Ultrasonics 38 (2000) 745–748 www.elsevier.nl/locate/ultras Improvement of the lateral resolution of finite-size hydrophones by deconvolution T. Boutkedjirt *, R. Reibold Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany Abstract In various fields of ultrasound applications, frequencies well above 10 MHz are used. As a consequence of this, ultrasound sensors, especially the piezoelectric hydrophones presently available which are used for the characterization of the respective fields, can no longer be considered as point receivers. By means of numerical deconvolution, the adverse averaging effect caused by the finite sensor size can be revoked. The efficiency of the deconvolution process is dealt with for both numerical simulations and experimental investigations. Best results were obtained using a reconstruction filter consisting of a combination of a Wiener filter, a pruning filter and an additional low-pass filter. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Deconvolution; Hydrophone aperture; Sound field reconstruction; Spatial averaging; Spatial resolution 1. Introduction hydrophone size and frequency are chosen to facilitate the comparison of the deconvoluted response of a large- aperture hydrophone with the response of a small- An increasing number of ultrasound applications, especially in medical diagnostics, use frequencies well aperture hydrophone serving as a reference. above 10 MHz. In order to characterize the respective fields, sensors with high spatial resolution are required. With the exception of specific laboratory devices, limits 2. Theory are set to the piezoelectric hydrophones at present available owing to their finite size. Great research effort 2.1. Modelling of the effect of a finite-size hydrophone is being undertaken to develop new types of ultrasound and the sound field reconstruction sensors overcoming these limitations [1,2]. Nevertheless, piezoelectric hydrophones are inexpensive and mature In an earlier paper [4], the averaging effect of a finite- devices which are easy to handle and have found broad size hydrophone on a harmonic sound field and its acceptance in the field. The extension of calibration reconstruction was investigated by means of a one- procedures to higher frequencies is a subject of various dimensional, linear model. Extending this model to two research groups [2,3] and of a new IEC standard. It is dimensions leads to the following expression of the therefore appropriate to consider alternative techniques complex amplitude V(x, y) of the hydrophone output to achieve the spatial resolution required. voltage: In this paper the adverse averaging effect is compen- V(x, y)=H v (x, y)EP(x, y)+N(x, y), (1) sated by numerically deconvoluting the aperture func- tion from the observed response of the finite-size where P (x, y) is the complex pressure amplitude of the receiver. The efficiency of the deconvolution process is investigated sound field. E denotes the two-dimensional shown for both numerical simulations and experimental spatial convolution product and H v (x, y) the spatial investigations. In order to demonstrate experimentally impulse response of the hydrophone for a given angular the potential of the technique, the conditions related to frequency v. N(x, y) is a supposed signal-independent noise. An estimated value P ˆ (x, y) of the sound field pressure * Corresponding author. Fax: +49-0531-592-1015. E-mail address: tarek.boutkedjirt@ptb.de (T. Boutkedjirt) P (x, y) can be retrieved from the output voltage V(x, y) 0041-624X/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0041-624X(99)00227-9