  The detection of the Stochastic Gravitational Wave Background (SGWB) is
essential for understanding black hole populations, especially for supermassive
black hole binaries. The recent promising results from various Pulsar Timing
Array (PTA) collaborations allude to an imminent detection. In this paper, we
investigate the relative astrometric gravitational wave detection method, which
can contribute to SGWB studies in the microhertz range. We consider the Roman
Space Telescope and Gaia as candidates and quantitatively discuss the survey
sensitivity in both the frequency and spatial domains. We emphasize the
importance of survey specific constraints on performance estimates by
considering mean field of view (FoV) signal subtraction and angular power
spectrum binning. We conclude that if the SGWB is at a similar level as in PTA
estimates, both Roman and Gaia have the potential to detect this
frequency-domain power excess. However, both Roman and Gaia are subject to FoV
limitations, and are unlikely to be sensitive to the spatial pattern of the
SGWB.
