Theoretical description of depth pulse sequences, on and off resonance, including improvements and extensions thereof

A general mathematical description of depth pulse sequences in terms of rotation matrices permits a single matrix, known as a cycle matrix, to be written down for each phase-cycled pulse in the overall sequence, such that the result for the total phase-cycled sequence is the product of the individual cycle matrices. It is straightforward to include the effect of the tilted rf axis off resonance and obtain exact solutions. The two types of phase-cycled pulse used in a depth pulse scheme are 2 theta [+/- x] and 2 theta [+/- x, +/- y] and for the general off-resonance case, four of the off-diagonal elements in the 2 theta [+/- x] cycle matrix, and all of the off-diagonal elements in the 2 theta [+/- x, +/- y] cycle matrix, are zero. These simplifications enable important improvements of depth pulse schemes for the elimination of high-flux signals, the reduction of signals from sample regions experiencing pulse angles differing from 90 degrees, and the avoidance of deleterious off-resonance effects such as the production of dispersion signals. In all cases, the dependence of signal intensity off resonance can be easily and exactly calculated. There are important applications in in vivo spectroscopy.