This process of heterodyne detection can also be thought of in terms of using a rotating reference frame. Instead of observing the precession of the transverse magnetization in a laboratory reference frame, a reference frame that rotates with a frequency m0 about the B0 direction can be used. Seen from this rotating reference frame, the transverse magnetization rotates at a frequency Am. If the rotation frequency is exactly matched to the Larmor frequency (i.e., m0 = rnL), then the (transverse) magnetization is stationary, and the static magnetic field B0 is effectively zero in this rotating frame of reference.

The concept of a rotating reference frame is quite powerful to describe the application of an oscillating magnetic field Bj. In the rotating frame, a magnetic field rotating at a frequency m0 will appear stationary. The effect of a radiofrequency pulse can be described in the rotating frame as a precession of the magnetization vector about the magnetic field that Bt is stationary.

2.4. Transverse Magnetization Decay: T2 and T2*

The loss of phase coherence of the transverse magnetization, characterized by the decay time T2, is slowest if the magnetic moments are embedded in a homogeneous sample and subjected to a homogeneous magnetic field. In the presence of field inhomogeneities and other factors that cause a spread of Larmor frequencies, the transverse magnetization decay is further shortened. To distinguish this latter situation, a time constant T2* is introduced that is characteristic of the exponential decay of the transverse magnetization in "heterogeneous" environments. It follows that T2* is always shorter than T2.

2.5. Longitudinal Magnetization Recovery: T1

After any radiofrequency excitation that tips the magnetization vectors away from the direction of the applied static magnetic field B0, the nuclear spins will over time realign themselves with the magnetic field to reach the same alignment as before the radiofrequency excitation. This process requires the exchange of energy between atomic nuclei and their environments. The recovery of the longitudinal magnetization component Mz in many cases follows an exponential function

where M0 denotes the equilibrium magnetization before any radiofrequency pulses are applied, and ^ gives the degree of inversion of the transverse magnetization, with ^ = J for a 90° pulse and ^ = 2 for a 180° pulse.

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