# Time Constant Tool: y = 1-2·exp(-x/400)

A simple exponential recovery may be turned into inversion recovery.

The construction of this recovery curve is simply 1 (representing full recovery,) *minus* two times exponential decay. This represents recovery after a 180° pulse. The 180° pulse *inverts* the spin system (sets all longitudinal magnetisation to -M_{0}, or -1 in a graph already normalised to M_{0}=1). The equation of this curve is, therefore, the equation of inversion recovery:

*S* = 1 - 2·exp(-*TR*/*T*1)

where *S* is signal intensity, *TR* is the repetition time and *T*1 is the longitudinal relaxation time.

The tool now considers the recovery and decay equations discussed thus far with different values of T1 and T2 (the time constants of the curves). Navigate below to the transverse decay section.

Remember, T1, T2 and T2* are time constants.