Broadband excitation of nuclei spin by refocused feedback

The ability to precisely control the spin states of nuclei in an ensemble is critical for advancing NMR spectroscopy. In this paper, we present a technique referred to as Refocused Feedback to construct RF pulses that enable uniform transitions of spin states across the continuous spectrum of chemical shifts. It is used to achieve uniform broadband excitation of nuclei ensemble. The RF pulses are designed based on strategically selected hypothetical initial and final conditions, with the pulse phase iteratively updated according to the feedback control law. The control sequence is then transformed for applications in real systems. This approach ensures uniform excitation across the continuous range of chemical shifts while digitally constructing the pulse sequence from discrete samples.