Methods of generating pulses for selectively exciting frequencies

Abstract

Methods of constructing pulse sequences to selectively excite frequency bands in NMR imaging, spectroscopic and optical systems are disclosed. In preferred embodiments, selective .pi./2, .pi., and refocusing hard and soft pulses are constructed for perturbing the spins of the system. In NMR imaging, for example, the desired magnetization is written as an (N+1)th order Fourier series in .omega.t, where .omega. is the off-resonance frequency. In addition, if all pulses have the same phase, then the z magnetization is known to be symmetric in frequency, and the resulting hard pulse sequence can be written as an Nth order Fourier cosine series. Given this Fourier series representing the desired z magnetization, an inversion may be used to determine the hard pulse sequence of N pulses which will actually yield the desired response. In particular, if one starts with a specification of a desired z magnetization not as a Fourier series in .omega.t, but rather as having certain desired values over several frequency ranges, the techniques of finite impulse response filters may be applied to yield the desired Fourier series representing the z and xy magnetizations. The optimal hard pulse sequence which yields that Fourier series may then be mathematically determined and applied to the system to yield the desired response. In accordance with another feature of the invention, the synthesized hard pulse sequence may be used to generate a soft pulse which has a frequency response over a broad range which is the same as that of the synthesized hard pulse sequence. The methods of the invention thus allow for the generation of optimal pulse sequences without the use of linear Fourier transform approximations to intrinsically nonlinear systems.