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Inspection and shape measurement of three-dimensional objects are widely needed in industries for quality monitoring and control. A number of visual or optical technologies have been successfully applied to measure three dimensional surfaces. Especially, the shape measurement using an interferometric principle becomes a successful methodology. However, those conventional interferometric methods to measure surface profile have an inherent shortcoming, namely 2π ambiguity problem. The problem inevitably happens when the object to be measured has discontinuous shape due to the repetition of interferometric signal with phase period of 2π . Therefore, in this paper, we choose as a shape measuring method Wavelength Shifting Interferometer (WSI) in which the absolute distance from the reference surface can be directly obtained from the amount of interferometric phase change. With the above advantage the coplanarity of ball grid array (BGA) can be easily evaluated and inspected, which is the major factor in the BGA surface mounting technology. The WSI is basically composed of a Twyman Green Interferometry and a tunable laser source. The proposed WSI so far by other researchers suffer from low measurement resolution because of the methodological roughness in obtaining interferometric phase change. Therefore, we propose a new algorithm, which can obtain a small amount of even fractional phase change by sinusoidal function fitting. To evaluate the effectiveness of the proposed sinusoidal function fitting algorithm, a series of measurements is conducted for discontinuously shaped specimens which have various heights. The proposed algorithm shows much more enhanced measurement resolution than other existing conventional algorithms such as zero crossing algorithm and Fourier transform algorithm. To measure the three dimensional shape of ball grid array with WSI, a series of simulations was performed for a hemispherical ball model in which the diffuse surface conditions are considered. The simulation results show that the three dimensional shape of a ball can be measured using WSI for purpose of BGA product inspections.
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