## 4 Applications of the Transient Regime  
### Fast and Simultaneous T\({}_{1}\) and T\({}_{2}\) Measurements  
In 1977, [PERSON] and [PERSON] [30] proposed the use of the transient time T* (Equation (4)) of the SSFP signal to measure T\({}_{1}\) and T\({}_{2}\) using two experiments. In the first experiment, the T\({}_{1}\)/T\({}_{2}\) ratio was determined by measuring the amplitude of the SSFP signals as a function of the flip angle \(\theta\). The second experiment involved measuring the transient time T* at the optimum flip angle, yielding the T\({}_{1}\) + T\({}_{2}\) value. These results were used for the determination of both relaxation times. Exploring the same dependence on the CWFP regime, [PERSON] et al. [9] demonstrated that it is not necessary to use these two experiments to measure T\({}_{1}\) and T\({}_{2}\) when \(\theta\) = 90\({}^{\circ}\). They proposed a fast method to measure both relaxation times in a single CWFP experiment using the evolution of the magnitude of the CWFP from the first pulse to the steady state (Figure 8A). In this figure, the initial  
Figure 7: Amplitude of CWFP signal of the irradiated methylates samples with phenyl-propanedione (PPD, a), monoacylphosphine oxide (MAPO, b) and canphorquinone (c) photoinitiators. part of the signal (dark grey region) is characterized by a strong oscillation of the amplitude following odd and even pulses [9]. The amplitude of this signal decays with T\({}_{2}\)*. When the oscillation ends, the signal was named a quasi-stationary state (QSS) (transition between dark and light grays regions). From the QSS point, the signal decays slowly with a time constant T* (light grey region), given by Equation (5), to reach the constant steady state amplitude \(\mid\)M\({}_{\rm ss}\mid\) (white region). For a CP-CWFP signal, the first oscillating signal (Figure 8B, dark grey) decays to a minimum signal (QSS). From this point, the signal also increases with T* (light grey) and reaches a constant steady state amplitude \(\mid\)M\({}_{\rm ss}\mid\) (white region) [27]. For \(\theta\) = 90\({}^{\circ}\) and \(\Phi\) = \((2n+1)\pi\), the transient time T* for the CWFP and CP-CWFP sequences in Equation (4) is only dependent on the relaxation times according to Equation (5):  
\[T^{*}=\frac{2T_{1}T_{2}}{T_{1}+T_{2}} \tag{5}\]  
A simple rearrangement of Equations (3) and (5), results in:  
\[\frac{T_{1}}{T_{2}}=\frac{M_{0}-\left|M_{\rm ss}\right|}{\left|M_{\rm ss}\right|} \tag{6}\]  
or the proper relaxations times:  
\[T_{1}=\frac{T^{*}/2}{\left|M_{\rm ss}\right|/M_{0}}\ \text{and}\ T_{2}=\frac{T^{*}/2}{ 1-\left|M_{\rm ss}\right|/M_{0}} \tag{7}\]  
Therefore, both relaxation times can be calculated in a single-scan CWFP or CP-CWFP experiment using the magnitude of M\({}_{0}\) (intensity after the first pulse), magnitude at steady state \(\mid\)M\({}_{\rm ss}\mid\), and T*, using Equation (7). The T* value is obtained by exponential fitting of the T* decay (light grey region in Figure 8). The obtained relaxation time values are equivalent to those obtained by inversion recovery (T1) and CPMG (T2) pulse sequences [37; 38]. The major source of error in CWFP and CP-CWFP experiments is the \(\mid\)M\({}_{0}\mid\) value, which is strongly dependent on the spectrometer dead time. Normally, the dead time has to be shorter than 10 \(\upmu\)s.  
The difference between CWFP and CP-CWFP sequences is the dynamic range (DR) of the T* signal that depends on the T\({}_{1}\)/T\({}_{2}\) ratio. Figure 9 provides a comparison of the CWFP (Figure 9A) and CP-CWFP (Figure 9B) transient regimes for samples with T\({}_{1}\)\(\approx\) T\({}_{2}\) and T\({}_{1}\)\(>>\) T\({}_{2}\). The T\({}_{1}\)\(\approx\) T\({}_{2}\) and T  
Figure 8: Numerically simulated signals showing the evolution of the **(A)** CWFP and **(B)** CP-CWFP signal magnitudes from the first pulse to the stationary state (\(\mid\)M\({}_{\rm ss}\mid\)) using T\({}_{1}\) = 150 ms, T\({}_{2}\) = 50 ms, T\({}_{\rm P}\) = 0.3 ms, and T\({}_{2}\)* = 20 ms.