(a) Analysis with simple Michelson method

**Figure 5** shows the intensity profiles of the reference and signal beams captured by a CCD placed behind the beam splitter. For the measurement of each profile, the other beam is blocked. Thus, they do not include the interference term in Eq. (1). The reference beam is reflected off the mirror (the Y-end mirror in **Figure 2**) and therefore its profile is Gaussian. The signal beam is reflected off the specimen whose surface is not as flat as the mirror. Consequently, its profile is somewhat deformed. When these intensities are subtracted from Eq. (1) for the evaluation of the relative phase in Eq. (2), this causes some part of the interference beam in its crosssectional area to miss interference. **Figure 6** indicates those non-interfering portion as a dip.

**Figure 5.** Reference and signal beam profiles.

Application of Optical Interferometry for Characterization of Thin-Film Adhesion http://dx.doi.org/10.5772/66205 71

**Figure 6.** Beam profile of interference term.

**3. Experimental results and discussion**

**3.2. Characterization of Michelson interferometer**

(a) Analysis with simple Michelson method

**Figure 5.** Reference and signal beam profiles.

A pair of platinum-titanium (Pt-Ti) coated silicon (Si) thin film specimens is used in the present experiments. The Si substrate is cut along the [1 0 0] plane and 750 μm in thickness. The Ti layer is coated on the Si substrate and the Pt is coated over the Ti layer. The thickness of the Pt and Ti layers are 100 nm and 10 nm, respectively. In one specimen (the treated specimen) of the pair, the Ti layer is coated after the substrate surface is treated with oxygen-plasma bombardment. This treatment makes the Si surface hydrophilic, and therefore strengthens the Ti-Si bond. In the other specimen (the untreated specimen), the Ti layer is coated without a

**Figure 5** shows the intensity profiles of the reference and signal beams captured by a CCD placed behind the beam splitter. For the measurement of each profile, the other beam is blocked. Thus, they do not include the interference term in Eq. (1). The reference beam is reflected off the mirror (the Y-end mirror in **Figure 2**) and therefore its profile is Gaussian. The signal beam is reflected off the specimen whose surface is not as flat as the mirror. Consequently, its profile is somewhat deformed. When these intensities are subtracted from Eq. (1) for the evaluation of the relative phase in Eq. (2), this causes some part of the interference beam in its crosssectional area to miss interference. **Figure 6** indicates those non-interfering portion as a dip.

**3.1. Thin film specimens**

70 Optical Interferometry

surface treatment.

The two profiles in **Figure 6** are taken from the same experiment where the specimen is driven by the acoustic transducer under the same condition; the driving frequency and amplitude being the same. The left and right profiles are obviously different. The left profile indicates that the interference term is positive and the left profile indicates that it is more negative. Since the phase change due to the film surface displacement is not large enough to change the sign of Eq. (6) (i.e., it is unlikely that *J*0(*δ*)<0), it is likely that the difference comes from a change in the reference phase difference (*δ*0 in Eq. (6)).

**Figure 7(a)** shows the interference term as a function of time when the acoustic transducer is on and off. Apparently, the fluctuation is significantly higher when the transducer is on. **Figure 7(b)** is the Fourier transform of **Figure 7(a)**. The peak frequency of the disturbance is less than 1 Hz which is lower than the frame rate of the CCD used in the experiment. This indicates that the phase fluctuation affects the approximated expression Eq. (5) when the transducer is on.

**Figure 7.** Variation of interference term as a function of time (left) and frequency (right).

It is likely that the temperature rise due to heat emitted from the transducer is one of the causes of the phase fluctuation. An independent temperature measurement indicates that the air temperature easily rises over 0.1°C within 1 s after the transducer is turned on, and that the temperature fluctuates by ±0.1°C approximately every few minutes. In one set of measurement in which the transducer is turned on and off every 3 min, a total temperature rise of 0.4°C is recorded over a period of 30 min. It is suspected that air convection causes the temperature fluctuation.

It is informative to make a rough estimate of the phase change due to the above temperature change. The optical phase change due to the temperature dependence of the refractive index of air can be expressed as follows.

$$d\phi = 2\pi \frac{l}{\lambda} \frac{\partial n}{\partial T} dT \tag{8}$$

Here *λ* is the wavelength, *l* is the path length, *n* is the refractive index of air and *dT* is the temperature change. The temperature coefficient ∂*n*/∂*T* of air is −0.87×10−6 (1/°C) [8]. The arm length of the interferometer used in this experiment is 10 (cm). The wavelength of the laser used in this study is 632.8 nm. So, the phase change due to a temperature change of ±0.1°C over the round trip in the interferometric arm is 20 (cm)/632.8 (nm) ×0.87×10−6×0.1=2.75% (of the period 2*π*). Accordingly, the phase error due to the air temperature change of 0.4°C observed over 30 min is 2.75×4 = 11.0% of the period.

The issues of the deformed phase front and the initial phase fluctuation observed in Figures 6 and 7 make it difficult to use Eq. (5) with the total intensity method. In the next section, the carrier fringe method that greatly reduces the influence of the initial phase fluctuation is discussed.
