Phase-function corrected diffusion model for diffuse reflectance of a pencil beam obliquely incident on a semi-infinite turbid medium.

Oblique incidence reflectometry (OIR) is an established technique for the estimation of tissue optical properties. However, a sensing footprint of a few transport mean-free paths is often needed when diffusion-regime-based algorithms are used. Smaller-footprint probes require improved light-propagation models and inversion schemes for diffuse reflectance close to the point of entry but might enable micro-endoscopic form factors for clinical assessments of cancers and precancers. The phase-function corrected diffusion theory presented by Vitkin et al. [Nat. Commun. 2, 587 (2011)] to the case of pencil beams obliquely incident on a semi-infinite turbid medium is extended. The model requires minimal computational resources and offers improved accuracy over more traditional diffusion-theory approximations models when validated against Monte Carlo simulations. The computationally efficient nature of the models lends itself to rapid fitting procedures for inverse problems. The analytical model is used in a nonlinear fitting algorithm to demonstrate the recovery of optical properties using a measurement footprint that is significantly smaller than needed in previous diffusion-regime OIR methods.