## 1 Introduction
[12] reported significant improvements by using oblique fibers, observing higher sensitivity to changes in the epithelium layer during measurements. [PERSON] et al. [3] used an inverse MC scheme to obtain the optical properties of the top layer by a 45\({}^{\circ}\) angled probe, and bottom layer optical properties with a flat tipped probe. However, the geometries for angled probes that they proposed are not amenable for internal organs due to critical issues with fibers while bending to a smaller radius [14]. [PERSON] et al. [11] in 2012, carried out a MC based comparative numerical study for various probe geometries. They reported that the perpendicular probe was more sensitive to the changes in stromal optical properties. However, the changes in epithelial scattering were reflected more prominently by the parallel-oblique fiber probe. Such a probe is suitable for epithelial precancer investigation and also clinically amenable. In 2014, [PERSON] et al. [15] measured SRR spectra using perpendicular as well as a 45\({}^{\circ}\) leveled optical fiber bundle. They used an inverse MC scheme to recover the reduced scattering coefficients of both the layers and the total hemoglobin (Hb) concentration of the bottom layer. It was reported that the data procured by the beveled probe recovered the reduced scattering coefficient of the top layer more accurately as compared to the perpendicular probe. The spot size of incident light on the tissue was 350 \(\upmu\)m, which limited the minimum SDS to 0.4 mm in the oblique probe. Reducing the minimum SDS further can recover the properties of the superficial layer even more accurately. There have been in-vivo studies to extract the optical properties of cervical tissue based on SRR using fiber optic probes [16; 17]. [PERSON] et al. [16] and [PERSON] et al. [17] could not extract optical properties of the superficial layer due to limitations of their probe geometries. To the best of our knowledge, the existing probes for epithelial cancer diagnosis have not been able to provide accurate optical properties of epithelium layer and its variation with the progression of pre-cancer. Hence, there is a need to develop an SRR based probe to acquire signals majorly from epithelium, aiding early-stage diagnosis of epithelium cancer. Choice of appropriate inverse scheme is crucial for accurate recovery of the optical parameters. These schemes typically thrive on the accuracy of the forward solver that generates the synthetic SRR at desired detector locations. The analytical solutions to diffusion approximated radiative transport equation (DA-RTE) have been used for estimation of optical parameters of diffusive media [8; 9; 18], for large SDSs. However, for small SDSs as well as for low-scattering media, photons get collected at the detectors before they are completely diffused, and hence it is erroneous to employ DA-RTE to model reflectance for such cases [19]. An MC method is a numerical equivalent to solve the RTE which is the analytical model for simulating accurate light transport in tissue. Therefore a variety of MC based reconstruction schemes such as empirical model [20; 21], MC fast and flexible inverse model [22; 23], perturbation MC model [24], scalable MC model [4; 22; 23; 25], MC look-up table (MC-LUT) based schemes [26; 27; 28; 29; 30], artificial neural network method [31] have been extensively used for estimation of optical properties of turbid media. Based on these studies, we have focused on: (1) a MC-based detailed comparative study of the efficacy of common probe-geometries for epithelial precancer diagnosis, and (2) accurate recovery of optical parameters of the top layer from SRR data collected by a novel fiber-optic probe using MC look-up table (MC-LUT) based inversion. This manuscript is organized as follows: Section 2 provides a brief theory of light propagation in turbid media and discusses the basic inverse problems involved. In Section 3 we study the efficacy of various probe geometries for epithelial precancer diagnosis.