Jian-yu Lu

Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations

The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J/sub 0/ Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed.<<ETX>>

Ultrasonic nondiffracting transducer for medical imaging

The nondiffracting J/sub 0/ Bessel beam is evaluated, and its application to medical imaging is suggested. Computer simulations and experimental results for a ten-ring annular Bessel shaded transducer are described. Both continuous-wave (CW) and pulse-wave (PW) excitations are shown and compared to conventional Gaussian beams. The nondiffracting beam has about 1.27-nm radius main lobe with a 20-cm depth of field compared to the Gaussian transducer of the same size with a 1.27-mm radius main lobe at a focus of 12 cm and 2*4-cm depth of field. The side lobes of the nondiffracting beam are the same as the J/sub 0/ Bessel function. The effects of heterogeneity due to tissue on the nondiffracting beam and on the focused Gaussian beam are also reported.<<ETX>>

Experimental verification of nondiffracting X waves

The propagation of acoustic waves in isotropic/homogeneous media and electromagnetic waves in free space is governed by the isotropic/homogeneous (or free space) scalar wave equation. A zeroth-order acoustic X wave (axially symmetric) was experimentally produced with an acoustic annular array transducer. The generalized expression includes a term for the frequency response of the system and parameters for varying depth of field versus beam width of the resulting family of beams. Excellent agreement between theoretical predictions and experiment was obtained. An X wave of finite aperture driven with realizable (causal, finite energy) pulses is found to travel with a large depth of field (nondiffracting length).<<ETX>>

2D and 3D high frame rate imaging with limited diffraction beams

A new 2D (two-dimensional) and 3D (three-dimensional) pulse-echo imaging method (Fourier method) has been developed with limited diffraction beams. In this method, a plane wave pulse (broadband) is used to transmit and limited diffraction beams of different parameters are used to receive. Signals received are processed to obtain spatial Fourier transform of object functions and images are constructed with an inverse Fourier transform. Because only one transmission is required to construct images, this method may achieve a high frame rate (up to 3750 frames/s for biological soft tissues at a depth of 200 mm). To demonstrate the efficacy of the method, both 2D C-mode and 3D images have been simulated using conditions that are typical for medical ultrasound. Results show that images of high resolutions (about 6 wavelengths at 200 mm) and low sidelobes (around -60 dB) can be constructed over a large depth of interest (30 to 200 mm) with a 50 mm diameter aperture. Experiments with the new method have also been carried out. 2D B-mode images have been constructed with conventional linear arrays. In the experiment, an ATS 539 tissue-equivalent phantom and two linear arrays were used. The first array had a center frequency of 2.25 MHz, dimension of 18.288 mm/spl times//spl times/12.192 mm, and 48 elements. The second had a center frequency of 2.5 MHz, 38.4 mm/spl times/10 mm in dimension, and 64 elements. Images of different fields of views were constructed from RF data acquired with these arrays using both the new and conventional dynamic focusing (delay-and-sum) methods. Results show that qualities of images constructed are almost identical with the two methods in terms of sidelobes, contrast, and lateral and axial resolutions. Phase aberration has also been assessed for the two methods, and results show that its influence is about the same on both methods. In addition, a practical imaging system to implement the new method is suggested and potential applications of the method are discussed.

Biomedical ultrasound beam forming

The principles of biomedical ultrasound beam forming control the quality of diagnostic imaging. Beam parameters associated with imaging quality are: (1) lateral and axial resolutions; (2) depth of field; (3) contrast and (4) frame rate. In this paper, we review some of the current beam forming techniques and their principles. We focus on trade-offs among the above four aspects of beam forming and relate them to system parameters such as aperture size, f-number (the ratio between focal length and aperture diameter), central frequency (wavelength), system bandwidth and sidelobes. Methods for steering conventional and limited diffraction beams with array transducers are also reviewed.

Experimental study of high frame rate imaging with limited diffraction beams

Limited diffraction beams have a large depth of field and have many potential applications. Recently, a new method (Fourier method) was developed with limited diffraction beams for image construction. With the method and a single plane wave transmission, both 2D (two-dimensional) and 3D (three-dimensional) images of a very high frame rate (up to 3750 frames/s for a depth of 200 mm in biological soft tissues) and a high signal-to-noise ratio (SNR) can be constructed with relatively simple and inexpensive hardware. If limited diffraction beams of different parameters are used in both transmission and reception and transducer aperture is shaded with a cosine function, high-resolution and low-sidelobe images can be constructed with the new method without montage of multiple frames of images [the image quality is comparable to that obtained with a transmit-receive (two-way) dynamically focused imaging system]. In this paper, the Fourier method was studied with both experiment and computer simulation for 2D B-mode imaging. In the experiment, two commercial broadband 1D array transducers (48 and 64 elements) of different aperture sizes (18.288 and 38.4 mm) and center frequencies (2.25 and 2.5 MHz) were used to construct images of different viewing sizes. An ATS539 tissue-equivalent phantom of an average frequency-dependent attenuation of 0.5 dB/MHz/cm was used as a test object. To obtain high frame rate images, a single plane wave pulse (broadband) was transmitted with the arrays. Echoes received with the arrays were processed with both the Fourier and conventional dynamic focusing (delay-and-sum) methods to construct 2D B-mode images. Results show that the quality (resolution and contrast) of constructed images is virtually identical for both methods, except that the Fourier method is simpler to implement. Both methods have also a similar sensitivity to phase aberration distortions. Excellent agreement among theory, simulation, and experiment was obtained.

