deduce fluorescence excited by the three portions of radiance. The resulting model of fluorescence for CIAD, while limiting to iso-transport properties at the excitation and emission wavelengths, is compared against the semi-empirical model for SF, revealing bi-phasic turning [0.5~2.6] at various geometric sizes [0.2, 0.4, 0.6, 0.8, 1.0 mm] and a change of three orders of magnitude in the absorption of the background medium. This model projects a strong reduction in fluorescence versus strong absorption at high scattering, which differs from the semi-empirical SF model’s projection of a saturating pattern unresponsive to further increases in the absorption. This framework of modeling fluorescence may be useful to project frequency-domain and lifetime pattens of fluorescence in an SF and CIAD.