Abstract: A method of generating an adiabatic FM pulse, comprising: selecting a starting trajectory for the pulse; and determining a velocity profile along the trajectory by constraining at least a portion of the velocity profile only to fulfill an adiabatic condition other than a frequency frame adiabatic condition. Preferably, the other adiabatic condition is one defined in a double-rotating reference frame.

Abstract: A method of NMR (nuclear magnetic resonance) excitation of a sample having a magnetic moment, including, applying a longitudinal magnetic field to the sample; and changing the magnetic moment in a substantially continuous manner by moving an effective magnetic-field vector &ohgr;e more than 90°, wherein for all portions of the sample in which the moment is changed, the angular velocity of the effective field vector at at least one angle, 90°+&agr;, is different from the angular velocity at 90°−&agr;.

Abstract: For determining appropriately the direction of diffusive motion detecting gradient magnetic field to be applied for the measurement of the diffusion coefficient of a region of interest, a determining method produces three diffusion-weighted images by use of imaging pulse sequences which apply diffusive motion detecting gradient magnetic fields (MPG) along the x axis, y axis and z axis: (steps S1-S3). It composes an image from the diffusion-weighted images by allotting red color, green color and blue color to the images: (step S4). It sets a region of interest on the intensity-inverted image: (step S6). It determines the direction of diffusive motion detecting gradient magnetic field (MPG) to be applied for the measurement of the diffusion coefficient of the region of interest based on the hue of the region of interest on the intensity-inverted image: (step S7).

Abstract: In a magnetic resonance transmission method and magnetic resonance transmission operating therewith a high-frequency power amplifier emits an output signal with an actual amplitude and an actual phase to a magnetic resonance transmission antenna. A fraction of the signal is digitilized in a magnetic resonance receiver and is supplied to a pulse controller that is realized in software. An analog magnetic resonance reception signal of an object can be supplied to the magnetic resonance receiver during the pulses. The pulse controller determines correction values for a generator amplitude and a generator phase with which a pulse generator is driven, the pulse generator being connected upstream relative to the high-frequency amplifier.

Abstract: A method for acquiring nuclear magnetic resonance measurements of a material uses a gradient tool. A modified CPMG sequence is used wherein the duration of the refocusing pulse is selected to maximize the SNR of the pulse echoes relative to a standard CPMG sequence in which the refocusing pulse has twice the duration of the tipping pulse.

Abstract: A medical diagnostic apparatus has a computer, a bus, processors, memories and an input arrangement, the imput arrangement including an adjustment arrangement for the nearly simultaneous adjustment of at least two input parameters, to which a processor is allocated for conversion into control parameters.

Abstract: A magnetic resonance signal is acquired from a JHH-coupled 1H within an object. After application of a wideband first radio-frequency magnetic pulse, a first frequency-selective radiation pulse is applied to a specific nucleus 1H coupled to a desired nucleus 1H through a homonuclear spin-spin coupling (JHH-coupling), thus multiple-quantum coherences between the nuclei 1H being generated. A second radio-frequency magnetic pulse is then applied. A second frequency-selective radiation pulse is then applied to the specific nucleus 1H to generate a single-quantum coherence of the desired nucleus 1H. Thus, a magnetic resonance signal can be acquired from the desired nucleus 1H. The acquisition of the signal is robust, adjustment in the phases of the radio-frequency magnetic pulses is not required, and an acquired spectrum is avoided from being visually complicated.

Abstract: An MRI system performs a pulse sequence to acquire image data from a subject. The RF power applied to the subject is monitored and the acquisition is altered if any one of three trip levels is exceeded. Each trip level is different and is associated with a different time interval over which applied RF power is measured.

Abstract: In a method for operating a magnetic resonance tomography apparatus that contains a basic field magnet, a gradient system with gradient coils and a control system that controls the currents in the gradient coils, among other things, on the basis of pulse sequences, noise that is caused by a pulse sequence upon implementation thereof is identified before a start of the pulse sequence. When an identified noise lies above a selectable value, the pulse sequence is modified, so that the modified pulse sequence does not exceed the selectable value when it is implemented.

