ECHOGRAPHIC DIFFRACTION FILTERS AND THE DIFFRACTION FUNCTION FOR RANDOM-MEDIA THROUGH AN INSTANTANEOUS TIME-FREQUENCY APPROACH

In the estimation of ultrasound attenuation in random scattering media, near-field and near-focus diffraction effects introduce bias because of their depth-dependent filtering behavior. A new approach is proposed that is aimed at the prediction and correction of these effects. It is based on the concept of instantaneous time-frequency representation of random signals, and it leads to a rigorous definition of the echographic diffraction filter. A thorough study is provided of this time-varying filter for axisymmetric planar and focused transducers. In this last case the diffraction filter depends on five parameters (time, frequency, transducer radius, focal length, and sound velocity). Through the study of invariance properties of the diffraction impulse response, it is shown that the five parameters combine into a unique dimensionless variable. Hence the complete diffraction behavior is derived from the knowledge of a universal one-variable function: the diffraction function. The physical origin of this property is discussed and a theoretical study of this function is presented. Also provided is a look up curve and a fitting rational approximation to allow easy diffraction-correction implementation. Experimental calibration of an echographic diffraction filter shows good agreement with the predicted diffraction function.