Variance of the Ultrasonic Signal from a Defect Beneath a Rough Surface
Rough surfaces degrade phase-sensitive ultrasonic immersion inspections differently depending on the relative size of the transducer, the wavelength, the rms height and the correlation length of the roughness, as well as the size and shape of the defect. In a series of papers, the present authors, often in collaboration with P. B. Nagy, have examined the effects of surface roughness on ultrasonic inspections; see e.g. [1–3]. In these papers, we simplified the problem by computing the average signal; obtained, in principle, by measuring the same defect beneath many different realizations of the rough surface. Of course, an inspector is interested in one particular signal from a defect beneath one particular surface. An interesting question is “When will the average signal be useful for describing the observations of the inspector?” Consider the two following extreme examples, which are based on the fact that the average signal will be greatly reduced by roughness when δk h > 1, where h is the rms height of the roughness and δk is the change in wavenumber upon crossing the surface. First, suppose that the correlation length, L, is relatively small. In this case, roughness changes the phase of the wavefront independently in many small regions (of size L 2) within the footprint of the transducer on the part’s surface. Since the signal is based on the addition of random changes in the phase from each of these regions, the amplitude of the inspector’s observed signal will be close to the average signal. For the second example, suppose that the correlation length is relatively large. In this case, there will be relatively few regions of size L 2 within the footprint of the transducer. Consequently, there will be large variations in the observed signal due to the statistics of small numbers.