Synthetic aperture focusing of ultrasonic data from multilayered media using an omega-k algorithm

The synthetic aperture focusing technique (SAFT) is used to create focused images from ultrasound scans. SAFT has traditionally been applied only for imaging in a single medium, but the recently introduced phase shift migration (PSM) algorithm has expanded the use of SAFT to multilayer structures. In this article we present a similar focusing algorithm called multi-layer omega-k (MULOK), which combines PSM and the ω-k algorithm to perform multilayer imaging more efficiently. The asymptotic complexity is shown to be lower for MULOK than for PSM, and this is confirmed by comparing execution times for implementations of both algorithms. To facilitate the complexity analysis, a detailed description of algorithm implementation is included, which also serves as a guide for readers interested in practical implementation. Using data from an experiment with a multilayered structure, we show that there is essentially no difference in image quality between the two algorithms.