Brent S. Robinson

Spatial coherence of the nonlinearly generated second harmonic portion of backscatter for a clinical imaging system

Correlation-based approaches to phase aberration correction rely on the spatial coherence of backscattered signals. The spatial coherence of backscatter from speckle-producing targets is predicted by the auto correlation of the transmit apodization (Van Cittert-Zernike theorem). Work by others indicates that the second harmonic beam has a wider mainlobe with lower sidelobes than a beam transmitted at 2f. The purpose of this paper is to demonstrate that the spatial coherence of backscatter for the second harmonic is different from that of the fundamental, as would be anticipated from applying the Van Cittert-Zernike theorem to the reported measurements of the second harmonic field. Another objective of this work is to introduce the concept of the effective apodization and to verify that the effective apodization of the second harmonic is narrower than the transmit apodization. The spatial coherence of backscatter was measured using three clinical arrays with a modified clinical imaging system. The spatial coherence results were verified using a pseudo-array scan in a transverse plane of the transmitted field with a hydrophone. An effective apodization was determined by backpropagating these values using a linear angular spectrum approach. The spatial coherence for the harmonic portion of backscatter differed systematically and significantly from the auto correlation of the transmit apodization.

The scattering of ultrasound by cylinders: Implications for diffraction tomography

The validity of wave equations employed as system models in acoustical diffraction tomography is investigated using simulations and measurements of the scattering of plane ultrasound waves by cylinders. It is demonstrated by simulation and experiment that it can be appropriate to neglect density fluctuations and shear waves, implying that the commonly used form of the wave equation suitably describes scattering by fluctuations of acoustic speed and absorption. Diffraction tomographic reconstructions of simulated data reveal the importance of absorption, the behavior of the real and imaginary parts of the reconstructed refractive index, and the relative advantages and limitations of the Born and Rytov approximate transformations.

Small element array algorithm for correcting phase aberrations using near-field signal redundancy. Part II: Experimental results

For part I see ibid., vol.47, p.29 (2000). A small element array algorithm for phase-aberration correction using near-field signal redundancy was proposed in part I. Using this algorithm, subarrays are formed to narrow the transmitted and received beams when collecting common midpoint signals, so that angle-dependent aberration profiles across the array can be measured. In this paper, this algorithm is tested on data collected from a phantom with a non-isoplanatic aberrator attached to the front surface of a phased array. The aberrator is made from cast room temperature vulcanizing (RTV) silicone rubber, which has a sound velocity of about 1.02 mm/spl middot//spl mu/s/sup -1/. Results show that the subarray technique can be used to measure and correct angle-dependent, phase-aberration profiles. The theoretical results regarding the performance of several implementation methods for dynamic near-field delay correction on subarrays are also experimentally tested using data from a phantom.

Spatial coherence of backscatter for the nonlinearly produced second harmonic for specific transmit apodizations

To be successful, correlation-based, phase-aberration correction requires a high correlation among backscattered signals. For harmonic imaging, the spatial coherence of backscatter for the second harmonic component is different than the spatial coherence of backscatter for the fundamental component. The purpose of this work was to determine the effect of changing the transmit apodization on the spatial coherence of backscatter for the nonlinearly generated second harmonic. Our approach was to determine the effective apodizations for the fundamental and second harmonic using both experimental measurements and simulations. Two-dimensional measurements of the transverse cross sections of the finite-amplitude ultrasonic fields generated by rectangular and circular apertures were acquired with a hydrophone. Three different one-dimensional transmit apodization functions were investigated: uniform, Riesz, and trapezoidal. An effective apodization was obtained for each transmit apodization by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. Predictions of the spatial coherence of backscatter were obtained using the pulse-echo Van Cittert-Zernike theorem. In all cases the effective apodization at 2f was narrower than the transmit apodization. We demonstrate that certain transmit apodizations result in a greater spatial coherence of backscatter at the second harmonic than at the fundamental.

Effect of changing the transmit aperture on the spatial coherence of backscatter for the nonlinearly generated second harmonic

The present work measures the effective apodizations for the fundamental and second harmonic and uses the Van Cittert-Zernike theorem to predict the spatial coherence of the second harmonic portion of backscatter. Two-dimensional pseudo-array scans of a transverse cross section of the finite amplitude ultrasonic fields generated by rectangular and circular apertures were performed with a hydrophone. Three transmit apodization functions were investigated: rectangular, Riesz, and trapezoidal. An effective apodization was obtained by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. In all cases the effective apodization at 2f was narrower than the transmit apodization. Our results demonstrate that choices of apodization can be identified that yield better spatial coherence at the second harmonic than at the fundamental.

