Electricity: measuring and testing – Particle precession resonance – Using a nuclear resonance spectrometer system
Reexamination Certificate
1999-02-22
2001-06-26
Oda, Christine (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using a nuclear resonance spectrometer system
Reexamination Certificate
active
06252402
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a method for correcting and/or calibrating magnetic fields, particularly for magnets in nuclear magnetic resonance imaging equipment.
2. Background Information
A method for correcting and/or calibrating magnetic fields is currently implemented by using passive ferromagnetic correction means, and coefficients are subdivided according to criteria which change from time to time, depending on magnet structure, field orientation, and other parameters.
The criteria adopted both on processing and on implementation only refer to the magnet structure and anyway are at least partially strongly empirical and governed by experience.
In practical and industrial implementation of such magnets, and especially of equipment making use thereof, such as particularly nuclear magnetic resonance imaging equipment, the use of well-known methods is time-consuming and costly, which affects both productivity and, in intrinsic connection, the final cost of the equipment.
SUMMARY OF THE INVENTION
The invention has the object to provide a method for correcting and/or calibrating magnetic fields of the type described hereinbefore, whereby a targeted and accurate correction may be performed, with a minimum of correction elements and a minimum number of steps.
The invention is substantially based on the acknowledgment that field errors or aberrations in the relevant volume, permeated by the field, are substantially produced by two causes, quite independent from each other. As will be apparent thereafter, thanks to this acknowledgment, the process for correcting and calibrating the magnetic field may be followed by such criteria as to allow the operation to be performed much more quickly and minimizing approaches of the heuristic type or only based on experience. Particularly, this acknowledgment is the basis of processes not depending on specific and instinctive knowledge, which is hardly transferable unless through constant practice. The acknowledgment whereon the invention is based consists in that the aberrations and errors of magnetic fields generated by any magnet structure whatsoever, with respect to a magnet field having predetermined characteristics, imposed by its specific use, are either of the systematic or of the asystematic type. The term aberrations of the systematic type refers to those aberrations caused by the geometrical and physical structure of the magnet, i.e. of the parts meant to generate the field. Conversely, asystematic errors are those deriving from fabrication tolerances, and involving differences between the characteristics of the magnet determined by a theoretical calculation of the field, and the real characteristics thereof. Asystematic errors have a substantially statistical distribution, and depend on fabrication accuracy, on the quality of the material in use, and on mounting and assembly tolerances of the magnet structure. Therefore, asystematic errors might even, under particularly favorable conditions, not appear in any field map, whereas systematic aberrations are always present, although statistically also modulated by construction tolerances.
Several approaches may be provided for the mathematical description of the behavior of the magnet field generated in space by a magnetic structure. The invention is also based on the further acknowledgment that an effective mathematical description of this behavior may be obtained by using, as a reference, the symmetries of the magnetic structure and hence of the field generated thereby, in combination with those of the controlled volume.
The symmetry-based approach has the advantage that it does not depend on a particular system of coordinates in subdividing errors and aberrations into systematic and asystematic groups, and that it simplifies the analysis of aberrations and the calculation of the parameters associated to the correction elements for any magnet structure whatsoever.
Therefore, the invention provides a method of the type described hereinbefore, in which the morphology of the sampling volume of the magnetic field is defined, the coefficients of the polynomial which can represent the magnetic field are analyzed and subdivided into independent groups, according to the symmetries of the selected reference system and of the relevant harmonic functions which are used in the description of the magnetic field, and the independent groups of coefficients are ordered according to the category of systematic or asystematic errors, in accordance with the symmetries of the magnetic structure and with respect to the selected reference system.
For an easier and immediate discrimination of coefficients, by minimizing the number of systematic coefficients, it is preferable to align the symmetries of the morphology of the sampling volume with those of the magnet structure.
The next processing steps derive from this fundamental concept. Particularly, the invention provides the following steps: generating the polynomial which represents the magnetic field with the final desired characteristics, in the form of a general field function consisting in the summation of harmonic terms, (i.e. of orthogonal terms, independent from each other), determining independent groups of coefficients, which describe systematic errors, according to the symmetries of the magnetic structure and with respect to the reference system selected for the controlled volume, processing the field sampling values by the polynomial expansion function, and separately comparing the independent groups of the actual measured coefficients, which describe the systematic errors, with those which describe the final desired characteristics of the field, correlating the polynomial expansion function which describes the field to a grid for positioning the correction elements, calculating the position, magnitude and number parameters of the correction elements by said correlation, as well as by reducing the absolute value of the coefficients under examination below a predetermined maximum value, and optimizing the number of correction elements and the magnitude parameters thereof, and arranging said correction elements in said positioning grid, according to the magnetization distribution, the number and the positions determined.
Moreover, the invention advantageously provides the separate treatment of independent groups of coefficients, with respect both to the category of systematic errors and to the category of asystematic errors.
The mathematical system describing in practical terms the method according to the invention brings to an equation system, which may be easily and quickly solved by numeric means.
If the concept of the invention is more deeply analyzed, the method according to the invention allows to know presumptively which significant errors, due to the finite shape of the magnetic structure, the so-called systematic errors, will occur in the magnetic field. By correcting systematic errors independently from the errors caused by fabrication tolerances, any treatment extended to asystematic errors is avoided.
The method to determine the correction elements for asystematic errors may follow the same steps as described as regards systematic errors.
The grids for positioning the correction elements may be different both as regards systematic errors and as regards asystematic errors.
Thanks to the above method, not only is the number of correction elements of systematic errors reduced, but the number of correction elements of asystematic errors is also dramatically and to a greater extent reduced. The equation system can be solved, if the structure thereof allows so, either precisely or in order to reduce the absolute value of the coefficients below a predetermined maximum value.
The number, position and magnetization distribution parameters of the correction elements for systematic errors, as well as the same parameters for the correction elements of asystematic errors, may be also determined without having to make a precise calculation or to meet maximum threshold requirements, by presumptivel
Coscia Gianluca
Sanfilippo Carlo
Trequattrini Alessandro
Burns Doane Swecker & Mathis L.L.P.
Esoate S.p.A.
Oda Christine
Vargas Dixomara
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