Neural distance fields (NDF) have emerged as a powerful tool for solving 3D computer vision and robotics downstream problems. While significant progress has been made in learning NDF from point cloud data obtained through a LiDAR scanner, a crucial aspect that demands attention is the supervision of neural fields during training, as ground-truth NDFs are not available for large-scale outdoor scenes. The existing works have approximated signed distance to guide model learning. The efficiency of the trained model heavily depends on the approximation of the signed distance. To this end, we propose a novel methodology leveraging second-order derivatives of the NDF for a better approximation of the signed distance that leads to improved neural field learning. To assess the efficacy of our methodology, we conducted comparative evaluations against prevalent methods for mapping and localization tasks. Our results demonstrate the superiority of the proposed approach compared to the state-of-the-art techniques, highlighting its potential for advancing the capabilities of neural distance fields in computer vision and graphics applications.