Amplitude-phase inhomogeneity

It must be stressed that the spin-echo sequence is applied only during the detection period and its unique purpose is to estimate the signal amplitude (in a sense, it is a replacement for the simple 90° pulse). Consequently, in an arrayed multi-block experiment whose purpose is to measure Ti(Br), only the X value is varied, while the delays 5 and 8 are kept constant in order to make sure that no T2(Ba) effects leak into the experimental relaxation curves. Moreover, to avoid contamination of the echo by FID residues due to imprecise settings of RF pulses and to Bi inhomogeneity, proper phase cycling is highly recommended. 

E0exp( — k" x) and H0exp( —k" x) are the amplitudes of the electric and magnetic waves, and = k x — ut is the phase of the waves. An equation of the form K x = constant, where K is any real vector, defines a plane surface the normal to which is K. Therefore, k is perpendicular to the surfaces of constant phase, and k" is perpendicular to the surfaces of constant amplitude. If k and k" are parallel, which includes the case k" = 0, these surfaces coincide and the waves are said to be homogeneous if k and k" are not parallel, the waves are said to be inhomogeneous. For example, waves propagating in a vacuum are homogeneous. 

Here <( t ) f(t")> is the autocorrelation function of the electromagnetic field. For the case of excitation by a conventional light source, where the amplitudes and the phases of the field are subject to random fluctuations, the field autocorrelation function differs from zero for time intervals shorter than the reciprocal width of the exciting source. In the limit 8v A, that is when the spectral width, 8v, of the source exceeds the inhomogenously broadened line width, the field autocorrelation function can be represented as a delta function... 

Lorentzian rf inhomogeneity, (—) ramped DCP with ideal rf, and (— ramped DCP with 5% Lorentzian rf inhomogeneity, (b) x- (solid line) and y-phase (dotted line) rf amplitudes for the 2.4 ms optimal control sequence marked by an arrow in (a). Upper and lower panels correspond to the N and C rf channels, respectively, (c) Experimental DCP (left) and DCP (the sequence in b) - spectra of glycine. Reproduced from Ref. 70 with permission. 

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