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Related Concept Videos

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

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A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
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Double Resonance Techniques: Overview01:12

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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Two-Dimensional (2D) NMR: Overview01:12

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The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
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Updated: Apr 3, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Consistent Quadratic Phase Formation in 3D Fast Spin Echo Using Frequency-Modulated RF Pulses.

Naoharu Kobayashi1, Michael Garwood1

  • 1Center for Magnetic Resonance Research, Department of Radiology, University of Minnesota, Minneapolis, Minnesota, USA.

Magnetic Resonance in Medicine
|April 2, 2026
PubMed
Summary
This summary is machine-generated.

Frequency-modulated pulses enable Magnetic Resonance Imaging (MRI) in challenging magnetic fields. This study introduces a method for consistent quadratic phase in 3D Fast Spin Echo MRI, improving image quality.

Keywords:
fast spin echofrequency‐modulated RF pulseinhomogeneous field MRIquadratic phase

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Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Pulse Sequence Design
  • Radiofrequency (RF) Engineering

Background:

  • Frequency-modulated (FM) RF pulses offer broadband excitation with low peak power, crucial for MRI in inhomogeneous magnetic fields.
  • The quadratic phase inherent in FM pulses complicates their use in Fast Spin Echo (FSE) due to differing spatial phase profiles in even and odd echoes.

Purpose of the Study:

  • To formulate the condition for generating a consistent quadratic phase in both echo components of 3D FSE using FM pulses.
  • To enable the use of FM pulses in the non-adiabatic regime for 3D FSE sequences.

Main Methods:

  • Formulated the consistent quadratic phase condition using Cayley-Klein parameters.
  • Compensated B1+-dependent phase in FM excitation by adjusting initial pulse phases.
  • Simulated 3D FM-FSE using extended phase graph (EPG) and validated with 3T experimental data.
  • Performed in vivo brain imaging with T1- and T2-weighted contrasts.

Main Results:

  • Achieved consistent quadratic phase in all echoes in 3D FM-FSE simulations under the formulated condition.
  • EPG simulations showed good agreement with experimental results.
  • B1+-dependent phase adjustment improved refocused echo magnitude profiles.
  • Demonstrated successful in vivo brain imaging with good T1- and T2-contrasts despite field inhomogeneity.

Conclusions:

  • Consistent quadratic phase in 3D FM-FSE allows FM pulse application in the non-adiabatic regime.
  • 3D FM-FSE is a promising pulse sequence for MRI applications in inhomogeneous magnetic fields.