Reconstruction from multi-view images is a fundamental challenge in computer vision that has been extensively studied over the past decades. Recently, neural radiance fields have driven significant advancements, especially through methods using implicit functions and volume rendering, achieving high levels of accuracy. A core component of these methods is the mapping that transforms an implicit function's output into corresponding volume densities. Despite its critical role, this mapping has received limited attention in existing literature. In this paper, we provide a comprehensive and systematic study of mapping functions, examining their properties and representations. We first outline the necessary conditions for the mapping function and propose a family of functions that meet these criteria, to ensure first-order unbiasedness. We further demonstrate that the mappings employed by NeuS and VolSDF, two representative neural implicit surface techniques, are special cases within this broader family. Building on our theoretical framework, we introduce several new mapping functions and evaluate their effectiveness through numerical experiments. Our approach offers a fresh perspective on this well-established problem, opening avenues for the development of new techniques in the field.