Articles | Volume 7, issue 1
https://doi.org/10.5194/mr-7-1-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/mr-7-1-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Feb 2026
Research article |
| 05 Feb 2026
| 05 Feb 2026
Robust bilinear rotations II
Yannik T. Woordes
Institute of Organic Chemistry and Institute for Biological Interfaces 4 – Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131 Karlsruhe, Germany
Institute of Organic Chemistry and Institute for Biological Interfaces 4 – Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131 Karlsruhe, Germany
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Preprint under review for MR
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Dual bilinear rotations are introduced, which lead to well-defined rotations for both heteronuclear spins I and S that depend on the presence or absence of a (large) coupling between them. It is therefore an extension of conventional bilinear rotations, which cause such a spin-system-dependent rotation only for the spin I. A general derivation of the approach is given and a quadruple J-resolved type experiment is introduced for demonstration.
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Dual bilinear rotations are introduced, which lead to well-defined rotations for both heteronuclear spins I and S that depend on the presence or absence of a (large) coupling between them. It is therefore an extension of conventional bilinear rotations, which cause such a spin-system-dependent rotation only for the spin I. A general derivation of the approach is given and a quadruple J-resolved type experiment is introduced for demonstration.
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Parallel NMR (nuclear magnetic resonance) detection enhances measurement throughput for high-throughput screening. However, local gradients in parallel detectors cause field spillover in adjacent channels, leading to spin dephasing and signal loss. This study introduces a compensation scheme using optimized pulses to mitigate gradient-induced field inhomogeneity through coherence locking. The proposed approach offers an effective solution for NMR probes with parallel, independently switchable gradient coils.
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In contrast to adiabatic excitation, recently introduced SORDOR-90 pulses provide effective transverse 90° rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x,y plane. Together with phase-matched SORDOR-180 pulses, this enables a direct implementation of the Böhlen–Bodenhausen approach for frequency-swept pulses for a type of 90°/180° pulse–delay sequence. Example pulse shapes are characterised, and an application is given with a 19F-PROJECT experiment.
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To increase experimental efficiency, information can be encoded in parallel by taking advantage of highly resolved NMR spectra. Here we demonstrate parallel encoding of optimal diffusion parameters by selectively using a resonance for each molecule in the sample. This yields a factor of n decrease in experimental time since n experiments can be encoded into a single measurement. This principle can be extended to additional experimental parameters as a means to further improve measurement time.
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Short summary
Bilinear rotations like BIRD, TANGO, BANGO, and BIG-BIRD are essential building blocks in modern nuclear magnetic resonance (NMR) spectroscopy that allow the rotation of an isolated spin without couplings (i.e., bilinear interactions) in one way, while rotating spins with a matched coupling in another way. Two ways for constructing particularly robust bilinear rotations (compensated for couplings, offsets, and B1 inhomogeneities, or COB/COB3) are provided and demonstrated in both theory and experiment.
Bilinear rotations like BIRD, TANGO, BANGO, and BIG-BIRD are essential building blocks in modern...
