Sigma Vector Calculations in Nodal Aberration Theory (NAT) and its Experimental Investigations

Nodal aberration theory investigates the aberrational behavior of misaligned optical systems. K. Thompson's novel approach to the sigma vector, the key concept for NAT, paved the way for the widespread application of the theory. This study details Thompson's real-ray-based method and its application in any two-mirror telescope. The method is implemented in a simulation of a Cassegrain telescope, and the sigma vector contributions are computed. For validation, the same misalignments with the simulation are applied to the high-precision Cassegrain telescope, and the sigma vector contributions are computed experimentally. The results of both cases are compared and found compatible.