Single Frequency Population

To build intuition about field maps, let us imagine a sample at a constant offset frequency from $f_{0}$ . Note that this simplistic representation of the field typically does not occur due to how the susceptibilities of the neighboring regions interact with one another to create the B₀ field offset (see the B₀ inhomogeneity section, but is shown as such for learning purposes. The sample is shown as a circle in Figure 5.8. As the frequency is not at the Larmor frequency, phase accumulation is observed at the different echo times and a phase difference map can be computed. The B₀ field map is then calculated using the echo times. Note that if ΔTE is too long, the phase could make more than a half revolution between the two echo times resulting in an erroneous B₀ field estimation. This is because phase is defined over $-\pi$ to $+\pi$ and the sampled points should respect the Nyquist criteria. In practice, this example field (constant offset) could easily be corrected by adjusting the transmit and receive frequency of the scanner.