Fig. 2: Phase-incremented (PI) SSFP approach to high-resolution NMR.

a Pulse sequence involving a train of NS signal-averaged scans excited by pulses of flip-angle α spaced by a repetition time TR, and relative phases φ_m incremented as shown over M uninterrupted experiments. b Single-site SSFP response vs relative phase increment φ_m for different flip angles α, assuming f = 0, T₁ = 5 s, T₂ = 2 s, and constant (zero) receiver phase. A similar response would arise from pulses with a constant phase as a function of the site’s offset. c Fourier coefficients {A_k} derived from Eq. [1], describing the SSFP response in (b); notice their rapid drop with increasing α. d β-coefficients derived from a least-square solution of \({\boldsymbol{L}}{\,\cdot \,}{\boldsymbol{\beta }}={\boldsymbol{C}}\), needed to recapitulate the illustrated filter centered at zero. e Actual frequency response resulting from applying the {β_m}-coefficients on M = 50 PI-SSFP experiments upon using NB = M/2 frequency bands, evidencing a deteriorating resolution with increasing flip-angle.