Fourier ptychographic microscopy (FPM) needs to realize well-accepted reconstruction by image segmentation and discarding problematic data due to artifacts caused by vignetting. However, the imaging results have long suffered from uneven color blocks and the consequent digital stitching artifacts, failing to bring satisfying experiences to researchers and users over the past decade since the invention of FPM. In fact, the fundamental reason for vignetting artifacts lies in that the acquired data does not match the adopted linear-space-invariant (LSI) forward model, i.e., the actual object function is modulated by a quadratic phase factor during data acquisition, which has been neglected in the advancement of FPM. In this Letter, we rederive a linear-space-variant (LSV) model for FPM and design the corresponding loss function for FPM, termed LSV-FPM. Utilizing LSV-FPM for optimization enables the efficient removal of wrinkle artifacts caused by vignetting in the reconstruction results, without the need of segmenting or discarding images. The effectiveness of LSV-FPM is validated through data acquired in both 4f and finite conjugate single-lens systems. © 2024 Optica Publishing Group (formerly OSA). All rights reserved.