Evaluation of the tilt to length coefficient induced by wavefront error for the LISA interferometric test bench

Space-based gravitational wave detectors are potentially limited by a noise source arising from the coupling between interferometric beam jitter and the interferometer’s length readout. A significant optical property responsible for this coupling is the wavefront error, defined as distortions in the phase profile of the laser beam. In this paper, we investigate this tilt to length (TTL) coupling induced by wavefront errors by developing two independent simulation tools that employ different computational methods to quantify the coupling amplitude. We analyze the characteristics of distortion-induced TTL coupling and present the relationship between the magnitude of wavefront distortions—expressed through a Zernike polynomial decomposition—and the resulting coupling amplitude. These results provide critical specifications for the design of an optical test bench intended to experimentally verify the performance of the LISA instrument on ground.