28 S. Yoshida et al. the nodes of the oscillation can be identified as dark fringes as the displacement on the node is always zero. By subtracting an image taken at a time step from the one taken another time step, we can form dark fringes at the nodes. If the frame rate is synchronized with the oscillation frequency, the bright fringe has a constant intensity and thereby we can analyze the intensity profile of the fringe image quantitatively. Low frequency phase noise compromises the quality of the fringe pattern generated by AF-ESPI. Here the word low frequency is used to mean phase noise comparable to the digital camera’s frame rate. If the phase noise changes the phase of the interferometric image between the two time steps used for the fringe formation, the dark fringe location is shifted. We need some measure to remove or compensate such phase noise. We previously developed an interferometric technique to characterize the adhesion property of a thin-film to the substrate [3, 4]. The thin-film specimen was oscillated sinusoidally with an acoustic transducer and the resultant oscillation amplitude was read out interferometrically. With an algorithm analogous to AF-ESPI, the oscillation amplitude can be estimated from the contrast of the interferometric fringe pattern. In the course of this development, we noticed that low frequency noise due to environmental factors such as ambient air temperature fluctuation could considerably compromise the accuracy of the measurement. We also found that the analysis in the spatial frequency domain could significantly reduce the influence of low frequency phase noise. The aim of this paper is to discuss low frequency phase noise and a way to reduce it. Data from the interferometric experiment for the above thin film adhesion characterization is used but the argument being made is applicable to other interferometric methods in general. The nature of low frequency phase noise is discussed in general. The reduction in low frequency phase noise by means of introduction of carrier fringes and frequency domain analysis is discussed. 5.2 Michelson Interferometer 5.2.1 One-Dimensional, Time Dependent Phase Analysis Figure 5.1 illustrates a typical Michelson-type interferometer. Laser light is split with a beam splitter into the reference arm and signal arm. The laser beam in the reference arm is reflected off a mirror and the laser beam in the signal arm is reflected off the surface of a specimen (in this study a thin film coated on a silicon substrate). An acoustic transducer attached to the specimen at the rear surface oscillates the specimen sinusoidally at a frequency set by the function generator. A fast photodiode placed behind the beam splitter can be used to detect the signal arm length change due to the film surface oscillation as the corresponding relative optical phase difference. The light intensity behind the beam splitter can be expressed as follows. I.t/ D2I0 C2I0 cosŒk.lso lro/ Ckdsin!t D2I0 C2I0 cosŒıo Cısin!t (5.1) Here I0 is the intensity of the reference and signal beams, k is the wave number of the laser light in (rad/m), lso and lro are the initial (physical) length of the signal and reference arms, ıo Dlso lro is the arm length difference, ıDkd and d are the oscillation amplitude of the specimen surface in (rad) and (m), and ! is the oscillation (driving) angular frequency of the specimen. Here the reference and signal beams are the non-interfering light beams in the reference and signal arms, Fig. 5.1 Michelson interferometer
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