Fig. 3

Simulation-based accuracy and precision analysis of relaxation times measurements in different spin ensemble states. The T₁ relaxation times in a and the T₂ relaxation time in b result from the same fit of a single simulated data set. The hybrid-state experiment is comparatively robust with respect to inhomogeneous broadening (here modeled by a Gaussian distribution of Larmor frequencies), as evident by the mean values staying within a 5% error margin (gray areas) up to a full width at half maximum (FWHM) of about 60 Hz. On the contrary, the transient state exhibits a substantial bias with increasing broadening. The steady-state experiment is robust to inhomogeneous broadening when avoiding \(T_2^ \ast\)-decay in the spoiled gradient-echo segment (transparent marks). In the presence of \(T_2^ \ast\)-decay, however, it also shows some systematic errors. This issue can be avoided at the cost of signal-to-noise ratio efficiency⁵³. Even when using the SNR-optimal steady-state approach, the observed noise (the error bars correspond to the standard deviation) is considerably higher compared to the hybrid state. Further, the observed noise approximates the limit set by the Cramér–Rao bound well (the reference shown at the far left is the ground truth with the Cramér–Rao bound as error bars)