Reconstruction of ultrasonic fields by deconvolving the hydrophone aperture effects. I. Theory and simulation.

In many ultrasound applications-especially in the area of medical diagnostics-conventional sensors and particularly piezoelectric hydrophones do not comply with the requirements for "point detectors". It therefore suggests itself to develop methods, which allow ultrasonic fields to be reconstructed from the spatially averaged measurement values with the necessary spatial resolution. In this publication, this task will be treated as an inverse problem. It will be shown by simulations that it is possible with the aid of reconstruction methods to invert the aperture effects of the sensor. Three different reconstruction methods are tested: (1) Wiener's method furnishes the best approximation of the field to be reconstructed in the sense of the minimum mean square error. (2) The power spectral equalization method is based on equalization between the spatial power spectral densities of the field to be reconstructed and that of its estimated value. (3) With the maximum a-posteriori method, the maximum a-posteriori probability density function for the reconstructed field is searched. The results of this paper show that the quality of reconstruction depends on the signal-to-noise ratio (SNR) and the spatial frequency bandwidth of the sound field investigated. Good quality reconstructions were obtained at correlation coefficients larger than 0.995 and an SNR of at least 40 dB. In general, the quality of reconstruction decreases with decreasing SNR and is unacceptable at SNR = 20 dB. The quality also decreases with decreasing axial distance from the source that is with increasing spectral frequency bandwidth.