Neural Radiance Fields (NeRFs) have transformed image-based 3D reconstruction through differentiable volumetric rendering, enabling high-quality novel view synthesis. However, their implicit volumetric nature is incompatible with the polygonal meshes needed for real-time graphics and simulation applications. The proposed model defines the volume density function as the Secant Hyperbolic Function applied to a signed distance function (SDF) representation. To enable accurate surface representation, the sharpness of the density transition is modulated by a spatially-varying parameter \(\beta (x)\) , which is learned through a multi-layer perceptron (MLP). Experimental results on the NeRF-Synthetic and Mip-NeRF 360 datasets demonstrate improved surface reconstruction accuracy and visual quality compared to NeRF2Mesh, highlighting the effectiveness of the proposed enhancements for efficient and high-fidelity real-time scene reconstruction.