Abstract

We predict the phenomenon of spiral-planar equivalence for steady-state photon diffusion associated with a cylindrical applicator. Recently we have derived a unified theory of steady-state photon diffusion in a homogenous medium bounded either externally (referred to as a concave geometry) or internally (referred to as a convex geometry) by an infinitely long circular cylindrical applicator [JOSAA, 27(3): 648-662 (2010)]. Despite the idealization of the geometry by assuming an infinite length of the applicator, the analytic prediction withholds the quantitative examinations based on experimental measurements, and finite-element solution of photon diffusion. An interesting finding is that the decay of photon fluence in a concave boundary is smaller in the azimuth direction but greater along the longitudinal direction, in comparison with that in a semi-infinite geometry along a straight line, for the same line-of-sight distance between the source and the detector. Conversely, the decay of photon fluence in a convex boundary is greater in the azimuth direction but smaller along the longitudinal direction, in comparison with that in a semi-infinite geometry along a straight line, for the same line-of-sight source-detector distance. These findings suggest that on the cylindrical applicator interface there should exist a spiral direction (oblique to both the azimuthal and longitudinal directions), along which the rate of photon fluence decay follows that along a straight line on a planar semi-infinite interface---which is called the spiral-planar equivalence. The spiral-planar equivalence is derivable analytically, and subject to quantitative evaluations. Validating the spiral-planar equivalence not only enriches the understanding of photon diffusion in cylindricalinterface geometry, but also provides unique semi-infinite-based imaging application in trans-lumenal diffuse optical sensing. The spiral-planar equivalence may be applicable to time-resolved photon-diffusion.

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