C-mode imaging of reflection ratio on curved surface of bone

An ultrasonic-based method has been proposed for measuring the spatial distribution of reflection ratio on the curved surface of a bone object. This method, employing a two dimensional transducer array, is based on the time reversible symmetry of wave propagation. A scattering matrix is defined for each scatter object from each combination of two transducers in the transducer array. By solving the eigenvalue problem based on the scattering matrix, the reflection ratio on the curved surface of each scatter object is derived. The largest eigenvalue of the scattering matrix corresponds to the reflection ratio when the incident angle of the ultrasound is normal to the object surface. At the same time, the eigenvector corresponds to the signal supplied to transducers which makes the wave front along the curved surface. In the simulation and experiments, the transducers array is 8 by 8 two dimensional transducers. From a theoretical viewpoint and experiments, we conclude that this new method is useful to measure the acoustic impedance of objects with curved surfaces such as spine bones or femurs.