Nuclear magnetic resonance imaging has proven itself to involving H z are needed and the remainder can be discarded.
One can then define a vector, g, with components g j ร
dH z / be a useful tool, particularly for biomedical applications, and much work has been devoted to improving the technique for dx j so that the effective magnetic field along the z direction experienced by the nuclei in a very small volume element various applications. To be able to take advantage of similar techniques for nuclear quadrupole resonance would be very dV centered at a position x can be written as useful for a number of applications. Matsui, Kose, and Inouye (1) have described a simple technique to obtain NQR H(x) ร
H 0 / grx.
[1] images using the 35 Cl signal from powders of NaClO 3 using static field gradients. Rommel et al. have described a tech-All nuclei in a plane described by grx ร
constant have the nique using RF field gradients with some success (2-4). In same transient response. The total response from all planes both of these cases, a simple magnetic field gradient of the can be considered to be the sum of coefficients [e.g., the form dB z /dz x 0, with all other components zero, is assumed number density of nuclei, N(x)] times a basis function (a and the powder distribution is removed using a deconvoludelta function in the frequency domain or a sinusoidal function procedure. Unfortunately, such a simple gradient cannot tion in the time domain). Since the basis functions form an be created in practice without violating Maxwell's equations.
orthonormal set, the deconvolution of the measured NMR The additional components of a real gradient field can have signal to form an image [e.g., to determine N(x) to some a significant impact on the ultimate success of NQR imaging degree of accuracy] is relatively straightforward. These simmeasurements of powders. For NMR imaging, a quantization ple relationships do not exist for NQR imaging. axis is defined by the large, externally applied magnetic field.
The interactions between a nucleus and electric-field gra-Contributions from the gradient coils perpendicular to this dients (EFG) in the presence of a small magnetic field, H, direction are negligible. There is no single principal axis have been described elsewhere (6). To observe the NQR system for the electric-field gradient (EFG) in a powder signal, a pulsed RF magnetic field, magnitude H 1 , is applied sample and hence there is no single quantization axis in an and the signal is observed. Solutions for the observed signal NQR measurement, and no part of the gradient field can be strength (after an RF pulse) for nuclear spin I ร
3 2 and neglected a priori. An alternate approach using field cycling and nonlinear gradients has been presented by Lee and Butler asymmetry parameter, h ร
0, were presented in closed form by Bloom et al. (7) many years ago with the assumptions (5), where the full gradient field also needs to be considered.
that
Three difficulties related to the coils which arise for NQR
The frequency of resonance and the transient response in imaging of powders are discussed below. First, without a the presence of RF are complicated functions of the orientacareful choice of RF, RF gradient, static, and/or static gradition of the EFG principal axes and the two applied fields. ent coils, the response from a small volume element, the Frequency splittings for I ร
3 2 and any value of h are pre-''point response,'' will vary from place to place within sample. Second, even if the point response is uniform, the cresented in Ref. ( ) and a generalization of the results in Ref. ation of the image is complicated by the nature of real gradi-(6) are presented by Pratt et al. (9). ent fields. Finally, as is well known, the point response is Bloom et al.'s results were presented in the time domain. more complicated for NQR, than for NMR, and the choice Their results are for the transient response following an RF of coils will have an influence on the ultimate resolution pulse, and there are two times involved-the pulse length obtained.
and the evolution time following the pulse. We have found In general, a gradient field can be described using a 3 1 it useful to consider the transient behavior in a 2-D frequency 3 tensor, G, with components G ij ร
dH i /dx j , where i and j domain. Bloom et al.'s results transformed to the frequency correspond to the x, y, or z direction. For NMR imaging, domain for a powder sample are shown in Fig. , assuming that the same RF coil is used for excitation and detection. unless very large gradients are used, only the three terms 84