  The absolute accuracy of the estimated parameters of gravitational wave
sources will be fundamentally limited by the calibration uncertainties of the
detectors in upcoming observation runs with the increased number of source
statistics. Photon calibrators have so far been the primary tools for absolute
calibration of test-mass displacement, relying on measurement of the photon
pressure. The current technological limit of the absolute calibration
uncertainty for gravitational-wave amplitudes is limited to a few percent, due
to the uncertainty in the laser power-standard maintained by the metrology
institutes. To reduce this uncertainty, this article proposes a novel
calibration method that combines a photon calibrator and a gravity field
calibrator. The gravity field calibrator achieves modulation of the
displacement of the test mass by generating a gravity gradient. In previous
studies, uncertainty in the distance between the test mass and the gravity
field calibrator has proven a serious source of systematic error. To suppress
this uncertainty, we propose a novel method that uses a combination of
quadrupole and hexapole mass distributions in the gravity field calibrator. We
estimate the absolute uncertainty associated with method to be as low as
0.17~%, which is ten times less than that of previous methods.
