Ultrasonic attenuation measurements at very high SNR: Correlation, information theory and performance

This paper describes a system for ultrasonic wave attenuation measurements which is based on pseudo-random binary codes as transmission signals combined with on-the-fly correlation for received signal detection. The apparatus can receive signals in the nanovolt range against a noise background in the order of hundreds of microvolts and an analogue to digital convertor (ADC) bit-step also in the order of hundreds of microvolts. Very high signal to noise ratios (SNRs) are achieved without recourse to coherent averaging with its associated requirement for high sampling times. The system works by a process of dithering – in which very low amplitude received signals enter the dynamic range of the ADC by 'riding' on electronic noise at the system input. The amplitude of this 'useful noise' has to be chosen with care for an optimised design. The process of optimisation is explained on the basis of classical information theory and is achieved through a simple noise model. The performance of the system is examined for different transmitted code lengths and gain settings in the receiver chain. Experimental results are shown to verify the expected operation when the system is applied to a very highly attenuating material – an aerated slurry.