Roll-to-roll (R2R) processing is a critical technique widely used in flexible electronics, sensors, solar cells, and display devices, where sheets or films are transported between rollers. A major challenge in R2R processing is maintaining the uniform thickness of the material, and irregularities in the back roll are one of the factors that can lead to periodic defects in thickness, significantly degrading product performance, lifespan, and quality. Despite the significance of irregularities during R2R processing, it has received limited attention in the existing literature. This paper proposes a Spatial Fourier Series Model (SFSM) designed to model periodic defects resulting from back roll irregularities under zigzag scanning, thereby addressing their impact on thickness uniformity. The model, leveraging a two-dimensional framework that integrates spatial and periodic signal components, enables the quantification of defects introduced by the back roll and characterizes their spatial distribution. The SFSM’s effectiveness is validated through a case study in an industrial setting, where the model accurately estimates back roll irregularities, demonstrating its reliability and precision. The simplicity and flexibility of the SFSM provide a universal solution for estimating periodic defects, reducing sensor costs, facilitating the design of subsequent controllers, and enhancing R2R manufacturing processes by improving thickness uniformity and product quality.