Design of sparse annular arrays for high-frequency imaging

Abstract

The design of a 35 MHz sparse annular array is described. The array was designed to provide < 125 µm resolution over an 8 mm imaging depth, while suppressing the secondary lobes to more than 60 dB below the main beam. The array has 10 equal- area elements and a 5 mm outer diameter. The array was designed with 110 µm equal-width kerfs, resulting in only a 50% active aperture. The simulated performance of the array was compared to a 5 mm diameter, 10-element array operating with a 100% active aperture. The -6 dB beamwidths of the sparse and full arrays were found to increase smoothly from 61 microns at a depth of 6 mm to 125 microns at 14 mm. For the sparse array, secondary lobes were suppressed by more than 60 dB over the entire 8 mm region, whereas the fully active array produced secondary lobes that were suppressed to -60 dB lobes only at depths greater than 10 mm. Obtaining better lateral resolution is always desirable in ultrasound imaging. The lateral resolution of an ultrasound imaging system is inversely proportional to the aperture of the transducer. For a linear/phased array, there is a linear relationship between the aperture and number of array elements. If the number of elements is doubled, the image resolution will improve by a factor of two. For an annular array, the aperture is proportional to the square-root of the number of elements. Therefore, four times the number of elements are required for a two times improvement in lateral resolution. Unfortunately, if the aperture is increased by simply enlarging the area of the array elements, higher secondary lobes will result. We have developed an annular array design that allows for a significant improvement in lateral resolution, without a corresponding increase in the number of elements or level of secondary lobes. Instead of expanding the aperture by increasing the area of the array elements, the space between the elements is enlarged. The resulting sparse array provides improved resolution and since the amplitude of secondary lobes is primarily determined by the area of the elements, an increase in the level of secondary lobes is avoided. II. THEORY The transient radiation pattern of an annular array can be calculated very efficiently using the impulse response method (1). The pressure p(r,t) produced by an ultrasound transducer at a location r can be calculated from: p(r,t) = pulse(t) * h(r,t) (1) The function pulse(t) contains information about the electromechanical response of the transducer. For most calculations it is adequate to define pulse(t) using a simple analytical expression chosen to reflect the shape and bandwidth of the anticipated experimental pulse. In the calculations performed throughout paper, pulse(t) is defined using a Gaussian modulated sinusoid with 50% bandwidth. The second function h(r,t) is called the spatial impulse response of the transducer. The spatial impulse response contains all the amplitude and phase information associated with the geometry of the array. In order to calculate the spatial impulse response for an annular array with transmit focusing, the impulse responses from individual annuli are delayed by the appropriate transmit delays and then summed. Similarly, to model the effect of receive beamforming, the impulse responses from different annuli are delayed using the appropriate receive delays and summed. The two-way response is found by convolving the total transmit impulse response with the total receive impulse response, and then convolving the result with a function representing the two-way electromechanical response of the transducer. The convolution result is demodulated and the peak amplitude is plotted in dB relative to the central axis. If this is repeated for different target locations, a cross-section of the two-way radiation pattern can be created at a chosen depth. The aperture size, frequency, focal distance, number