Design of multi-frequency acoustic kinoforms

Complex diffraction limited acoustic fields can be generated from a single element transducer using inexpensive 3-D printable acoustic kinoforms. This is extremely promising for a number of applications. However, the lack of ability to vary the field limits the potential use of this technology. In this work, this limitation is circumvented using multi-frequency acoustic kinoforms for which different acoustic fields are encoded onto different driving frequencies. An optimisation approach based on random downhill binary search is introduced for the design of the multi-frequency kinoforms. This is applied to two test cases to demonstrate the technique: a kinoform designed to generate the numerals “1,” “2,” and “3” in the same plane but at different driving frequencies, and a kinoform designed to generate 3 sets of eight foci lying on a circle with a driving-frequency-dependent radius. Field measurements from these samples confirmed that multi-frequency acoustic kinoforms can be designed that switch between different arbitrary, pre-designed, acoustic field patterns in the target plane by changing the driving frequenc

Advanced photoacoustic image reconstruction using the k-Wave toolbox

Reconstructing images from measured time domain signals is an essential step in tomography-mode photoacoustic imaging. However, in practice, there are many complicating factors that make it difficult to obtain high-resolution images. These include incomplete or undersampled data, filtering effects, acoustic and optical attenuation, and uncertainties in the material parameters. Here, the processing and image reconstruction steps routinely used by the Photoacoustic Imaging Group at University College London are discussed. These include correction for acoustic and optical attenuation, spatial resampling, material parameter selection, image reconstruction, and log compression. The effect of each of these steps is demonstrated using a representative in vivo dataset. All of the algorithms discussed form part of the open-source k-Wave toolbox (available from http://www.k-wave.org)

ElasticMatrix: A MATLAB toolbox for anisotropic elastic wave propagation in layered media

Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with boundary conditions imposed at each interface. While these methods are well-known, coding the required matrix formation, inversion, and analysis for general multi-layered systems is non-trivial and time-consuming. Here, a new open-source toolbox called ElasticMatrix is described which solves the problem of acoustic and elastic wave propagation in multi-layered media for isotropic and transverse-isotropic materials where the wave propagation occurs in a material plane of symmetry. The toolbox is implemented in MATLAB using an object oriented programming framework and is designed to be easy to use and extend. Methods are provided for calculating and plotting dispersion curves, displacement and stress fields, reflection and transmission coefficients, and slowness profiles

Quantifying Numerical Errors in the Simulation of Transcranial Ultrasound using Pseudospectral Methods

Effective transcranial transmission of focused ultrasound is desirable for various therapeutic applications. Time-reversal (TR) focusing based on numerical simulations of ultrasound propagation can be used to correct for the aberrating skull layer. For weakly heterogeneous media, k-space and pseudospectral time domain (PSTD) methods have been shown to have increased accuracy and efficiency compared to the finite-difference time domain (FDTD) methods typically used in TR. However, their suitability for highly heterogeneous, transcranial simulations is less clear. Here, this is established in terms of spatial and temporal sampling requirements through numerical testing and comparison with FDTD schemes. PSTD schemes are shown to give equal or better accuracy compared to FDTD schemes for modelling propagation through tissue-realistic heterogeneities, which, combined with the reduction in numerical dispersion obtained with k-space correction, recommends them for use in simulated TR

Stackable acoustic holograms

Acoustic holograms can be used to form complex distributions of pressure in 3D at MHz frequencies from simple inexpensive ultrasound sources. The generation of such fields is vital to a diverse range of applications in physical acoustics. However, at present, the application of acoustic holograms is severely hindered by the static nature of the resulting fields. In this work, it is shown that by intentionally reducing the diffraction efficiency of each hologram, it is possible to create stackable acoustic holograms that can be repositioned to reconfigure the combined acoustic field. An experimental test-case consisting of two holograms, each designed to generate a distinct distribution of acoustic foci, is used to demonstrate the feasibility of this approach. Field scans taken for four different positions of the two holograms confirm that the individual patterns for each hologram can be arbitrary translated relative to one another. This allows for the generation of a much greater range of fields from a single transducer than could be created using a single hologram

