## 1 Introduction  
About 80-90% of human cancers develop in the epithelium layer [1] where early signs of the disease appear [2; 3; 4]. The early signs manifest in its optical properties, making it crucial to probe the epithelium in order to diagnose pre-cancer. The epithelium layer is the outermost layer of skin and typically 100-500 \(\upmu\)m thick [2]. To optically probe the changes occurring in the epithelium layer, one needs to collect the photons which have had interactions predominantly in the epithelium layer. Therefore, it becomes important to understand the geometries of collection and delivery of light which govern depth selection. Typical elements of probe geometry include source-detector separation (SDS), and angular orientation of incidence and collection of light. In this context, a common technique for probing various depths is spatially resolved reflectance (SRR). In SRR, light beam incident on the tissue interacts with cellular components and is collected after absorption and scattering inside the medium, at different spatial positions. This technique allows one to probe various depths inside the tissue through the spatially collected light. SRR based technique was first proposed by [PERSON] et al. [5] in 1992 to non-invasively recover the optical parameters of the tissue. Similarly, spatially resolved fluorescence has also been used to recover the optical properties of tissues [6; 7]. For clinical applications, fiber-based SRR probes are desirable. One of the early developments of SRR based fiber optic probe was by [PERSON] et al. [8]. This probe consisted of six detector fibers with the closest detector placed at 2.0 mm from the source. They implemented a diffusion approximatedradiative transport equation (DA-RTE) based model to quantify the optical properties of the epithelial tissue. For an epithelial tissue, diffusion approximation does not hold good close to the source. Therefore, a large variance (\(\sim\)30%) was observed in the recovered optical parameters reported by them. In another study [9], a fiber optic probe was incorporated for SRR collection from a two-layered phantom with a 6 mm thick upper layer. For such a phantom where the thickness of the top layer is significantly larger than the optical mean free path [10], diffuse photons are observed in the superficial layer itself due to large number of scattering events (greater than 100). Therefore, using DA-RTE-based recovery, while 23% error in the optical parameters was obtained for a 2 mm thick superficial layer, the error reduces to 8% for a 10 mm thick superficial layer. In 2011, [PERSON] et al. [4] designed a probe consisting of a source fiber of diameter 200 \(\upmu\)m and 7400 bundled plastic fibers of diameter 20 \(\upmu\)m for SRR collection and extracted the optical parameters of homogeneous phantoms with about 6% and 4.3% errors in absorption and scattering coefficients respectively. Subsequently numerical studies were carried out on two layer models, and the optical parameters of epithelium and stroma were extracted separately. All the fiber optic probes discussed above were oriented perpendicular to the collection surface. These studies are not suitable for recovering the optical properties of a thin epithelium layer (200-500 \(\upmu\)m) because the SRR collected in the perpendicular geometry has a low sensitivity [11; 12] to epithelial perturbations. Moreover, these studies utilized diffusion approximations (DA-RTE) for recovery of the optical parameters which does not hold for epithelial tissue. It is thus crucial to evaluate various feasible probe geometries as well as use the complete RTE as the photon transport model for recovering optical parameters of the epithelial tissue. Several groups across the globe have carried out Monte-Carlo (MC) simulations to evaluate geometries for optimal designing of a probe for epithelial precancers. A detailed study of various fiber-optic probe geometries can be found in [13]. [PERSON] et al. [3] and [PERSON] et al.