The influences of ambiguity phase aberration profiles on focusing quality in the very near field--part I: single range focusing on transmission

Timing-error-difference calibration of a two-dimensional array imaging system using the overlapping-subaperture algorithm

Timing errors in the transmitting and receiving electronic channels of an imaging system can generate different transmission and reception phase-aberration profiles. To decide if these two profiles need to be measured separately, an overlapping-subaperture algorithm has been proposed in a previous paper to measure the difference between timing errors in transmitting and receiving channels connected to each element in a two-dimensional array. This algorithm has been used to calibrate a custom built imaging system with a curved linear two-dimensional array, and the results are presented in this paper. The experimental results have demonstrated that the overlapping-subaperture algorithm is capable of calibrating the timing-error-difference profile of this imaging system with a standard deviation of only a few nanoseconds. Experimental results have also shown that the time-error-difference profile of this imaging system is smaller than one tenth of a wavelength and there is no need to measure the transmission and reception phase-aberration profiles separately. The derived average phase-aberration profile using the near-field signal-redundancy algorithm can be used to correct phase aberrations for both transmission and reception.

Correction of tissue-motion effects on common-midpoint signals using reciprocal signals

The near field signal redundancy algorithm for phase-aberration correction is sensitive to tissue motion because several separated transmissions are usually needed to acquire a set of common-midpoint signals. If tissues are moving significantly due to, for example, heart beats, the effects of tissue motion on common-midpoint signals need to be corrected before the phase-aberration profile can be successfully measured. Theoretical analyses in this paper show that the arrival-time difference between a pair of common-midpoint signals due to tissue motion is usually very similar to that between the pair of reciprocal signals acquired using the same two transmissions. Based on this conclusion, an algorithm for correcting tissue-motion effects on the peak position of cross-correlation functions between common-midpoint signals is proposed and initial experimental results are also presented.

Timing-error-difference calibration using reciprocal signals

Timing errors in transmission and reception electronic channels of medical ultrasound imaging systems are generally smaller than one-tenth of a wavelength and do not influence the focusing quality of the system. However, these errors influence the performance of the near-field-signal-redundancy algorithm for correcting phase-aberrations generated by speed heterogeneity in the medium due to its high sensitivity to errors. The effect of timing errors is to make the transmission and reception phase-aberration profiles different. When the difference is much smaller than the period of the signal, an algorithm has been proposed in a previous work to measure the average of the transmission and reception phase-aberration profiles, and it can be used as an approximation to correct phase-aberrations on both transmission and reception. However, when the difference is large, the transmission and reception phase-aberration profiles need to be measured separately. In this paper, several algorithms that use reciprocal signals are proposed to measure the difference profile of the transmission and reception phase-aberration profiles. Their performances are theoretically analyzed, simulated, and experimentally tested. From the measured average and difference profiles, the transmission and reception phase-aberration profiles can be derived separately and used to correct phase-aberrations on transmission and reception, respectively.

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 timeconsuming 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 phaseaberration 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-twocolumn NFSR algorithm.

Single- and double-difference algorithms for position and time-delay calibration of transducer-elements in a sparse array

A method for the calibration of the position and time delay of transducer elements in a large, sparse array used for underwater, high-resolution, ultrasound imaging has been described in a previous work. This algorithm is based on the direct algorithm used in the global positioning system (GPS), but the wave propagation speed is treated as one of the to-be-calibrated parameters. In this article, the performance of two other commonly used GPS algorithms, namely the single-difference algorithm and the double-difference algorithm, is evaluated. The calibration of the propagation speed also is integrated into these two algorithms. Furthermore, a novel, least-squares method is proposed to calibrate the time delay associated with each transducer element for these two algorithms. The performances of these algorithms are theoretically analyzed and evaluated using numerical analysis and simulation study. The performance of the direct algorithm, the single-difference algorithm, and the double-difference algorithm is compared. It was found that the single-difference algorithm has the best performance among the three algorithms for the current application, and it is capable of calibrating the position and time delay of transducer elements to an accuracy of one-tenth of a wavelength.

