Fourier transform approach to materials characterization with the acoustic microscope

Abstract

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Evaluation of Dispersion Modes for Layered Structures Using Focused Acoustic Waves

“…An inversion algorithm between V(z) and R(B) has been mentioned earlier in optics and is further demonstrated in a work of Hildebrand and Liang [6,7] in acoustics for the reflection coefficient function measurement at liquid-solid interface of substrate materials. We here generalize the method for the layered structure problem where the reflection coefficient function R( BJ) is not only an incident angle dependent function but also a frequency dependent one.…”

“…The weighting function can be considered as the multiplication of the direct and inverse pupil function of the acoustic lens and it can be obtained by (5) where F-1 is the inverse Fourier transform operation and Vg(z), called the probe's geometrical response, is a V(z) response corresponding to that obtained from an ideal reflection having R(p) '" 1 for any incident angle and frequency. So we can get the R(P) under normalized form: (6) Knowing that k, = ~ k~ -1[2 p2 and k, = ko sin B, we obtain the reflection coefficient R( B)…”

Confocal Interference Microscopy

“…In acoustic microscopy, the low frequency of the measured signal ensures that the complex amplitude ofthe resulting signal can be measured directly [Hildebrand et al, 1983]. The defocus signal is commonly referred to as V(z), signifying the variation in transducer output-voltage with defocus distance.…”

Investigation of Thin Layers Ceramic Structures Based on Doppler Scanning Acoustic Microscopy

“…To realize this powerful technique, it is necessary to measure both amplitude and phase of the V(z) function. Generally, it is not trivial to measure the phase of high-frequency tone burst signals with accuracy, so a special complicated precision phase measurement system was designed [3].…”

“…To realize this powerful technique, it is necessary to measure both amplitude and phase of the V(z) function. Generally, it is not trivial to measure the phase of high-frequency tone burst signals with accuracy, so a special complicated precision phase measurement system was designed [3].Another approach to obtain both amplitude and phase information, is based on the use of a Continuous Wave Reflection SCanning Acoustic Microscope [4,5]. In this device, the Continuous Wave V(z) curve is defmed as…”