Related Experiment Video
Updated: May 4, 2026

Quantitative Magnetic Resonance Imaging of Skeletal Muscle Disease
Published on: December 18, 2016
Analytical approximations to inhomogeneously broadened, radiation damped free precession and echo signals
1Department of Chemistry, One Shields Avenue, University of California, Davis, CA 95616, United States.
Abstract:
The Dirac-Frenkel-Maclachlan (DFM) variation of parameters approach to approximately solving the time dependent Schrödinger equation is used to generate free precession and echo signals from the Bloch equations corrected for the effects of radiation damping and inhomogeneous broadening. Following a brief description of how the DFM method can be applied to the non-linear Bloch equations, two figures of merit designed to evaluate how a DFM optimized approximation compares with the exact solution is provided. This framework is used to optimize and evaluate the performance of six trial functions describing inhomogeneously broadened, radiation damped free precession and echo signals. The trial functions are then used to analyze the resolution enhancement and signal attenuation produced by pulse sequences that suppress radiation damping.
Related Concept Videos
NMR Spectrometers: Resolution and Error Correction
Doppler Effect - II
Atomic Nuclei: Larmor Precession Frequency
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
Doppler Effect - I

