Evaluation of the transverse oscillation method using the Cramer-Rao lower bound.

The transverse oscillation method enables lateral displacement tracking by generating an oscillation orthogonal to the conventional RF signal. The widely varying methods used in the field to create such oscillations and perform displacement estimation make it difficult to compare the expected performance of alternative techniques. We derive closed-form expressions for the oscillating pressure fields produced by two common apodization functions-the rectangular and bi-lobed Gaussian apodizations-after heterodyning demodulation is applied to separate the orthogonally-oscillating signals. With these fields and spectra we present a form of the Cramer-Rao lower bound for ultrasonic signals that contains a spectrum shape term, allowing theoretical prediction of relative performance across different techniques and parameter choices. Simulations show good agreement with the trends predicted by the theoretical results for the chosen class of aperture functions. The simulations demonstrate the importance of frequency-space analysis in devising a transverse oscillation scheme and suggest that the study of other classes of aperture functions and field formation techniques should be continued to further improve the accuracy of lateral displacement tracking.