Curvilinear 3-D Imaging Using Row-Column-Addressed 2-D Arrays With a Diverging Lens: Feasibility Study

Abstract

Abstract-Constructing a double-curved row-columnaddressed (RCA) 2-D array or applying a diverging lens over the flat RCA 2-D array can extend the imaging field-of-view (FOV) to a curvilinear volume without increasing the aperture size, which is necessary for applications such as abdominal and cardiac imaging. Extended FOV and low channel count of double-curved RCA 2-D arrays make 3-D imaging possible with equipment in the price range of conventional 2-D imaging. This study proposes a delay-and-sum beamformation scheme specific to double-curved RCA 2-D arrays and validates its focusing ability based on simulations. A synthetic aperture imaging sequence with single element transmissions is designed for imaging down to 14 cm at a volume rate of 88 Hz. Using a diverging lens with f-number of -1 circumscribing the underlying RCA array, the imaging quality of a double-curved λ/2-pitch 3 MHz 62+62 RCA 2-D array is investigated as a function of depth within a curvilinear FOV of 60°×60°. The simulated double-curved 2-D array exhibits the same full-width-at-halfmaximum values for a point scatterer within its curvilinear FOV at a fixed radial distance compared with a flat 2-D array within its rectilinear FOV. The results of this study demonstrate that the proposed beamforming approach is accurate for achieving correct time-of-flight calculations, and hence avoids geometrical distortions.

3-D imaging using row-column-addressed 2-D arrays with a diverging lens: Phantom study

“…For a speed of sound of 1540 m/s, 182 µs is required to acquire a single image line to a depth of 14 cm including penetrating the lens. For 62 emissions this is equivalent to a volume rate of 88 Hz, and it is the same sequence used in the simulation study in [9]. Hilbert transformed RF data are used for beamforming a low-resolution volume for every emission and finally, by summing all the low-resolution volumes in phase, a high-resolution volume is generated.…”

“…The probe is connected to the experimental ultrasound scanner SARUS [11]. The measured Hilbert transformed RF signals are beamformed using a MATLAB (MathWorks Inc., Massachusetts, USA) implementation of the delay-andsum (DAS) beamformer specific to curved RCA arrays [9]. To remove the otherwise apparent secondary echoes originating from the either ends of line-elements, roll-off apodization regions are placed at both ends of each element [3], [12].…”

“…The red dashed lines are illustrating the wave fronts at different time instances. A beamforming approach was proposed in [9] to accurately calculate the correct time-of-flights of the wave fronts using a diverging lens, and hence avoiding geometrical distortions. However, for the proposed beamfoming approach, the curvature of the wave fronts has to be estimated based on the physical properties of the lens in contact with the imaging medium.…”

“…However, manufacturing double curved transducer elements in two dimensions is challenging for both CMUT and piezoelectric transducer technologies. Another approach to spread the acoustic energy uses a double curved diverging acoustic lens on top of the RCA array [8], [9]. Using a lens makes it easier to fabricate curved arrays, as it is not needed to manufacture curved elements, and also making a lens is a well-tested technology.…”

“…Using a lens makes it easier to fabricate curved arrays, as it is not needed to manufacture curved elements, and also making a lens is a well-tested technology. An in-depth study of the possibilities in this approach has been previously investigated based on simulations by the authors [9].…”