Analysis of the higher-order echoes in SSFP

In the steady-state free precession (SSFP) with an applied linear gradient, the transverse magnetizations are periodically distributed. Fourier analysis of this periodic distribution leads to the understanding of many interesting phenomena in SSFP. It is found that there are many other higher-order echoes in SSFP in addition to the previously known echoes. By deriving general description of the transverse magnetization of SSFP and by expanding the echo time independent term with Fourier series, the higher-order echoes including the two previously known FISP and CE-FAST are understood and explained. These higher-order echoes are studied in detail by both computer simulation and experiments and their results are reported.