How Do We Measure It?

This change in frequency depends on many things, but the small shift that is due to the magnetization of $^3$He is the only shift that depends on the direction of the $^3$He spins. Therefore, we can isolate the shift if we can change the direction of the spins while keeping everything constant. We do this by means of frequency sweep AFP (applying an oscillating field that is in resonance with the $^3$He nuclei's precession in an applied magnetic field - this is very similar to how NMR is performed).

We measure the frequency before and after the ``flip''. This isolates everything else and leaves us with (twice) the frequncy shift due to the $^3$He polarization.

$$\nu \uparrow - \nu \downarrow = \nu_{all} - \nu_{all} + \nu_{^3He \uparrow} -\nu_{^3He \downarrow}$$ (3)

But,

$$\nu \uparrow = - \nu \downarrow \mathrm{and} \nu_{^3He \uparrow}= -\nu_{^3He \downarrow}$$

If you have looked over the shoulder of someone performing EPR, Fig.1, will look familiar, but enhanced for this conversation.

Figure 1: EPR Measurement. Example of EPR measurment with features of interest to target expert noted.