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

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

A flat acoustic lens to generate a Bessel-like beam.

The interest in tailoring light in all its degrees of freedom is steadily gaining traction, driven by the tremendous developments in the toolkit for the creation, control and detection of what is now called structured light. Because the complexity of these optical fields is generally understood in terms of interference, the tools have historically been linear optical elements that create the desired superpositions. For this reason, despite the long and impressive history of nonlinear optics, only recently has the spatial structure of light in nonlinear processes come to the fore. In this review we provide a concise theoretical framework for understanding nonlinear optics in the context of structured light, offering an overview and perspective on the progress made, and the challenges that remain. 

https://www.oejournal.org/data/article/export-pdf?id=62b2cbe299d8816244ff952c

Nonlinear optics with structured light

The second-harmonic generation with laser beams transformed by internal conical refraction in a biaxial crystal was studied in a cascaded two-crystal arrangement, where the biaxial crystal transformed the input Gaussian beam and another nonlinear crystal was used for frequency doubling of the produced conical refraction pattern. Several specific second-harmonic beam profiles obtained for various positions of the nonlinear crystal along the beam propagation direction are considered and discussed.

Frequency doubling with laser beams transformed by conical refraction in a biaxial crystal

Limited-diffraction beams are a class of waves that may be localized in space and time. Theoretically, these beams are propagation invariant and can propagate to an infinite distance without spreading. In practice, when these beams are produced with wave sources of a finite aperture and energy, they have a very large depth of field, meaning that they can keep a small beam width over a large distance. Because of this property, limited-diffraction beams may have applications in various areas such as medical imaging and tissue characterization. In this paper, fundamentals of limited-diffraction beams are reviewed and the studies of these beams are put into a unified theoretical framework. Theory of limited-diffraction beams is further developed. New limited-diffraction solutions to Klein-Gordon Equation and Schrodinger Equation, as well as limited-diffraction solutions to these equations in confined spaces are obtained. The relationship between the transformation that converts any solutions to an (-1)-dimensional wave equation to limited-diffraction solutions of an -dimensional equation and the Lorentz transformation is clarified and extended. The transformation is also applied to the Klein-Gordon Equation. In addition, applications of limited-diffraction beams are summarized.

Ultrasonic Imaging with Limited‐Diffraction Beams

We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order 2 n, and that the axial pressure amplitude is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.

Desheng Ding

Papers

Second-harmonic generation of the nth-order Bessel beam.