Optical metrology alignment and impact on the measurement performance of the LISA Technology Package

Aside from LISA Pathfinder's top-level acceleration requirement, there is a stringent independent requirement for the accuracy of the optical metrology system. In case of a perfectly aligned metrology system (optical bench and test masses) it should rather be independent of residual displacement jitter due to control. However, this ideal case will not be achieved as mechanical tolerances and uncertainties lead to a direct impact of test mass and spacecraft displacement jitter on the optical measurement accuracy. In this paper, we present a strategy how to cover these effects for a systematic requirement breakdown. We use a simplified nonlinear geometrical model for the differential distance measurement of the test masses which is linearized and linked to the equations of motion for both the spacecraft and the two test masses. This leads from test mass relative displacement to a formulation in terms of applied force/torque and thus allows to distinguish the absolute motion of each of the three bodies. It further shows how motions in each degree of freedom couple linearly into the optical measurement via DC misalignments of the laser beam and the test masses. This finally allows for deriving requirements on the alignment accuracy of components and on permittable closed-loop acceleration noise. In the last part a budget for the expected measurement performance is compiled from simulations as no measurement data is available yet.