Constraining first-order pupil locations of rotationally symmetric imaging systems

We derive the constraints to control first-order pupil locations of rotationally symmetric imaging systems with up to four elements. Using the matrix method, we show that a minimum of three elements are necessary to freely specify pupil locations in all case scenarios. Driven by applying the framework to the Laser Interferometer Space Antenna (LISA), we solve the equations for the special case of infinite conjugates of an afocal system. This work lays the foundation for applying the higher-order pupil aberration theory to optical design.