Abstract: A magnetic resonance imaging (MRI) system (100) performs optimized chemical-shift excitation. A computer system (110) performs a constrained numerical optimization to determine radio frequency (RF) pulse amplitudes, phase angles, and interpulse intervals for a binomial-like RF pulse sequence that will excite magnetization (41) of a selective one of two chemical species, such as water and fat for example, of a subject (102) in relatively less time and that may therefore be used at lower magnetic fields. A static magnet (132) produces a magnetic field along a predetermined axis relative to the subject Pulse sequence apparatus (134, 152, 154, 156, 158) creates magnetic field gradients with the magnetic field, applies RF pulsed magnetic fields, and receives resulting RF magnetic resonance (MR) signals. Pulse sequence control apparatus (142) controls the pulse sequence apparatus to apply the binomial-like RF pulse sequence to the subject.

Abstract: A safety system for a gas process or facility for measuring the concentration of a specified gas in an area or chamber and determining whether it is safe to allow access to such area or chamber. In particular, the safety system is adapted for use in a gas sterilization facility having one or more sterilization chambers, wherein the safety system measures the concentration of the sterilizing gas and unlocks the door of the sterilization chamber if the level of the sterilizing gas in the sterilization chamber is below a predetermined limit. The safety system further limits access to the sterilization chamber after a predetermined period of time if the door of the sterilization chamber is not opened due to the possible continued desorption of the sterilizing gas from the articles into the sterilization chamber.

Abstract: A magnetic resonance (MR) imaging system equipped with real-time imaging capability and method of interactively prescribing image contrast are disclosed herein. The MR imaging system includes a sequence controller for constructing MR imaging pulse sequences and a waveform memory for storing waveform segments. The MR imaging system allows an operator to interactively prescribe image contrast mechanism prior to and/or during real-time imaging. The use of image contrast waveform segments, only as needed, minimizes unnecessary MR scan time.

Abstract: A prescan process for an MR fast spin echo (FSE) pulse sequence adjusts the phases of the RF excitation pulse and RF refocusing pulses in the FSE pulse sequence to reduce the spatially invariant phase errors (zeroth order). The prescan process also calculates the value of a readout gradient compensation pulse, a phase-encoding gradient compensation pulse and a slice-select gradient compensation pulse to reduce the first order phase shifts along the readout, phase-encoding, and slice-select gradient axes.

Abstract: An interactive magnetic resonance (MR) imaging system includes a MR imaging device, a network coupling the MR imaging device and a remote facility, an operator interface coupled to the MR imaging device and the network, a memory coupled to the MR imaging device, and a sequence controller coupled to the memory. The MR imaging device is configured to acquire and reconstruct MR data in real-time of a current imaging section and display a MR image in real-time of the current imaging section. The network provides remote services to the MR imaging device. The operator interface permits an operator to select from a plurality of image contrast mechanisms. The memory stores a plurality of image contrast waveform segments and at least one imaging waveform segment. Each of the plurality of image contrast waveform segments and the at least one imaging waveform segment is distinctly addressable such that each waveform segment can be independently accessed from the memory.

Abstract: A method of compensating a phase error of a phase encoding gradient pulse in fast spin echo (FSE) imaging, wherein a bipolar type phase encoding gradient pulses for tuning are applied between a 90° RF signal and a first 180° RF signal in a FSE sequence to obtain a tuning value. Alternatively, an additional 180° RF signal is applied between a 90° RF signal and a first 180° RF signal in a FSE sequence, and then phase encoding gradient pulses for tuning are applied between the additional 180° RF signal and the first 180° RF signal to obtain a tuning value. The phase errors of the phase encoding gradient pulses are compensated for using the obtained tuning value. Accordingly, a ringing artifact or blurring phenomenon of an image can be reduced in the FSE imaging, and the contrast of an image can be improved.

Abstract: An asymmetric spin-echo (ASE) sequence having a variable asymmetry (&Dgr;TE) with respect to the RF pulse is used for imaging paramagnetic, diamagnetic or ferromagnetic instruments within tissues during interventional MRI procedures. The degree of asymmetry introduced determines an apparent size of the imaged instrument. In one embodiment of the invention, the amount of asymmetry is varied as a function of the phase encoding gradient steps. In this manner, the sequence is made sensitive to local gradients in the magnetic field but left insensitive to large scale variations such as those introduced by main magnetic field inhomogeneities.

Abstract: With an intention to improve picture quality without increasing the overall number of times of data collection and to restrain artifacts resulting from differences in noise structure between parts differing in the number of times of addition, the total number V of views is equally divided into eight, and the areas of the two ends of each V/8, where the absolute value of the quantity of phase encoding is the greatest, are reduced in the number of times of addition by ½ of the reference number of times N, because their contributions to picture quality is small. The remaining middle 6V/8 areas are increased in the number of times of addition by ½ of the reference number of times N, because their contributions to picture quality are great, and further to alleviate the non-continuity of the variations of the number of times of addition, the number of times of addition in the middle 6V/8 areas is varied so as to follow either a Hamming function or a Hanning function.

