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Ray tracing boudary value problems: simulation and SAFT reconstruction for ultrasonic testing
(2016)
The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave propagation through the material, in particular travel times between two points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points. In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the eikonal equation. The implementation of such a two point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools. As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value problem allows a straightforward derivation of the ray path from a given transducer position to any pixel in the reconstruction area and reduces the computational cost considerably.
Electromagnetic waves with frequencies between 0.1 and 10 THz are described as THz-radiation (T-ray). The ability to penetrate dielectric materials makes T-rays attractive to reveal discontinuities in polymer and ceramic materials. THz-Time Domain Spectroscopy Systems (THz-TDS) are available on the market today which operates with THz-pulses transmitted and received by optically pumped semiconductor antennas. In THz-TDS the travelling time (ToF) and shape of the pulse is changed if it interacts with the dielectric material and its inherent disconti-nuities. A tomogram of the object under the test can be reconstructed from time of flight diffraction (ToFD) scans if a synthetic focusing aperture (SAFT) algorithm is applied. Otherwise, planar discontinuities like cracks in plastics or delaminated lay-ers in composites can be abstracted as layers located at any angle in relation to the outer sample surface direction. A tomogram from the scanned sample can then be reconstructed in case the interactions of electromagnetic pulses with the existing in-herent interfaces are detectable and a model is assumed which describes the device under the test as multilayer structure composed of thin layers with different dielec-tric properties.
A short description of both the SAFT – and Optical Layer algorithm for the recon-struction of the inherent structure is initially given. Measurements on representative samples with a variety of artificially produced small and large scale. Reconstructed tomograms are presented to discuss and evaluate the benefits and limits of the two different reconstruction approaches.