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

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.

Is the Kramers-Kronig relationship between ultrasonic attenuation and dispersion maintained in the presence of apparent losses due to phase cancellation?

Phase cancellation effects can compromise the integrity of ultrasonic measurements performed with phase sensitive receiving apertures. A lack of spatial coherence of the ultrasonic field incident on a phase sensitive receiving array can produce inaccuracies of the measured attenuation coefficient and phase velocity. The causal (Kramers-Kronig) link between these two quantities in the presence of phase distortion is investigated using two plastic polymer materials, Plexiglas and Lexan, that exhibit attenuation coefficients that increase linearly with frequency, in a fashion analogous to that of soft tissue. Flat and parallel plates were machined to have a step of a thickness corresponding to an integer number of half wavelengths within the bandwidth investigated, 3 to 7 MHz. Insonification of the stepped portion of each plate produces phase cancellation artifacts at the receiving aperture and, therefore, in the measured frequency dependent attenuation coefficient. Dispersion predictions using two different forms of the Kramers-Kronig relations were performed for the flat and the stepped regions of each plastic plate. Despite significant phase distortion and a detection system sensitive to these aberrations, the Kramers-Kronig link between the apparent attenuation coefficient and apparent phase velocity dispersion remains intact.

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.

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.

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

Most phase aberration measurement algorithms have an ambiguity for constant and tilted phase aberration profiles. Based on the Fresnel (near field) approximation with single range focusing and the Fraunhofer (far field) approximation, constant and tilted phase aberration profiles change the position of the focal point only and do not influence the image focusing quality. Therefore, ambiguity phase aberration profiles are generally considered to be harmless and ignored in those algorithms and related theoretical analyses. However, Fresnel and Fraunhofer approximations may become invalid under many medical ultrasound imaging situations, e.g., when the imaging field is in the very near field (f-number approximately 1). In the very near field, although it is known that constant and tilted phase aberration profiles may degrade the focusing quality, it seems that there is a lack of quantitative analysis results in the literature about their influences, and this is the purpose of the current paper. In this paper, a quantitative analysis with a very near field approximation is performed for single range focusing on transmission, which is a commonly used transmission focusing method in medical ultrasound imaging. The tolerable levels of constant and tilted phase aberration profiles are derived as a function of the imaging system's f-number and wavelength. Because some phase aberration measurement algorithms may also have an ambiguity for quadratic phase aberration profiles, they are also included in the analysis. The theoretical results are compared with numerical and simulation results. These results have shown that the influences of tilted and quadratic phase-aberration profiles can be ignored only under certain conditions in the very near field.