Abstract: The present invention aims to reduce degradation in image quality due to residual magnetization. In a pulse sequence of a high-speed spin echo process, a pre-pulse is applied before an excitation pulse, and a correction pulse for correcting a phase error caused by the pre-pulse is applied before an initial inversion pulse.

Abstract: The present invention, in one form, provides compensation for the effects of an oscillatory B0 eddy current Be(t) in an NMR apparatus. In an NMR apparatus having a transmitter generating a spin excitation signal and a receiver detecting an NMR signal, applied gradient signals are analyzed to estimate a resulting oscillatory B0 eddy current Be(t). The frequency of either the transmitter or the receiver of the NMR apparatus, or both, is shifted in frequency by an amount proportional to Be(t) to achieve compensation.

Abstract: An additional apparatus for a control device for a magnetic resonance tomography apparatus converts an output signal emitted by the control device from an initial frequency into a second frequency. Magnetic resonance signals are excited by the modified output signal. The excited magnetic resonance signals are received. The auxiliary apparatus converts the reception signal back into the initial frequency.

Abstract: The present invention relates generally to magnetic resonance imaging (MRI), and more particularly to a method and apparatus for efficient MRI tissue differentiation using an RF pulse designed to provide a frequency response combining a magnetization transfer contrast and fat saturation simultaneously. The invention includes creating a spectrally selective suppression pulse having an RF pulse profile designed to produce a frequency response with adequate fat suppression and selecting a spectrally selective suppression amplitude to produce a magnetization transfer contrast between two different tissue types, such as between proteinated tissue and water-based tissue. The invention also includes applying the spectrally selective suppression pulse with a flip angle selected to optimize fat suppression and magnetization transfer contrast saturation simultaneously.

Abstract: In fast imaging of a multi-echo method represented by a fast spin echo (FSE) method, a pulse sequence is arranged such that a basic condition relating to a CPMG method is satisfied and a spoiler gradient magnetic field pulse is independently applied immediately after a flop pulse. The spoiler gradient magnetic field pulse for suppressing an undesired signal is applied by a predetermined amount or more so as to prevent superimposition of other gradient magnetic field components such as a phase encoding component, a rewind component, etc., and to prevent a residual component of an FID signal caused by a certain RF pulse from being refocused by a subsequent RF pulse.

Abstract: A method for magnetic resonance imaging (NMR) subjects a sample of magnetic spins, having differing Larmor frequencies and located in an external magnetic field, to a sequence of at least two radio frequency pulse sequences in time separation tm with respect to each other, wherein the difference in Larmor frequencies is due to the type of nuclei, to the inhomogeneities of the magnetic field utilized, or through action of an additional magnetic field gradient and wherein the first radio frequency pulse sequence effects excitation of, relative to the distribution of Larmor frequencies, periodic modulation of the z-magnetization having a modulation separation 2&Dgr;&ohgr; and the second radio frequency pulse sequence transfers this periodic modulating z-magnetization into transverse magnetization leading to signal production.

Abstract: The invention relates to an MR method in which the deterioration of the image quality by the concomitant gradients is reduced or eliminated by imposing a temporal variation on the magnetic fields acting in the examination zone during the time interval between the excitation of the nuclear magnetization and the reception of the MR signal such that the spatial distribution of the phase error upon reception of the MR signal is at least approximately the same for all sequences.

Abstract: A method of nuclear quadrupole resonance testing a sample comprising a first type substance containing quadrupolar nuclei and a second type substance which may give rise to spurious signals which interfere with response signals from the quadrupolar nuclei, comprises applying a pulse sequence to the sample to excite nuclear quadrupole resonance, the pulse sequence comprising at least one pair of pulses; detecting response signals; and comparing, for the or each such pair, the respective response signals following the two member pulses of the pair, the pulse sequence being such that the respective spurious signals following the two member pulses can be at least partially cancelled by the comparison without the corresponding true quadrupole resonance signals being completely cancelled; and for the or each such pair, the two member pulses being of like phase.

