Publication

Optimization of shaped selective pulses for NMR using a quaternion description of their overall propagators

Geoffrey Bodenhausen
1992
Journal Articles

Abstract

New amplitude-modulated radio-frequency pulses are proposed that allow one to achieve selective excitation, de-excitation, inversion, and refocusing of spin-1/2 systems in NMR. The rotation angles and axes are well defined over a chosen bandwidth, regardless of the initial conditions. These universal pulses are derived from the idea of Gaussian pulse cascades, but their design is guided by new principles. The amplitude profiles are optimized by calcg. the quaternions representing the propagators of the overall rotations as a function of offset. This procedure provides a more general approach to pulse design than the usual optimization of the response to some initial condition. [on SciFinder (R)]

Official source

https://infoscience.epfl.ch/entities/publication/4532fc32-2407-4f73-95ef-185dac675700

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Geoffrey Bodenhausen
1992
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/4532fc32-2407-4f73-95ef-185dac675700

About this result

Related concepts (32)

Quaternions and spatial rotation

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis.

Quaternion

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative. Quaternions are generally represented in the form where a, b, c, and d are real numbers; and 1, i, j, and k are the basis vectors or basis elements.

Rotation

Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.

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Optimization of shaped selective pulses for NMR using a quaternion description of their overall propagators

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