Miniature stochastic nuclear magnetic resonance

A stochastic nuclear magnetic resonance (NMR) system comprising:

• a permanent magnet to apply a bias magnetic field to a sample;
• an active shim to compensate a spatial inhomogeneity in the bias magnetic field applied to the sample by the permanent magnet;
• an electromagnet to apply a stochastically pulsed radio-frequency magnetic field to the sample;
• a detector to sense responses from the sample to the stochastically pulsed radio-frequency magnetic field;
• a processor, operably coupled to the detector, to determine a spin density of the sample based on the responses from the sample;
• and
• a steel shim encasing the permanent magnet and having a size and a shape selected so that the steel shim superimposes with regions of flux density of the bias magnetic field that are higher than 0.4 T.

A stochastic nuclear magnetic resonance (NMR) system, comprising:

• a permanent magnet to apply a bias magnetic field to a sample;
• an active shim to compensate a spatial inhomogeneity in the bias magnetic field applied to the sample by the permanent magnet;
• an electromagnet to apply a stochastically pulsed radio-frequency magnetic field to the sample;
• a detector to sense responses from the sample to the stochastically pulsed radio-frequency magnetic field;
• and
• a processor, operably coupled to the detector, to determine a spin density of the sample based on the responses from the sample,
• wherein the active shim comprises a flexible printed circuit board having traces with shapes based on the spatial inhomogeneity in the bias magnetic field.

A method comprising:

• applying a bias magnetic field to a sample with a permanent magnet;
• compensating a spatial inhomogeneity in the bias magnetic field with an active shim;
• applying a stochastically pulsed radio-frequency magnetic field to the sample;
• detecting responses from the sample to the stochastically pulsed radio-frequency magnetic field;
• and
• determining a spin density of the sample based on the responses from the sample,
• wherein compensating the spatial inhomogeneity comprises compensating for a third-order spherical harmonic spatial inhomogeneity in the bias magnetic field.