Generalised bisection method for optimum ultrasonic ray tracing and focusing in multi-layered structures

Ultrasonic testing has been used for many decades, proving itself very efficient detecting defects in industrial sectors. The desire to apply ultrasonic geometrically complex structures, and anisotropic, inhomogeneous materials, together with the advent of more powerful electronics software, is constantly pushing applicability waves their limits. General ray tracing models, suitable calculating proper incident angle single element probes time delay phased array, are currently required. They can support development new imaging techniques, as Full Matrix Capture Total Focusing Method, execution challenging inspections. This paper introduces a generalized iterative method computation paths, when source target separated by multiple material interfaces two dimensional three domains. manuscript starts review well-known bisection method, extends cases increasing complexity. An application example, field in-process weld inspection, shows that introduced generalised enable optimum incidence angles focal delays accurate focusing. There no restriction on analytical be surjective. Interface folding permitted. It not necessary know, priori, what sequence crossed rays. presented implementation completes each iteration 4 ms, case interface, 960 ms 52 interfaces.