Abstract: A radio-frequency signal receiving unit, particularly for Nuclear Magnetic Resonance imaging machines, including a signal receiving coil (1), whose outputs (101, 201) are connected to a signal amplifier (2). The coil (1) is in balanced connection with the signal amplifier (2), i.e. connected thereto in such a manner that none of its two outputs (101, 201) is permanently connected to the ground. A particular kind of balanced amplifier is suggested to which the balanced outputs (101, 201) of the coil are connected through balanced means for optimizing the Noise Figure of the amplifier (3).

Abstract: A magnetic resonance (MR) imaging system equipped with real-time imaging capability and methods of interactively prescribing image contrast are disclosed herein. The MR imaging system includes a sequence controller for constructing MR imaging pulse sequences and a waveform memory for storing waveform segments. The MR imaging system allows an operator to interactively prescribe image contrast mechanism prior to and/or during real-time imaging. The use of image contrast waveform segments, only as needed, minimizes unnecessary MR scan time.

Abstract: A method for acquiring nuclear magnetic resonance measurements of a material. The method includes inducing a static magnetic field in the material, and inducing a first radio frequency magnetic field in the material to reorient nuclear magnetic spins in the material. The first radio frequency magnetic field has an amplitude and a duration selected to reorient the nuclear magnetic spins by about 90 degrees from their alignment with the static magnetic field. A second radio frequency static magnetic field is induced in the material. Nuclear magnetic resonance signals are detected after inducing the second radio frequency magnetic field. The steps of inducing the first and second radio frequency magnetic fields and detecting signals are repeated and the detected signals are stacked.

Abstract: A Fourier transformation in a measured data matrix (MD) with the discrete measured data (x.sub.j,k) is implemented for all k=0 . . . N-1, respectively in the following steps, whereby it is defined: w=e.sup.-2i.pi./Na) The measured signals (x.sub.j,k) are acquired with an rf-phase modulation of the nuclear magnetic resonance signals according to a chirp function w.sup.j.spsp.2.sup./2,b) The arising data are convoluted with a second chirp (w.sup.-(j-k).spsp.2.sup./2) and entered into an auxiliary data matrix (HD),c) The image data matrix is acquired from the auxiliary data matrix (HD) by Fourier transformation in at least one further direction.

Abstract: In a magnetic resonance apparatus for providing an image of a sample a birdcage resonator 12 is provided with its axis parallel to the magnetic field of the apparatus. A radio-frequency source 36 is connected to the resonator 12 so as to generate a magnetic field by a first resonance mode of the resonator and a detector 44, 46 is connected to the resonator 12 so as to detect any signal received by the resonator in its second, orthogonal mode.

Abstract: The invention is a nuclear magnetic resonance sensing apparatus comprising a magnet for inducing a static magnetic field in a region containing materials to be analyzed. The static magnetic field is polarized generally along the axis of the apparatus. The static magnetic field has a predetermined maximum longitudinal and maximum radial amplitude gradient. The apparatus includes a transmitter antenna for generating a radio frequency magnetic field in the region for exciting nuclei of the materials to be analyzed by conducting a radio frequency current through the transmitter antenna. The apparatus includes a receiving antenna for detecting a nuclear magnetic resonance signal from the excited nuclei. In a particular embodiment, the transmitter antenna and receiver antenna consist of coil pairs, each coil in a pair separated from the other by 90 degrees, to generate a circularly polarized RF magnetic field and to perform quadrature detection of the NMR signals.

Abstract: An MRI system performs a calibration prescan in which NMR projections are produced using either a spiral acquisition pulse sequence (FIG. 3) or a series of pulse sequences at a corresponding series of projection angles. The signal energies of the projections are summed to produce NMR calibration data. The signal energy in a prescribed region of interest may be calculated to provide the optimal RF transmit power when using local coils.

Abstract: An antenna for a magnetic resonance device comprises an antenna conductor structure and capacitors connected thereto. The antenna conductor structure and/or the capacitors are connected to a water cooling system.

Abstract: The ghost artifacts appearing in images produced by an MRI system are measured. An image of a reference phantom is acquired and the ghost artifacts are measured by cross correlating a ghost correlation matrix with the image. The ghost correlation matrix is produced from the image and the cross correlation is computed as the ghost correlation matrix is moved across the image along either the phase encoding or frequency encoding axes.