Phase aberration correction using ultrasound radiation force and vibrometry optimization

We describe a phase aberration correction method that uses dynamic ultrasound radiation force to harmonically vibrate an object using amplitude modulated continuous wave ultrasound. The phase of each element of an annular array transducer is adjusted to maximize the radiation force and obtain optimal focus of the ultrasound beam. The maximization of the radiation force is performed by monitoring the velocity of scatterers in the focus region. We present theory that shows focal optimization with radiation force has a well-behaved cost function. Experimental validation is shown by correction of manual defocusing of an annular array as well as correcting for a lens-shaped aberrator placed near the transducer. A Doppler laser vibrometer and a pulse-echo Doppler ultrasound method were used to monitor the velocity of a sphere used as a target for the transducer. By maximizing the radiation force-induced vibration of scatterers in the focal region, the resolution of the ultrasound beam can be recovered after aberration defocusing.

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.

Position and time-delay calibration of transducer elements in a sparse array for underwater ultrasound imaging

This paper describes a novel method for the calibration of the position and time delay of transducer elements in a large, sparse array used for underwater, high-resolution ultrasound imaging. This method is based on the principles used in the global positioning system (GPS). However, unlike GPS, in which the wave propagation speed is generally assumed known, the sound propagation speed in the water usually is unknown and it is calibrated simultaneously in this method to achieve high calibration accuracy. In this method, a high-precision positioning system is used to scan a single hydrophone (used for transmission) in the imaging field of the array. The hydrophone transmits pulses at selected positions, and the transducer elements in the sparse array receive the transmitted signals. Time of flight (TOF) values between transducer elements and hydrophone positions then are measured. From a series of measured TOF values, the position and time delay values for each transducer element as well as the propagation speed can be calibrated. The performances of the calibration algorithm are theoretically analyzed and evaluated with numerical calculations and simulation studies. It is found that this method is capable of calibrating the positions and time delays of transducer elements with high accuracy.

Spatial coherence analysis applied to aberration correction using a two-dimensional array system

Complex degree of coherence functions are computed using synthetic and measured ultrasound data to demonstrate noteworthy aspects of coherence analysis in the context of aberration correction. Coherence functions calculated from synthetic data illustrate the importance of proper normalization of the constituent cross-correlation integrals when weak elements and receiver directivity are significant factors. The synthetic data also show that a spike can occur at the zero-lag position of the coherence function when the signal-to-noise ratio is reduced by element directivity near the edges of a large aperture. The latter observation is confirmed by experimental data acquired through tissue-mimicking distributed aberration phantoms using a low f-number two-dimensional array system. The coherence of data acquired at neighboring elements is not changed by time-shift compensation of transmit and receive focusing, but time-shift compensation does improve the coherence of echoes measured over larger separations. The resulting increase in coherence widths evaluated at levels between 0.2 and 0.5 is correlated with narrower -10 dB and -20 dB effective widths in focuses visualized using single-transmit images. Iterative focus compensation methods may benefit from aberration estimation algorithms that take advantage of these longer-range correlations in random-scattering waveforms.

The influences of ambiguity phase aberration profiles on focusing quality in the very near field part II: dynamic range focusing on reception

In Part I of this work, the influences of ambiguity phase aberration profiles, including constant, tilted, and quadratic profiles, on focusing quality have been quantitatively analyzed with the very near field approximation for single range focusing on transmission. In this paper, their influences are analyzed in a very different situation: dynamic range focusing on reception, which is commonly used in medical ultrasound imaging for beam formation on reception. It is shown that the results for dynamic range focusing on reception are dramatically different from those for single range focusing on transmission. For example, constant phase aberration profiles are harmless to focusing quality for single range focusing on transmission but become harmful for dynamic range focusing on reception. The analysis also shows that, compared with single range focusing on transmission, dynamic range focusing on reception is much more sensitive to ambiguity phase aberration profiles, which have adverse effects on focusing quality even in the near field and far field. These significant differences are caused by the fundamental differences between single range focusing and dynamic range focusing as well as between transmission and reception. Numerical and simulation results are also derived to test the correctness and accuracy of the theoretical results.