  Supermassive black hole binary systems (SMBHB) are standard sirens -- the
gravitational wave analogue of standard candles -- and if discovered by
gravitational wave detectors, they could be used as precise distance
indicators. Unfortunately, gravitational lensing will randomly magnify SMBHB
signals, seriously degrading any distance measurements. Using a weak lensing
map of the SMBHB line of sight, we can estimate its magnification and thereby
remove some uncertainty in its distance, a procedure we call "delensing." We
find that delensing is significantly improved when galaxy shears are combined
with flexion measurements, which reduce small-scale noise in reconstructed
magnification maps. Under a Gaussian approximation, we estimate that delensing
with a 2D mosaic image from an Extremely Large Telescope (ELT) could reduce
distance errors by about 30-40% for a SMBHB at z=2. Including an additional
wide shear map from a space survey telescope could reduce distance errors by
50%. Such improvement would make SMBHBs considerably more valuable as
cosmological distance probes or as a fully independent check on existing
probes.