Abstract: New methods of generating optimal inversion pulses and adiabatic pulses in magnetic resonance imaging are disclosed. Trajectories, maximum sweep rates, and velocity profiles are used in defining an optimal pulse, over support regions. Adiabatic pulses are optimized by using the trajectory as a constraint of optimization, but selecting trajectories with velocity profiles, without using the adiabatic condition as a constraint for optimizing the velocity profile. A method or inverting MR spins substantially, independently of the pulse duration, by selecting a transition width between 1.4 and 1.9 and dividing that width by the pulse duration is disclosed; and A new method of inverting adiabatic, MR, amplitude modulated spins, with a trajectory defined by sin .alpha./cos .alpha., where .alpha.<0.9 and at least 50% of the trajectory is outside, in a z-x rotating frame of reference that rotates at the instantaneous frequency of the RF pulse is also taught.

Abstract: An inversion pulse for wideband application is obtained from a simple nonlinear amplitude modulation wherein the amplitude is modulated in accord with A(t)=A.sub.0 {1-.vertline. sin .beta.t.vertline..sup.n } and the entire pulse is frequency modulated such that the phase varies as .phi.(t)=.phi..sub.0 +1/2 kt.sup.2.

Abstract: A sweep generator 230 applies a range of frequencies to an rf coil 140 to detect the resonant frequency of a field generated by a magnet 125a,b. A frequency to current converter 220 applies an auxiliary magnetic field to tune an MRI apparatus to the resonant frequency of the rf coil. A flexible coil of one turn (300) or two or more turns (500) has a plurality of segments (301-307; 501-513). One of the belt has a contact k0, (k0'), which is electrically connectable to one or more contacts k1, (k1'), k2, (k2'), etc. located between the ends of the segments. For each connection to successive contacts, the length of the coil and its inductance increases by the added impedance .DELTA.L.sub.ij between contacts k.sub.i and k.sub.j. That increase of inductance is nullified by capacitors .DELTA.C.sub.sij located between segments.

Abstract: This invention relates to a technique for compensating for the inhomogeneity of the field generated by the RF coil (B1) in a nuclear magnetic resonance experiment. Current techniques for achieving accurate flip angles with non-uniform B1 transmit fields, are based upon modulation of the RF waveform. Inherent disadvantages of any RF-based compensation is an increased pulse length and/or increased RF power. Moreover, for some important applications, e.g. multi-slice excitation, no suitable pulses are known. We present an alternative strategy involving a Bz field whose spatial variation is correlated with that of the B1 field. This spatial correlation between the fields allows Bz-based compensation for the effects of B1 inhomogeneity. Successful operation over a wide bandwidth and range of B1 intensities may be achieved without any modification of the RF pulses. An alternative approach for compensating for B1 inhomogeneity is to apply a rapid oscillatory phase-modulation to an existing RF pulse waveform.

Abstract: Determining the magnitude of the calibration RF pulse using the signal phase rather than the signal amplitude.

Abstract: This invention includes methods for analyzing data generated by various solid-state NMR experiments, including rotational echo double resonance (REDOR), transferred echo double resonance (TEDOR), dipolar recoupling at the magic angle (DRAMA), dipolar recoupling with a windowless sequence (DRAWS), and melding of spin-locking and DRAMA (MELODRAMA). The methods are based alternately on a new analytical transform or the maximum entropy method and their multi-dimensional extensions. They permit simultaneous, multiple distance measurements of high accuracy and precision, even from nuclei with identical chemical shifts. By providing high quality easily obtained distance measurement from disordered solid state materials, this invention also improves drug discovery and design through fast determination of structures of pharmaceutical lead compounds, drug molecules, or their targets.

Abstract: A multiband RF pulse is produced using the SLR method. A single-band RF pulse is produced and employed to determine correction factors. The SLR polynomial coefficients for each excited band are calculated and corrected, and then combined to form a composite SLR polynomial from which the multiband RF pulse is produced.

Abstract: Fast spin echo pulse sequences are adjusted to reduce, or eliminate image artifacts caused by Maxwell terms arising from the linear imaging gradients. The waveforms of the slice selection, phase encoding and readout gradients are adjusted in shape, size or position to eliminate or reduce the phase error caused by the spatially quadratic Maxwell terms.

Abstract: A gradient magnetic field generation apparatus according to the present invention comprises a gradient coil, an assistant voltage selector for generating first and second control signals in accordance with an input waveform signal, the first control signal being the same as or similar to, the input waveform signal, a delay circuit for delaying the first control signal for a first delay time, a delay circuit for delaying the second control signal for a second delay time, a main power for amplifying the delayed first control signal and applying a voltage to a gradient coil, an assistant power for generating an assistant voltage for assisting the main power in accordance with the delayed second control signal, and a delay controller for individually controlling the first and second delay times.

