Search

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere?s elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation. [ABSTRACT FROM AUTHOR]

A rigorous method is developed to investigate the generation of a negative (attracting) force acting in the opposite direction of wave propagation using a limited-diffracting single annular piezo-ring transducer. Based on the Rayleigh? Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions, the expression for the incident velocity potential field (which is an exact solution of the Helmholtz equation) is derived analytically, and exact closed-form partial-wave series expansions for the incident and scattered fields are obtained without any approximations. The total (incident + scattered) field expression is used to evaluate the time-averaged acoustic radiation force (ARF) on a sphere centered on the beam's axis in a nonviscous fluid. Numerical predictions for the scattering and ARF performed with particular emphasis on the annular-ring's radial thickness, the distance separating the sphere from the acoustic source, the size of the transducer, as well as the sphere's elastic properties, reveal some conditions where a pulling axial ARF directed toward the annular ring-source surface arises. The simplicity and reliability of the annular-ring geometry demonstrated here provides a substantial solution with widespread applications in the experimental design of acoustical limited-diffracting beams operating over an extended axial depth-of-field for contactless and dexterous particle manipulation. [ABSTRACT FROM AUTHOR]

In this paper, the translational addition theorem for spherical functions is employed to calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere arbitrarily suspended in an inviscid fluid. The procedure is also based on the partial-wave expansion method, which depends on the beam-shape and scattering coefficients. Given a set of beam-shape coefficients (BSCs) for an acoustic beam relative to a reference frame, the translational addition theorem can be used to obtain the BSCs relative to the sphere positioned anywhere in the medium. The scattering coefficients are obtained from the acoustic boundary conditions across the sphere's surface. The method based on the addition theorem is particularly useful to avoid quadrature schemes to obtain the BSCs. We use it to compute the acoustic radiation force exerted by a spherically focused beam (in the paraxial approximation) on a silicone-oil droplet (compressible fluid sphere). The analysis is carried out in the Rayleigh (i.e., the particle diameter is much smaller than the wavelength) and Mie (i.e., the particle diameter is of the order of the wavelength or larger) scattering regimes. The obtained results show that the paraxial focused beam can only trap particles in the Rayleigh scattering regime. [ABSTRACT FROM AUTHOR]

The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent. [ABSTRACT FROM PUBLISHER]

Vibroacoustography (VA) is an ultrasound-based modality sensitive to stiffness and free from speckle and possesses some advantages over conventional ultrasound imaging in terms of image quality. The primary objective here is to show its feasibility in detecting/imaging kidney stones (KSs) in vitro . In VA, two intersecting ultrasound beams driven at two different frequencies f_1 and f_2, respectively, are focused within a freshly excised porcine kidney attached to a solid frame with elastic rubber bands, while the amplitude of the acoustic emission pressure field produced at the difference frequency Δ f = \vert f_1 − f_2 \vert is detected by a low-frequency hydrophone. The received low-frequency signal is bandpass filtered and amplified, then digitized by a 14-bits/sample digitizer. The data are then recorded on a computer and processed numerically to construct the images. 2-D magnitude VA images are obtained at different depths within the kidney before and after stone implantation, showing kidney features and stones shapes. Experiments conducted in a water tank on a chalk sphere as well as a series of excised kidneys in which stones are artificially embedded show that all the implanted stones are detected at all chosen depths, when compared with an X-ray fluoroscopy taken to be the reference image. The resulting VA images, obtained from a nonionizing type of radiation (i.e., ultrasound waves) as compared to fluoroscopy, are speckle free unlike conventional ultrasound images. The results presented in this preliminary feasibility study show that VA allows imaging KSs in vitro, and provide the impetus to further develop and investigate VA imaging in a clinical setting for in vivo applications. [ABSTRACT FROM PUBLISHER]