New Double-Quantum Filtering Schemes

New double-quantum filtering (DQF) schemes are theoretically developed by reformulating the equations describing the double-quantum (DQ) signal. The equations describing the second- and third-rank DQ signals are simplified by restricting the RF phases as required for DQF. The equations are then factorized into two terms representing the separate contribution to the DQ signal from the RF pulses involved in the preparation and evolution times. This allows analysis of the DQ signal of a particular DQF scheme separately for each of these times in a concise manner. By use of the reformulated equations, the conventional DQF scheme is shown to be only one of four possible DQF schemes. The three new DQF schemes offer some desirable properties over the conventional DQF scheme. In the conventional DQF scheme, the third-rank DQ signal declines rapidly to null as the flip angles of the creation and readout RF pulses deviate from 90° to 54.7° or 125.3°. In addition, the second- and third-rank DQ signals in the conventional DQF scheme are opposite in their polarities, resulting in attenuation of the total DQ signal due to destructive interference between them. In one of three new DQF schemes, the DQ signal does not vanish at 54.7° and 125.3°, but varies smoothly with the same functional dependence on the RF flip angles as the second-rank DQ and triple-quantum signals. Furthermore, in two of the three new DQF schemes, the second- and third-rank DQ signals have the same polarity so that the total DQ signal may be enhanced through constructive interference between them. These features of new DQF schemes have been confirmed experimentally.