Abstract: Chemical shift imaging with spectrum modeling (CSISM) models the general chemical shift spectrum as a system with N distinct peaks with known resonant frequencies and unknown amplitudes. Based on the N peak spectrum model, a set of nonlinear complex equations is set up that contains N+1 unknowns of two kdnds: the magnitudes of the N peaks, and a phasor map caused by main magnetic field inhomogeneity. Using these equations, the timing parameters for shifting the 180.degree. RF refocusing pulses for acquiring spin-echo images are optimally chosen. Corresponding timing parameters for other pulse sequences can also be optimized similarly. Using the chosen timing parameters, a plurality of images are acquired. Next, acquired image data are automatically processed to solve the complex linear equations. First, the phasor map is found by fitting various phasor map values over a small number of pixels, or "seeds", that are picked sparsely in a field of view.

Abstract: A magnetic resonance imaging method comprises exciting spins in an investigation volume via a radio frequency pulse and the signal produced thereby is subsequently read-out after appropriate spatial encoding following a short echo time te. Repetition of the sequence required for spatial encoding occurs in a time interval tr under appropriate variation of the spatially encoding gradient. The radio frequency pulse utilized for excitation has a short time duration and therefore a large excitation band width so that a projection image through a thick projection slice is produced under application of no slice selection gradient or with only a weak slice selection gradient. The time interval tr is sufficiently minimized that the image recording time required for recording of an image lies in the range of one EKG cycle or below. This process of recording a projection image is continuously repeated and a contrast medium bolus administered during the course of this sequential recording.

Abstract: An eddy current correction method is provided for use in an MR system disposed to generate difflusion-weighted echo planar images by employing a bipolar diffusion-weighting gradient as well as the nominal components in an echo planar imaging pulse sequence. The correction method comprises the steps of deriving eddy current parameters (i.e., amplitude and time constant) associated with each eddy-current-induced magnetic field component caused by the diffusion-weighting gradient, and generating a set of correction terms, each of the correction terms being a function of the parameters. The method includes the further steps of modifyg a set of ideal echo planar imaging gradients and the receiver phase and frequency to respectively offset the eddy current induced magnetic field gradient and the spatially independent B.sub.0 -magnetic field. The modification occurs in two stages.

Abstract: In accordance with the invention, spatially invariant B.sub.0 eddy currents induced by a slice-selection gradient, G.sub.Z in an MRI system, are compensated by phase modulating the RF excitation pulse with a compensating function. In one embodiment, the compensating function is based on a measure of the integral of the B.sub.0 eddy current. In another embodiment, a scaled copy of the excitation gradient can be used as an approximation of the compensating function.

Abstract: A nuclear magnetic resonance sensing apparatus, comprising a magnet for inducing a static magnetic field in a region containing materials to be analyzed. The magnet has a longitudinal axis and substantially uniform magnetization along the axis. The apparatus includes a system for generating a radio frequency magnetic field to excite nuclei of the materials to be analyzed, which includes a first antenna having an axial length shorter than a length along the axis over which the magnet has said substantially uniform magnetization. The axial length of the first antenna is shorter in a direction of motion of the apparatus so that the radio frequency magnetic field excites the nuclei where they are substantially prepolarized by the static magnetic field to an equilibrium state along the direction of motion. The apparatus includes a system for receiving nuclear magnetic resonance signals from the excited nuclei.

Abstract: An RF pulse for an NMR pulse sequence is designed in the NMR system using an inverse SLR transformation method. The polynomials required for the SLR transformation are calculated using a weighted least mean squares ("WLMS") process in which an initial weighting function is employed along with the desired pulse profile that is input by the NMR system operator. The operator can also specify the phase profile as an input to the WLMS process.

Abstract: A symmetric RF coil for use in a probe for NMR apparatus comprises an odd number of turns having generally straight portions and arc-shaped portions wound alternately in series on the curved surface of a cylindrical sample region. An additional pair of arc-shaped segments connect to the outermost turn to form continuous end rings, and to split the current on the outermost turn to the continuous end rings. Such an RF probe coil possesses material symmetry provided by the additional arc-shaped segments and RF symmetry as a result of the symmetry in current flow generated by the split in current of the outermost turn to the continuous end rings. The symmetric odd-turn RF coil achieves NMR performance at the same level of even-turn coils with high RF homogeneity, and is suitable for high resolution NMR applications. The coil inductance of the present invention bridges the gap between even-turn coils, and facilitates improved optimization of the resonance circuits over the entire operating range.