Traditional object detection models often lose the detailed outline information of the object. To address this problem, we propose the Fourier Series Object Detection (FSD). It encodes the object's outline closed curve into two one-dimensional periodic Fourier series. The Fourier Series Model (FSM) is constructed to regress the Fourier series for each object in the image. Thus, during inference, the detailed outline information of each object can be retrieved. We introduce Rolling Optimization Matching for Fourier loss to ensure that the model's learning process is not affected by the sequence of the starting points of the labeled contour points, speeding up the training process. The FSM demonstrates improved feature extraction and descriptive capabilities for non-rectangular or elongated object regions. The model achieves AP50 = 73.3% on the DOTA 1.5 dataset, which surpasses the state-of-the-art (SOTA) method by 6.44% at 66.86%. On the UCAS dataset, the model achieves AP50 = 97.25%, also surpassing the performance indicators of the SOTA methods. Furthermore, we introduce the object's Fourier power spectrum to describe outline features and the Fourier vector to indicate its direction. This enhances the scene semantic representation of the object detection model and paves a new pathway for the evolution of object detection methodologies.