Pulse Design For Ensemble Bloch Systems

Pulse design is widely applied in the NMR spectroscopy and MRI technique. Now, the MRI machine in all of the hospital around the world uses rotation pulse to do imagining. This thesis started with some background of NMR spectroscopy and some mathematics tools. In this thesis, we provided to ways to do pulse design. The first one was based on Fourier series expansion. By this method, designers can overcome the difficulties to get high resolution NMR spectroscopy due to radio frequency field inhomogeneity and chemical shift. What made this method more practical was that we combined this method with the well-known SLR algorithm. The results of Fourier expansion were wonderful. The second method was based on differential geometry. Since the solution to the Bloch equation is on the Bloch sphere, it has an obvious geometric meaning. The thesis started this method with Frenet frame which is an important concept in differential geometry. At last, we concluded that all the great circles of Bloch sphere are the solutions to Bloch system. This idea was applied to do the pulse design.