Efficient computation of delay law for imaging structure with a complex surface

Ultrasonic array immersion inspection can be used for detecting defects in a structure with a complex surface, where a liquid coupling layer is used to couple ultrasonic waves from an array probe into the solid structure. In order to increase imaging speed, this paper presents an efficient way to compute delay laws without compromising the measurement accuracy. In the proposed imaging process, the surface geometry is first measured by forming an image in the couplant layer. This leads to a set of discrete points that define the surface profile of the structure. The propagation delay from an array element to a point in the structure is determined by a grid search of candidate ray-path through each surface point to identify the one that yields the shortest travelling time according to Fermat's principle. Time delays in the structure are first generated on a coarse mesh and then these values are linearly interpolated to find the time delays to each image pixel. The computed delay laws are finally used to reconstruct the structure image. An analytical model is developed to build the relationship between estimated delay law errors and array inspection configuration. The proposed analytical model of delay law error is validated by the experimental results. The finding is that, for the normal incident immersion inspection of a 65 mm thick Aluminum sample with a 0.03 mm^-1 curved surface using 5 MHz ultrasonic arrays, a surface can be adequately described by points spaced at 1 mm and that delay laws can be computed on a grid spaced at 3 mm. With these parameters, the reduction in amplitude of a point target in the structure can be guaranteed to be less than 1 dB.