The cross algorithm for phase-aberration correction in medical ultrasound images formed with two-dimensional arrays

Common-midpoint signals in the near-field signal-redundancy (NFSR) algorithm for one-dimensional arrays are acquired using three consecutive transducer elements. An all-row-plus-two-column algorithm has been proposed to implement the one-dimensional NFSR algorithm on two-dimensional arrays. The disadvantage of this method is that its ambiguity profile is not linear and a time- consuming iterative method has to be used to linearize the ambiguity profile. An all-row-plus-two-column-and-a- diagonal algorithm has also been proposed. Its ambiguity profile is linear, but it is very sensitive to noise and cannot be used. In this paper, a novel cross algorithm is proposed to implement the NFSR algorithm on two-dimensional arrays. In this algorithm, common-midpoint signals are acquired using four adjacent transducer elements, which is not available in one-dimensional arrays. Its advantage includes a linear ambiguity profile and a higher measurement signal-to-noise ratio. The performance of the cross algorithm is evaluated theoretically. The region of redundancy is analyzed. The procedure for deriving the phase- aberration profile from peak positions of cross-correlation functions between common-midpoint signals is discussed. This algorithm is tested with a simulated data set acquired with a two-dimensional array, and the result shows that the cross algorithm performs better than the all-row-plus-two- column NFSR algorithm.

Statistically significant differences in the spatial coherence of backscatter for fundamental and harmonic portions of a clinical beam

Correlation-based approaches to phase aberration correction rely on the spatial coherence of backscattered signals. The spatial coherence of backscatter was measured using a clinical linear array with a modified clinical imaging system (ATL HDI 5000). The spatial coherence results were verified using a 14 mm/spl times/14 mm pseudo-array scan in a transverse plane of the transmitted beam with a 0.6 mm hydrophone. An effective apodization was determined by backpropagating these values using a linear angular spectrum approach. The effective apodizations were compared with the spatial coherence measurements using the Van Cittert-Zernike theorem. The spatial coherence for the fundamental beam exhibited good agreement with the autocorrelation of the transmit apodization. The spatial coherence for the harmonic differed systematically and statistically from the autocorrelation of the transmit apodization. Additionally, our experimental results verify that the effective apodization of the nonlinearly-generated harmonic beam is more aggressive than the transmit apodization.

An Experimental Study of Diffraction Tomography under the Born Approximation

Diffraction tomography under the Born approximation was studied experimentally to help assess its potential utility for clinical imaging, particularly in the detection and classification of breast disease. The Born approximation is convenient to use since, being linear, it leads to simple and efficient inversion algorithms. However, its appropriateness for clinical imaging is questionable. In these experiments, particular care was taken to minimise errors of the data acquisition and image reconstruction processes in an effort to isolate the effects of the choice of the Born scattering model on the overall performance of diffraction tomography. Diffraction tomograms of a tissue mimicking breast phantom are compared with both X-ray and ultrasound computed tomograms The results indicate that, even under conditions when the assumptions of the Born approximation are violated, useful images can be obtained. Such images though not quantitatively accurate maps of the complex refractive index, allow identification of the major internal structures.

Implementation of the near-field signal redundancy phase-aberration correction algorithm on two-dimensional arrays

Near-field signal-redundancy (NFSR) algorithms for phase-aberration correction have been proposed and experimentally tested for linear and phased one-dimensional arrays. In this paper the performance of an all-row-plus-two-column, two-dimensional algorithm has been analyzed and tested with simulated data sets. This algorithm applies the NFSR algorithm for one-dimensional arrays to all the rows as well as the first and last columns of the array. The results from the two column measurements are used to derive a linear term for each row measurement result. These linear terms then are incorporated into the row results to obtain a two-dimensional phase aberration profile. The ambiguity phase aberration profile, which is the difference between the true and the derived phase aberration profiles, of this algorithm is not linear. Two methods, a trial-and-error method and a diagonal-measurement method, are proposed to linearize the ambiguity profile. The performance of these algorithms is analyzed and tested with simulated data sets.

Impact of propagation through an aberrating medium on the linear effective apodization of a nonlinearly generated second harmonic field

Techniques based on the nonlinearly generated second harmonic signal (tissue harmonic imaging) have rapidly supplanted linear (fundamental) imaging methods as the standard in two-dimensional echocardiography. Enhancements to the compactness of the nonlinearly generated second harmonic (2f) field component with respect to the fundamental (1f) field component are widely considered to be among the factors contributing to the observed image quality improvements. The objective of this study was to measure the impact of phase and amplitude aberrations resulting from propagation through an inhomogeneous tissue, on the beamwidths associated with: the fundamental (1f); the nonlinearly generated second harmonic (2f); and the linearly propagated, effective apodization signal at the same (2f) frequency. Modifications to the transmit characteristics of a phased-array imaging system were validated with hydrophone measurements. Results demonstrate that the characteristics of the diffraction pattern associated with the linear-propagation effective apodization transmit case were found to be in good agreement with the detailed spatial characteristics of the nonlinearly generated second harmonic field. The effects of the abdominal wall tissue aberrators are apparent for all three of the beam profiles studied. Consistent with the improved image quality associated with harmonic imaging, the aberrated nonlinearly generated second harmonic beam was shown to remain more compact than the corresponding aberrated fundamental beam patterns in the presence of the interposed aberrator.