Torus Factor—The Relationship between Radiofrequency Field and Radial Position in Toroid Cavity Probes
Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is...
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| Veröffentlicht in: | Journal of magnetic resonance (1997) Jg. 146; H. 1; S. 157 - 164 |
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| Abstract | Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is sufficient to describe the relationship between this radiofrequency field and the radial distance from the center axis of the torus. Because accurate determination of the torus factor is essential to optimize toroid cavity NMR experiments or conduct toroid cavity imaging, a fast numerical algorithm for accurate, precise, and convenient determination of torus factors from pulse width-dependent signal intensities is introduced. In addition, the new algorithm provides for 99% confidence intervals around the refined torus factors. A computer program in which the optimization progress is visualized during the torus factor refinement is presented. Upon completion of the program, the best-fit simulated data and the residuals between best fit and experimental data are provided. |
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| AbstractList | Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is sufficient to describe the relationship between this radiofrequency field and the radial distance from the center axis of the torus. Because accurate determination of the torus factor is essential to optimize toroid cavity NMR experiments or conduct toroid cavity imaging, a fast numerical algorithm for accurate, precise, and convenient determination of torus factors from pulse width-dependent signal intensities is introduced. In addition, the new algorithm provides for 99% confidence intervals around the refined torus factors. A computer program in which the optimization progress is visualized during the torus factor refinement is presented. Upon completion of the program, the best-fit simulated data and the residuals between best fit and experimental data are provided. Copyright 2000 Academic Press. Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is sufficient to describe the relationship between this radiofrequency field and the radial distance from the center axis of the torus. Because accurate determination of the torus factor is essential to optimize toroid cavity NMR experiments or conduct toroid cavity imaging, a fast numerical algorithm for accurate, precise, and convenient determination of torus factors from pulse width-dependent signal intensities is introduced. In addition, the new algorithm provides for 99% confidence intervals around the refined torus factors. A computer program in which the optimization progress is visualized during the torus factor refinement is presented. Upon completion of the program, the best-fit simulated data and the residuals between best fit and experimental data are provided. Copyright 2000 Academic Press.Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is sufficient to describe the relationship between this radiofrequency field and the radial distance from the center axis of the torus. Because accurate determination of the torus factor is essential to optimize toroid cavity NMR experiments or conduct toroid cavity imaging, a fast numerical algorithm for accurate, precise, and convenient determination of torus factors from pulse width-dependent signal intensities is introduced. In addition, the new algorithm provides for 99% confidence intervals around the refined torus factors. A computer program in which the optimization progress is visualized during the torus factor refinement is presented. Upon completion of the program, the best-fit simulated data and the residuals between best fit and experimental data are provided. Copyright 2000 Academic Press. Toroid detectors are resonators for high-pressure in situ NMR spectroscopy or one-dimensional rotating-frame imaging. One of their unique qualities is a mathematically well-defined nonuniform radiofrequency field confined to the inside of the detector. A single parameter (i.e., the torus factor) is sufficient to