Binary Volume Acoustic Holograms

In recent years, high-resolution additive manufacturing has enabled a diverse range of low-cost methods for ultrasonic wave-front shaping. Acoustic holograms, in particular, allow for the generation of arbitrary diffraction-limited acoustic fields at megahertz frequencies from single-element transducers. These are phase plates that function as direct acoustic analogs to thin optical holograms. In this work, it is shown that, by using multiple polymer three-dimensional (3D) printing, two-material (binary) acoustic analogs to "thick"or volume optical holograms can also be generated. First, an analytic approach for designing a volume hologram that diffracts a set of input fields onto a desired set of output fields is briefly summarized. Next, a greedy-optimization approach based on random downhill binary search able to account for the constraints imposed by the chosen fabrication method is introduced. Finally, an experimental test case designed to diffract the field generated by a 2.54-cm planar lead zirconate titanate (PZT) transducer onto eight distinct patterns dependent on the direction of the incident field is used to validate the approach and the design method. Field scans of the eight target fields demonstrate that acoustic analogs of optical volume holograms can be generated using multipolymer printing and that these allow the multiplexing of distinct fields onto different incident field directions

A Monitor Function for Spectral Moving Mesh Methods Applied to Nonlinear Acoustics

Spectral methods have made linear acoustics simulations highly computationally efficient, but they currently lose their efficiency when modelling nonlinear waves with regular grids. Moving mesh methods can address this by distributing mesh nodes to minimise the number of nodes needed to represent a waveform. In this paper, a monitor function is presented which is designed specifically for spectral moving mesh methods. In comparison with past monitor functions, this new monitor function significantly improves the convergence rate of the spectral moving mesh method when applied to Burgers’ equation

Generating arbitrary ultrasound fields with tailored optoacoustic surface profiles

Acoustic fields with multiple foci have many applications in physical acoustics ranging from particle manipulation to neural modulation. However, the generation of multiple foci at arbitrary locations in three-dimensional is challenging using conventional transducer technology. In this work, the optical generation of acoustic fields focused at multiple points using a single optical pulse is demonstrated. This is achieved using optically absorbing surface profiles designed to generate specific, user-defined, wavefields. An optimisation approach for the design of these tailored surface profiles is developed. This searches for a smoothly varying surface that will generate a high peak pressure at a set of target focal points. The designed surface profiles are then realised via a combination of additive manufacturing and absorber deposition techniques. Acoustic field measurements from a sample designed to generate the numeral “7” are used to demonstrate the design method

Single Pulse Illumination of Multi-Layer Photoacoustic Holograms for Patterned Ultrasound Field Generation

A new method for the creation of patterned, focused, optically generated acoustic fields using a single optical pulse is introduced. This utilises multi-layer `holograms' composed of several spatially separate absorbing layers. Each layer is individually patterned so as to focus at a set of targeted points. To create the patterns, a ray-tracing model was implemented to calculate the impulse response of pixels within each absorbing layer to a set of targeted points. An optimisation approach was then used to find the optimal pattern for each layer to create a field evenly focused at each of the target points. The method was validated using both numerical simulations and acoustic field measurements. It was demonstrated that a 3×3 array of acoustic foci could be generated from a 3-layer hologram using a single laser pulse

Control of broadband optically generated ultrasound pulses using binary amplitude holograms

In this work, the use of binary amplitude holography is investigated as a mechanism to focus broadband acoustic pulses generated by high peak-power pulsed lasers. Two algorithms are described for the calculation of the binary holograms; one using ray-tracing, and one using an optimization based on direct binary search. It is shown using numerical simulations that when a binary amplitude hologram is excited by a train of laser pulses at its design frequency, the acoustic field can be focused at a pre-determined distribution of points, including single and multiple focal points, and line and square foci. The numerical results are validated by acoustic field measurements from binary amplitude holograms, excited by a high peak-power laser