Quadratic approximation in focusing with linear arrays

Pierre Cervenka (1)

1 DALEMBERT - Institut Jean Le Rond d'Alembert

Imaging systems based on linear arrays with delay-and-sum beamforming require estimating the path differences between each pixel and the array elements. Considering the quadratic approximation, the linear part is related to the steering direction whereas the quadratic term refers to the curvature of the wavefront. The several ways for handling this approximation are presented, e.g., closest second order development for each pixel, paraxial development, Fresnel approximation, down to the Fraunhofer (linear) approximation. The domains of validity of these developments are scarcely described in the literature. They are estimated here by considering the largest error encountered on the array in the path differences. The quadratic approximation is usually considered as not enough efficient in terms of either the computation savings, or the extent of the domains of validity. It is shown that settings of practical interest can be found by optimizing the quadratic coefficient as a function of range. This procedure yields the computation saving of the paraxial approximation, still keeping quite large angular domains of validity. The solutions are conveniently displayed with general graphs where ranges are counted in array lengths, and array lengths are given in wavelength units.

Mots clés: Quadratic approximation; Fresnel approximation; Linear array; Focalization

Domaines: Acoustique [physics.class-ph]

Pierre Cervenka. Quadratic approximation in focusing with linear arrays. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810646⟩