Intensity diffraction tomography (IDT) encompasses a class of optical microscopy techniques designed to reconstruct the three-dimensional refractive index (RI) distribution of a sample from a series of two-dimensional intensity-only measurements. However, reconstructing artifact-free RI maps remains a fundamental challenge in IDT owing to the loss of phase information and the missing-cone problem. Neural fields (NF), a deep learning framework increasingly adopted in computer vision and graphics, offer a promising approach by using a neural network to map 3D spatial coordinates to optical properties—such as color, opacity, and refractive index. we propose a method called Intensity Diffraction Tomographic Compressed Imaging based on Residual Neural Fields (IDTCI-RNF). Our approach integrates a compressed sampling mechanism into the IDT imaging model and employs a self-supervised deep learning framework enhanced with 3D Total Variation (3DTV) regularization to preserve edge details. The proposed method enables high-quality reconstruction of 3D refractive index distributions from low-dimensional discrete intensity measurements. Experimental results demonstrate that IDTCI-RNF produces high-contrast, artifact-free RI maps and outperforms existing methods in retaining structural edges and fine details.