The Laser Interferometer Space Antenna (LISA) will open the signal-rich 100 μHz to 1 Hz gravitational wave window. LISA is expected to be limited by acceleration noise in the low frequency range and noise associated with the optical measurement system above a few mHz. Of the latter, apparent length changes due to spacecraft angular jitter are among the most critical contributors. One of the coupling mechanisms is via wavefront error in the transmitted beam. Utilizing a Zernike polynomial decomposition of such wavefront error, we introduce and explore the validity of extremely fast best fit polynomial expansion based noise recreation tools that provide a clear picture for which transmit beam perturbations couple most strongly with spacecraft jitter into LISA noise.

Mode expansion methods (MEMs) have been used in both the scientific and commercial world to accurately propagate monochromatic light fields. Compared to classical methods for light propagation from scalar diffraction theory, it is often less costly and much more easily implemented into optical chains. We provide an analytic expression for the overlap between incoming and outgoing Hermite Gauss (HG) TEM modes over an aperture with potential wavefront error represented by Zernike terms for the purpose of propagating light through apertures. We show agreement between our results and those of prior studies of the topic, as well as an application of this method to an ongoing interferometry mission.

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The LIGO-Virgo-Kagra (LVK) collaboration has detected gravitational waves from 90 Compact Binary Coalescences. In addition to fortifying the linearized theory of General Relativity (GR), the statistical ensemble of detections also provides prospects of detecting nonlinear effects predicted by GR, one such prediction being the nonlinear gravitational memory effect. For detected stellar and intermediate mass compact binaries, the induced strain from the memory effect is one or two orders below the detector noise background. Additionally, since most of the energy is radiated at merger the strain induced by the memory effect resembles a step function at the merger time. These facts motivate the idea of coherently stacking up data streams from recorded GW events at these merger times so that the cumulative memory strain is detected with a sufficient SNR. GW detectors essentially record the integrated strain response at time scales of the round trip light travel time, making future space-based long arm interferometers like LISA ideal for detecting the memory effect at low frequencies. In this paper, we propose a method that uses the event catalog of ground-based detectors and searches for corresponding memory strains in the LISA data stream. Given LVK's O3 science run catalog, we use scaling arguments and assumptions on the source population models to estimate the run time required for LISA to accumulate a memory SNR of 5, using triggers from current and future ground-based detectors. Finally, we extend these calculations for using beyond LISA missions like ALIA, AMIGO, and Folkner to detect the gravitational memory effect. The results for LISA indicate a possible detection of the memory effect within the 10 year LISA mission lifetime and the corresponding results for beyond LISA missions are even more promising.