describe the relationship between this radiofrequency field and the radial distance from the center axis of the torus. Because accurate determination of the torus factor is essential to optimize toroid cavity NMR experiments or conduct toroid cavity imaging, a fast numerical algorithm for accurate, precise, and convenient determination of torus factors from pulse width-dependent signal intensities is introduced. In addition, the new algorithm provides for 99% confidence intervals around the refined torus factors. A computer program in which the optimization progress is visualized during the torus factor refinement is presented. Upon completion of the program, the best-fit simulated data and the residuals between best fit and experimental data are provided. |
| Author | Woelk, Klaus |
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| Cites_doi | 10.1006/jmra.1995.1153 10.1016/S0079-6565(96)01037-0 10.1006/jmra.1993.1259 10.1006/jmrb.1994.1023 10.1006/jmra.1996.0139 10.1137/0111030 10.1006/jmra.1994.1147 |
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| Keywords | radiofrequency field gradient Brent algorithm rotating-frame imaging torus factor toroid cavity detector |
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| References | Woelk, Rathke, Klingler (RF4) 1993; 105 Press, Teukolsky, Vetterling, Flannery (RF14) 1992 Brent (RF13) 1973 Woelk, Rathke, Klingler (RF1) 1994; 109 Woelk, Gerald, Klingler, Rathke (RF5) 1996; 121 Metz, Boehmer, Bowers, Moore (RF9) 1994; 103 Lehnhof (RF15) 1997 Boudot, Canet, Brondeau (RF8) 1990; 87 (RF16) 1997 Hoult (RF3) 1979; 33 Woelk, Rathke (RF11) 1995; 115 Marquardt (RF12) 1963; 11 Woelk, Zwank, Bargon, Klingler, Gerald, Rathke (RF6) 1998 Rathke, Klingler, Gerald, Kramarz, Woelk (RF2) 1997; 30 Metz, Boehmer (RF7) 1988; 6 Hoult, Richards (RF10) 1976; 24 Metz (10.1006/jmre.2000.2144_RF7) 1988; 6 Woelk (10.1006/jmre.2000.2144_RF5) 1996; 121 Woelk (10.1006/jmre.2000.2144_RF1) 1994; 109 Boudot (10.1006/jmre.2000.2144_RF8) 1990; 87 Woelk (10.1006/jmre.2000.2144_RF4) 1993; 105 Hoult (10.1006/jmre.2000.2144_RF3) 1979; 33 Woelk (10.1006/jmre.2000.2144_RF6) 1998 Metz (10.1006/jmre.2000.2144_RF9) 1994; 103 Press (10.1006/jmre.2000.2144_RF14) 1992 (10.1006/jmre.2000.2144_RF16) 1997 Lehnhof (10.1006/jmre.2000.2144_RF15) 1997 Brent (10.1006/jmre.2000.2144_RF13) 1973 Hoult (10.1006/jmre.2000.2144_RF10) 1976; 24 Rathke (10.1006/jmre.2000.2144_RF2) 1997; 30 Marquardt (10.1006/jmre.2000.2144_RF12) 1963; 11 Woelk (10.1006/jmre.2000.2144_RF11) 1995; 115 |
| References_xml | – volume: 30 start-page: 209 year: 1997 end-page: 253 ident: RF2 article-title: Toroids in NMR spectroscopy publication-title: Prog. NMR Spectrosc. – volume: 11 start-page: 431 year: 1963 end-page: 441 ident: RF12 article-title: An algorithm for least squares estimation of nonlinear parameters publication-title: J. Soc. Industr. Appl. Math. – year: 1973 ident: RF13 publication-title: Algorithms for Minimization without Derivatives – volume: 33 start-page: 183 year: 1979 end-page: 197 ident: RF3 article-title: Rotating frame Zeugmatography publication-title: J. Magn. Reson. – volume: 87 start-page: 385 year: 1990 end-page: 394 ident: RF8 article-title: Spatial labeling by a radiofrequency field gradient. DANTE-Z profile, probed by one-dimensional nutation imaging publication-title: J. Magn. Reson. – volume: 109 start-page: 137 year: 1994 end-page: 146 ident: RF1 article-title: The toroid cavity NMR detector publication-title: J. Magn. Reson. 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Math. doi: 10.1137/0111030 – volume: 109 start-page: 137 year: 1994 ident: 10.1006/jmre.2000.2144_RF1 article-title: The toroid cavity NMR detector publication-title: J. Magn. Reson. A doi: 10.1006/jmra.1994.1147 – volume: 33 start-page: 183 year: 1979 ident: 10.1006/jmre.2000.2144_RF3 article-title: Rotating frame Zeugmatography publication-title: J. Magn. Reson. – year: 1973 ident: 10.1006/jmre.2000.2144_RF13 |
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| Title | Torus Factor—The Relationship between Radiofrequency Field and Radial Position in Toroid Cavity Probes |
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