Fig. 6.

Bounding the relationship between cross-talk and gain. The exact solution (eq (43)) is derived using the normalised product of a zeroth and first order Bessel function when $B_2$ and $B_1$ are parallel. The gyromagnetic ratio is assumed to be 7 Hz nT⁻¹, the true amplitude of the modulating field is assumed to be 60 nT and the frequency of the field is 923Hz (based on QuSpin OPMs, but the bound is still valid for any OPM utilising modulating fields as long as $\frac{\gamma B_1}{\omega }<1.08$-maximum of the Bessel function product). Left of the origin the approximation is a lower bound on the cross talk induced gain changes while right of the origin it is an upper bound on the cross-talk induced gain changes. Note that these curves deviate further from linearity for positive cross-talk. It should also be noted that for realistic values of cross-talk the ( ±10%) this bound is a reasonable approximation for both positive and negative gain changes.