Extended high-frame rate imaging method with limited-diffraction beams

Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging

High frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings high frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings

A general-purpose high frame rate (HFR) medical imaging system has been developed. This system has 128 independent linear transmitters, each of which is capable of producing an arbitrary broadband (about 0.05-10 MHz) waveform of up to plusmn144 V peak voltage on a 75-ohm resistive load using a 12-bit/40-MHz digital-to-analog converter. The system also has 128 independent, broadband (about 0.25-10 MHz), and time-variable-gain receiver channels, each of which has a 12-bit/40-MHz analog-to-digital converter and up to 512 MB of memory. The system is controlled by a personal computer (PC), and radio frequency echo data of each channel are transferred to the same PC via a standard USB 2.0 port for image reconstructions. Using the HFR imaging system, we have developed a new limited-diffraction array beam imaging method with square-wave aperture voltage weightings. With this method, in principle, only one or two transmitters are required to excite a fully populated two-dimensional (2-D) array transducer to achieve an equivalent dynamic focusing in both transmission and reception to reconstruct a high-quality three-dimensional image without the need of the time delays of traditional beam focusing arid steering, potentially simplifying the transmitter subsystem of an imager. To validate the method, for simplicity, 2-D imaging experiments were performed using the system. In the in vitro experiment, a custom-made, 128-element, 0.32-mm pitch, 3.5-MHz center frequency linear array transducer with about 50% fractional bandwidth was used to reconstruct images of an ATS 539 tissue-mimicking phantom at an axial distance of 130 mm with a field of view of more than 90deg. In the in vivo experiment of a human heart, images with a field of view of more than 90deg at 120-mm axial distance were obtained with a 128-element, 2.5-MHz center frequency, 0.15-mm pitch Acusori V2 phased array. To ensure that the system was operated under the limits set by the U.S. Food and Drug Administration, the mechanical index, thermal index, and acoustic output were measured. Results show that higher-quality images can be reconstructed with the square-wave aperture weighting method due to an increased penetration depth as compared to the exact weighting method developed previously, and a frame rate of 486 per second was achieved at a pulse repetition frequency of about 5348 Hz for the human heart

Pulse-echo imaging using a nondiffracting beam transducer

Conventional ultrasonic transducers generate beams that diffract as they travel. This phenomenon causes images produced in B-mode to be degraded in the far-field of the transducers. Focused transducers are used to improve image quality. Unfortunately, focused transducers have short depth of field. Although multiple pulse transmissions focused at several depths are used to increase the effective depth of field, imaging frame rate is reduced dramatically leading to blurred images of moving objects such as the heart. We present a family of transducers that produce nondiffracting beams of large depth of field. Therefore, uniformly high resolution throughout the imaging area can be obtained without sacrificing the imaging frame rate. In addition, the nondiffracting property of these beams makes the correction for beam diffraction negligible in tissue characterization. This paper reports the results of computer simulations as well as in vitro and in vivo pulse-echo imaging experiments with a nondiffracting transducer. Images are compared to those obtained by conventional focused Gaussian shaded beam transducers and a commercial ACUSON 128 B-scanner. The new transducer has much longer depth of field with higher sidelobes than conventional transducers of the same aperture. Sidelobes can be reduced using the new transducer to transmit and the dynamically focused transducer to receive.

A study of two-dimensional array transducers for limited diffraction beams

The newly developed limited diffraction beams such as the Bessel beams and X waves have a large depth of field and approximate depth-independent property. They have possible applications in medical imaging, color Doppler imaging, tissue characterization, and nondestructive evaluation of materials, and in other wave related physical branches such as electromagnetics and optics. However, limited diffraction beams are currently produced with an annular array transducer that has to be steered mechanically. In this paper, we study the feasibility of steering these beams with a two-dimensional array, and show that there will be almost no distortion of beams if the effective aperture reduction of the array is properly compensated so that the beams have a constant transverse profile as they are steered. In addition, methods for reducing the complexity of the electronic multiplexing of the array elements are proposed. We also investigate the influences of the interelement distance and the size of array elements on the sidelobes and grating lobes of limited diffraction beams as the beams are steered. They are similar to those previously reported for conventional beams.<<ETX>>