Derivation of stability requirements and control effort analysis for space nulling interferometers

During the current preliminary design phase of NASA's Terrestrial Planet Finder mission, optical performance requirements need to be translated into dynamic requirements such as aperture shear (AS), optical pathlength difference (OPD), and differential aperture tilt (AT). This paper presents a methodology that specifies allowable variances on AS, OPD, and AT in order to achieve the level of null depth required by the TPF mission. These dynamic requirements can then be used in a trade study to compare various nulling interferometer configurations. They also reveal the relationship between important design parameters and the optical performance. Another design tool introduced in this paper is the control effort analysis. It assesses the control effort required for different interferometer architectures based on the derived dynamic requirements. The paper describes both the open-loop stability and closed-loop control effort analyses in detail and illustrates the effectiveness of these tools for various TPF architectures.