**4. Conclusion**

in this frequency range, the transfer function represents the elastic property of the film-substrate interface. The lower the spectrum peak the greater the oscillation on the film surface,

The transfer function shown in **Figure 14** is obtained for five rows near the vertical center of the fringe image. By repeating the same procedure for other rows, it is possible to draw a map of the transfer function. **Figure 15** shows a three-dimensional map obtained in this fashion for four specimens; the untreated, treated, and bare silicon specimens. Here one horizontal axis is the row number and the other horizontal axis is the driving frequency. The top two plots are the cases when silicon substrates only are used (called the bare silicon specimens), and the bottom two plots are cases when the treated and untreated specimens are used. The treated and untreated specimens are attached to two different acoustic transducers. To eliminate the effect associated with the use of the different transducer, one bare silicon specimen is attached to the same transducer as the treated specimen and the other bare silicon specimen is attached

which can be interpreted as the greater oscillation of the interface.

78 Optical Interferometry

to the other transducer used for the untreated specimen.

**Figure 15.** Fourier spectrum peak for several rows as a function of driving frequency.

The two plots for the bare silicon specimens appear to be flat, indicating that the bare silicon specimens do not have clear frequency dependence in the oscillation. On the other hand, the An optical interferometric method to characterize the elastic behavior of the interface of thinfilm systems is discussed. The thin-film specimen is configured as one of the end-mirrors of a Michelson interferometer with the film side facing the beam splitter. The specimen is oscillated sinusoidally with an acoustic transducer. The harmonic response of the film surface to the acoustic oscillation is detected as relative optical phase difference between the two interferometric arms. An algorithm to estimate the amplitude of the film surface oscillation from the relative optical phase measurement is discussed.

Environmental noise that compromises the relative phase measurement is analyzed. The use of a carrier fringe system in conjunction with analysis in the spatial frequency domain is proposed as a method to reduce the influence of environmental noise is discussed. Under some conditions, the effectiveness of the proposed method is demonstrated with experiment.

A sample set of data obtained with Pt-Ti-Si thin-film system is presented. The three-dimensional mapping of the adhesion strength obtained with the carrier fringe method indicates some behavior of the film surface that can be interpreted as representing the so-called blister effect. It is interesting to note that the blister-like behaviors observed in the surface-treated and non-treated specimen are different from each other. This observation is of particular interest to us as non-destructive evaluation of the blister effect is not easy. More investigation is under way.
