High resolution low frequency ultrasonic tomography

Ultrasonic reflection tomography results from a linearization of the inverse acoustic scattering problem, named the inverse Born approximation. The goal of ultrasonic reflection tomography is to obtain reflectivity images from backscattered measurements. This is a Fourier synthesis problem and the first step is to correctly cover the frequency space of the object. For this inverse problem, we use the classical algorithm of tomographic reconstruction by summation of filtered backprojections. In practice, only a limited number of views are available with our mechanical rig, typically 180, and the frequency bandwidth of the pulses is very limited, typically one octave. The resolving power of the system is them limited by the bandwidth of the pulse. Low and high frequencies can be restored by use of a deconvolution algorithm that enhances resolution. We used a deconvolution technique based on the Papoulis method. The advantage of this technique is conservation of the overall frequency information content of the signals. The enhancement procedure was tested by imaging a square aluminium rod with a cross-section less than the wavelength. In this application, the central frequency of the transducer was 250 kHz so that the central wavelength was 6 mm whereas the cross-section of the rod was 4 mm. Although the Born approximation was not theoretically valid in this case (high contrast), a good reconstruction was obtained.