Fig. 1

The unnormalized probability density of the field distribution, represented in arbitrary units on the Y-axis, is shown in red for the first measurement with a phase accumulation time \(\tau = \tau _0\), and in green for the measurement with \(\tilde{\tau } = 1.05\tau _0\). The resulting probability density from both measurements, along with its envelope, is shown in purple. It is seen that the phase change of the resulting signal acquires a period of \(\frac{\tau _0}{\tilde{\tau }-\tau _0}\), i.e. \(\frac{1}{1.05-1} {\Delta \Phi } = 20 {\Delta \Phi }\), which effectively expands the measurement range by factor of 20. The arrows at the top of the figure indicate the flux range in which the measurements are unambiguous for a standard measurement with \(\tau = \tau _0\) (red) and for a pair of measurements with times \(\tau = \tau _0\) and \(\tilde{\tau } = 1.05\tau _0\) (purple). The greater the range of the flow of a pair of measurements, the closer the phase selection times for each pair of measurements are to each other.