Diffraction correction for focused transducers in attenuation measurements in vivo

Diffraction effects are a cause of error when estimating the frequency dependent attenuation of ultrasound in biological tissues in the reflection mode. Comparison of attenuation values estimated in vivo by different investigators using different types of transducers makes calibration and correction for diffraction necessary. In this paper, we present experimental results for in vivo calibration and correction for the diffraction effect for focused transducers. We also study numerically the diffraction filter in a time-frequency representation, and show that for a focused probe, there is a region in the time-frequency domain where the frequency slope of the diffraction filter does not vary with time. The main consequence for in vivo estimation is that for a given probe, it is possible to select both the distance between the region of interest and the probe, and the frequency limits, such that the attenuation thus estimated is unbiased by the diffraction effect. This result, obtained by numerical calculations, is confirmed by experimental calibration of a foam phantom and in vivo muscle.