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Monday, November 30, 2009

B1 Homogeneity

High resolution NMR spectroscopists spend a great deal of time shimming the magnet to ensure that the static magnetic field, Bo is homogeneous. This is because the transverse magnetization precesses about Bo. The Larmor equation implies that if there is a distribution in Bo across the volume of the sample, there will be a distribution of frequencies for each resonance line (i.e. the NMR resonances will be broad). The more homogeneous Bo across the sample volume, the sharper the NMR lines.

There is another field we must consider when doing NMR experiments - the magnetic field due to the RF pulse in the rotating frame of reference. In the rotating frame of reference, during the application of a pulse, an "on resonance" NMR line experiences an effective field, Beff equal to the magnetic field due to the pulse, B1. B1 is a static magnetic field in the rotating frame of reference. Due to the finite dimensions of the coil in the probe with respect to the sample, the B1 field will not be homogeneous across the entire volume of the sample. For example, a 90° pulse for the sample in the center of the coil will not be equal to a 90° pulse for the sample near the edges of the coil. While an x phased pulse is being applied to an equilibrium magnetization vector, the magnetization will precess about the x' axis in the rotating frame in the z-y' plane exactly like transverse magnetization precesses about the z axis in the x-y plane. While the magnetization precesses in the z-y' plane during the pulse, it is affected by the inhomogeneity in the B1 field. The inhomogeneity of the B1 field can be measured by doing a simple pulse calibration, applying longer and longer pulses well beyond that needed for a 360° pulse. After the pulse, the magnetization vectors precess again about Bo, and can be measured. The magnitude of the magnetization for a 90°, (90° + 360°), (90° + 720°) ..... etc. pulse will depend on the B1 homogeneity. An example of this is shown in the figure below. The figure shows a simple 1H pulse calibration for the decoupler coil of a 5 mm broadband NMR probe. The B1 homogeneity is expressed as the ratio of intensity for an 810° pulse compared to that from a 90° pulse. In this case the B1 homogeneity is 0.43. Much higher B1 homogeneity would be expected for an inverse detection probe.

2 comments:

Julio said...

Hello Glen,
Thank you for your blog. I have been reading it for years now and it has always been very useful.
Regarding this post, why did you compare 810 deg with 90 deg, and not 450 (90+360) with 90 deg?

I would assume if there is a perfectly homogeneous B1 field (and no relaxation) the magnetization should be the same at 450 and 90 degrees.

Regards

Julio Cardenas
The University of Arizona
Tucson, AZ. USA

Glenn Facey said...

Julio,

Thank you for the question. I chose to look at the ratio of intensity of an 810 degree pulse to that of a 90 degree pulse as this is the convention usually used by NMR probe manufacturers to evaluate the RF inhomogeneity of the coil.

You are correct to say that in the absence of relaxation and B1 inhomogeneity one would expect that the intensity of the signal using a 450 degree pulse (and indeed an 810 degree pulse) would be the same as that of a 90 degree pulse.

Glenn