FIG. 1.

(a) Top left: Exploded view of the coils generating the MPI signal. Top right: The assembled coils with a sample in place. (b) Schematic of the apparatus used to generate and measure the signal from the magnetic nanoparticles. The output of the lock-in amplifier was used as the drive frequency for the audio amplifier. The input of the lock-in amplifier was set to each harmonic frequency in succession by the control computer to read the signal at that frequency. A $1\mathrm{s}$ time constant was used so the lock-in amplifier required at least $3\mathrm{s}$ to settle but we allowed at least $5\mathrm{s}$ for the reading to stabilize. The noise effective bandwidth of the lock-in amplifier with the time constant and filter setting used was $0.08\mathrm{Hz}$ $(5∕64\mathrm{Hz})$. The pickup coil was in series with the balancing coil. The position of the balancing coil was far enough from the sample that it detected no measurable signal from the nanoparticles. The position of the balancing coil was adjusted to null the detected signal at the drive frequency and fixed in that position. The resonant drive coil damped the harmonics from the power amplifier.