Experimental Determination of the Ultrasonic Echo from a Pointlike Reflector Using a Tomographic Approach

One important parameter for an ultrasonic transducer is the echo it yields from a pointlike reflector. It can be measured directly but there are however certain problems connected with this. This reflector must have such a size that it can be considered a point, which results in a very weak echo and consequently a low SNR. We propose an alternative method to calculate the echo from a pointlike reflector by measuring the echoes from sliding halfplanes. Using a tomographic way of reasoning, we can calculate the single point echo from these measurements. Our approach was to find basis functions that are suitable for the inversion of the measurements. These basis functions depend on which norm and weight function you choose. Numerical solutions are given for chosen weight functions and the inversion is shown for the measurements.