A computationally efficient method for the calculation of the transient field of acoustic radiators

Lee, Chankil; Benkeser, P.J.

doi:10.1121/1.410439

Cited by 9 publications

(8 citation statements)

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“…results from the combination of the Hooke's law: (2) with the general motion equation: is the stiffness matrix with the elastic constants ij c (e.g. [10]).…”

Section: A Approachmentioning

confidence: 99%

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Four-dimensional directivity pattern for fast calculation of the sound field of a phased array transducer

Voelz

2012

2012 IEEE International Ultrasonics Symposium

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A new approach is presented for an efficient calculation of the complete four-dimensional wave propagation in a transversely isotropic elastic half-space excited by a normal oriented impulsive point force. The sound field will be represented by the dynamic Green's functions for the particle displacement. The Green's functions will be derived by a solution of the elastodynamic wave equation with integral transform methods applying the Cagniard-de Hoop-method.We transform the Green's functions into a four-dimensional directivity pattern by normalizing the time axis. The formulation of the directivity pattern provides a very short calculation time for the complete four-dimensional sound field of a rectangular transducer element of a phased array probe using a point source synthesis. The calculation results in a complete transient time function for the three spatial directions of the particle movement in each point of the half-space. The complete time function of the three-dimensional sound field of a phased array transducer can be calculated by a convolution with the measured time function of the probe and the superposition of the delayed sound fields of multiple transducer elements. This approach provides an efficient method for optimizing the delay laws in phased array applications with consideration of all excited wave modes.We present the derivation of the four-dimensional directivity pattern and calculate sample simulations for the sound field of a phased array probe. Further we compare the modeling with the wave propagation in solids measured by an electrodynamic probe.

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“…results from the combination of the Hooke's law: (2) with the general motion equation: is the stiffness matrix with the elastic constants ij c (e.g. [10]).…”

Section: A Approachmentioning

confidence: 99%

“…[2]). Several mathematical models describe the sound field of a point source on the surface of a half-space (e.g.…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional directivity pattern for fast calculation of the sound field of a phased array transducer

Voelz

2012

2012 IEEE International Ultrasonics Symposium

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“…͑2͒ and the derivation is presented in the Appendix. Although it is developed for the linear array with a cylindrically curved surface, the method can be adapted to the cases of circular arrays 28 and transducers with conical and spherical surfaces, 30 or perhaps the case of a transducer with an arbitrarily curved surface. Consider a source with a curved surface S, represented by zϭ f (x,y) under the Cartesian coordinates, as in Sec.…”

Section: The Indirect Angular Spectrum Approachmentioning

confidence: 99%

Extension of the angular spectrum approach to curved radiators

Stepinski

1999

The Journal of the Acoustical Society of America

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The angular spectrum approach ͑ASA͒ is conventionally applied to the evaluation of acoustic fields from planar radiators because it is usually based on the 2-D Fourier transform ͑or the zero-order Hankel transform in the axisymmetrical case͒ which is implemented only in a plane. The present paper is intended to extend the ASA to more general cases where radiators have curved surfaces. For this purpose, two approaches are developed. The first one is the extended ASA and is derived in a general way. From this approach, the angular spectrum of a curved radiator is given by a double integral that does not take the 2-D Fourier transform form, and thus cannot be implemented using 2-D fast Fourier transform ͑FFT͒ but by numerical integration. The second approach is the indirect ASA that gives the angular spectrum via 2-D Fourier transforming an initial field pre-calculated in a plane. The method for calculating the initial field is proposed based on the method developed by Ocheltree and Frizzell for planar sources. An example is given of a linear array with a cylindrically concave surface, and in this case, the angular spectrum ͑the double integral͒ from the extended ASA reduces to a single integral. The angular spectra of the array are calculated using both approaches and compared. The comparison has shown that the angular spectra obtained from both approaches are in excellent agreement. The accuracy and efficiency of the two approaches are studied in the numerical implementation. In this example, the extended ASA has been shown to be more efficient and more accurate than the latter approach. Both approaches can be applied to arbitrarily curved transducers. In the general case where the double integral cannot be reduced to a single integral, the latter approach can be more efficient.

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“…Lockwood and Willette [23] proposed a high-speed solution for computing the SIR in the near field of a baffled planar rectangular transducer. Lee et al [24] suggested a computationally efficient method, but it involves far field approximation. San Emeterio et al [18] proposed a close-form description about the derivation of analytical expressions for the time-domain spatial impulse response of a rectangular piston by considering the projection position of the field point under several conditions.…”

Section: Introductionmentioning

confidence: 99%

A Fast Method to Calculate the Spatial Impulse Response for 1-D Linear Ultrasonic Phased Array Transducers

Zou

Sun

Dong

et al. 2016

Sensors

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A method is developed to accurately determine the spatial impulse response at the specifically discretized observation points in the radiated field of 1-D linear ultrasonic phased array transducers with great efficiency. In contrast, the previously adopted solutions only optimize the calculation procedure for a single rectangular transducer and required approximation considerations or nonlinear calculation. In this research, an algorithm that follows an alternative approach to expedite the calculation of the spatial impulse response of a rectangular linear array is presented. The key assumption for this algorithm is that the transducer apertures are identical and linearly distributed on an infinite rigid plane baffled with the same pitch. Two points in the observation field, which have the same position relative to two transducer apertures, share the same spatial impulse response that contributed from corresponding transducer, respectively. The observation field is discretized specifically to meet the relationship of equality. The analytical expressions of the proposed algorithm, based on the specific selection of the observation points, are derived to remove redundant calculations. In order to measure the proposed methodology, the simulation results obtained from the proposed method and the classical summation method are compared. The outcomes demonstrate that the proposed strategy can speed up the calculation procedure since it accelerates the speed-up ratio which relies upon the number of discrete points and the number of the array transducers. This development will be valuable in the development of advanced and faster linear ultrasonic phased array systems.

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A computationally efficient method for the calculation of the transient field of acoustic radiators

Cited by 9 publications

References 0 publications

Four-dimensional directivity pattern for fast calculation of the sound field of a phased array transducer

Four-dimensional directivity pattern for fast calculation of the sound field of a phased array transducer

Extension of the angular spectrum approach to curved radiators

A Fast Method to Calculate the Spatial Impulse Response for 1-D Linear Ultrasonic Phased Array Transducers

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