Free induction decay

Free induction decay: induced voltage as a function of time

The free induction decay ( FID , from English free induction decay ), the measurement signal which designates nuclear magnetic resonance according to the displacement of the equilibrium magnetization of the nuclear spins in the external magnetic field by means of a resonant high-frequency pulse. This signal is created by the induction of a voltage in the detection coil and decays approximately exponentially . No high-frequency alternating fields are applied during signal readout; therefore the decay is called "free". The measurement of the FID was first described in 1946 by Felix Bloch ; the term free induction decay can be found in 1950 by Erwin Hahn .

The induction signal is caused by the precession of the non-equilibrium magnetization of the nuclear spins in the external magnetic field (according to convention: external magnetic field in the z-direction). The non-equilibrium magnetization can be achieved by short-circuit (“pulsed”) resonant alternating magnetic fields with the Larmor frequency of the nuclear spins. If the magnetization vector has a non-vanishing component in the xy plane (transverse plane), then the precessing nuclear spins induce a corresponding, oscillating voltage in the detection coil surrounding the sample.

The envelope of the amplitude of the induction signal decreases approximately exponentially; the time constant is the transverse relaxation time : ${\displaystyle S(t)}$ ${\displaystyle T_{2}}$

${\displaystyle S(t)=S(0)\exp {\left({\frac {-t}{T_{2}}}\right)}}$.

A significantly faster signal drop is often measured in real samples. This is caused by slightly different Larmor frequencies of the individual nuclear spins, which are caused by field inhomogeneities in the external magnetic field and by local variations in susceptibility within the sample. The different Larmor frequencies lead to a dephasing of the nuclear spins and thus to a faster decay of the transverse magnetization. Therefore, only the time constant can be determined from the exponential curve of the FID signal : ${\displaystyle T_{2}^{*}}$

${\displaystyle {\frac {1}{T_{2}^{*}}}={\frac {1}{T_{2}}}+{\frac {1}{\Delta T}}}$

This is (often also referred to as ) a time constant that is caused by the inhomogeneities of the experimental setup. ${\displaystyle \Delta T}$ ${\displaystyle T_{2}'}$

Individual evidence

1. ^ Felix Bloch: Nuclear Induction . In: Physical Review . tape 70 , no. 7/8 , 1946, pp. 460-474 , doi : 10.1103 / PhysRev.70.460 .
2. ↑ Erwin L. Hahn: Spin Echoes . In: Physical Review . tape 80 , no. 4 , 1950, p. 580-594 , (e.g. BS 583, left column) , doi : 10.1103 / PhysRev.80.580 .
3. ↑ ^{a b} Neil E. Jacobsen: NMR Spectroscopy Explained . John Wiley & Sons, Inc., Hoboken, NJ, USA August 10, 2007, ISBN 978-0-470-17335-0 , doi : 10.1002 / 9780470173350 .
4. ^ Richard G. Brewer, RL Shoemaker: Optical Free Induction Decay . In: American Physical Society (APS) (ed.): Physical Review A . 6, No. 6, December 1, 1972, ISSN 0556-2791 , pp. 2001-2007. doi : 10.1103 / physreva.6.2001 .  
5. ↑ Dominik Weishaupt: How does MRI work? : an introduction to the physics and function of magnetic resonance imaging . Springer, Berlin / New York 2006, ISBN 978-3-540-30067-0 , OCLC 262692885 .