Imaging with pure phase encoding

The different information obtainable from a chemical-shift weight and a relaxation-parameter image is illusiraled in Fig. 8.3,2 Pra3] In covulcanization of different rubber sheets, for example, sheets from SBR and NR, an interface may arise depending on the materials and the conditions of vulcanization (Fig. 8.3.2(a)). A sufficiently long acquisition delay t without chemical-shift refocusing introduces the chemical-shift 

In the high-field approximation the space-dependent thermodynamic-equilibrium density matrix po(r) is proportional to l fr) (cf. eqn (2.2.58)). A 90° pulse converts this density matrix into p (0+, r) oc U(r) = [l+(r) -I- l (r)] /2, where U is the x-component of the spin operator, 1+ = 1 + il -, and L = 1 — il. In the subsequent free-precession period the density matrix evolves for a time t under the spin Hamiltonian Hx(r) (cf. eqn (3.1.1)) and under the influence of the applied gradient, which introduces a phase evolution given by kr = —yGrti, where k is the experimental variable, 

The different spin interactions k active during the evolution period can be the chemical shielding, the dipolar, and the quadnipolar interactions. All of these interactions commute with the 1 operator. 

For given values of field gradient and evolution time, i.e. for a given k vector, the total NMR signal s k) is determined by the integral of the density matrix over the sample volume, 

Equation (8.3.2) is the quantum-mechanical formulation of (5.4.8). The prefactor —i is missing in (8.3.2), because the equation has been derived from the pulse response and not from a perturbation expansion (cf. Section 5.4.1). The similarity of both equations becomes more obvious by writing (8.3.2) in Liouville space, where the density matrix 

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