  With a hybrid MEG--MRI device that uses the same sensors for both modalities,
the co-registration of MRI and MEG data can be replaced by an automatic
calibration step. Based on the highly accurate signal model of ultra-low-field
(ULF) MRI, we introduce a calibration method that eliminates the error sources
of traditional co-registration. The signal model includes complex sensitivity
profiles of the superconducting pickup coils. In ULF MRI, the profiles are
independent of the sample and therefore well-defined. In the most basic form,
the spatial information of the profiles, captured in parallel ULF-MR
acquisitions, is used to find the exact coordinate transformation required. We
assessed our calibration method by simulations assuming a helmet-shaped
pickup-coil-array geometry. Using a carefully constructed objective function
and sufficient approximations, even with low-SNR images, sub-voxel and
sub-millimeter calibration accuracy was achieved. After the calibration,
distortion-free MRI and high spatial accuracy for MEG source localization can
be achieved. For an accurate sensor-array geometry, the co-registration and
associated errors are eliminated, and the positional error can be reduced to a
negligible level.
