Digital Signal Processing Simulations for a 2-D Ultrasonic Array System

A new ultrasonic system based on a 2-D cylindrical array with capability of electronic scanning and 3D beam-forming was developed. Such a system can operate in harsh environments for casing inspection (diameter, ovality, corrosion, thickness, cracks) and for assessment of the material behind casing. The most important challenges of such a system are: (a) operation in highly attenuative media (up to 12 dB/cm/MHz) with ambient conditions of up to 175oC and 1400 bar, (b) the large number of array elements (N=800) and the volume restrictions for the array electronics (around 1000cm 3 ), which requires a high level of integration. The system operates in a frequency band that corresponds to the fundamental thickness resonance of the casing (200 - 700 kHz). Using Sigma Delta modulators (SDM) for mixed signal processing facilitates integration and reduces the number of interconnections. It is well known that increasing the oversampling ratio (OSR) of SDM increases the dynamic range of the signals. The system is limited by the maximum sampling frequency that together with the input frequency of up to 1 MHz defines the OSR. In the paper we present the digital processing algorithms for casing measurements based on the response of an ideal plate, and make a theoretical analysis of the effect of several parameters of the digital processing chain on the casing measurements. We conclude that, in the presence of noise, the averaging effect of the array beamforming greatly improves the measurements, allowing the use of SDM with relatively low OSRs.