This paper introduces a novel approach to designing Frequency Selective Surfaces (FSS) for dichroic mirrors in Deep Space antennas. Unlike conventional periodic FSS designs, the proposed method employs a quasi-periodic structure, with each unit cell tailored to its specific local incidence angle. This approach aims to compensate for losses induced by extreme inci-dence angles, enhancing the overall performance of the dichroic mirror. The unit cell chosen for this study exhibits a range of design degrees of freedom, making it well-suited for this novel approach. Additionally, this unit cell offers advantages in terms of broad bandwidth behavior and 3D-printing compatibility, addressing key requirements for Deep Space antenna applications. The paper outlines the methodology for constructing the quasi-periodic structure and presents preliminary performance metrics, demonstrating the potential for improved performance in Deep Space antenna systems. Future work will focus on implementing the proposed design methodology and further optimizing the quasi-periodic surface.