Relighting a single low-light image is a crucial and challenging task. Previous works primarily focused on brightness enhancement but neglected the differences in light and shadow variations, which leads to unsatisfactory results. Herein, an illumination field reconstruction (IFR) algorithm is proposed to address this issue by leveraging physical mechanism guidance, physical-based supervision, and data-based modeling. Firstly, we derived the Illumination field modulation equation as a physical prior to guide the network design. Next, we constructed a physical-based dataset consisting of image sequences with diverse illumination levels as supervision. Finally, we proposed the IFR neural network (IFRNet) to model the relighting progress and reconstruct photorealistic images. Extensive experiments demonstrate the effectiveness of our method on both simulated and real-world datasets, showing its generalization ability in real-world scenarios, even training solely from simulation.