Continuous wavelet transform based nanoscale strain field measurement using Moire interferometry with phase shifting

Moiré Interferometry (MI) provides real-time full strain field measurement for the structure under the dynamic loading. It has been successfully applied to the reliability testing of the electronic packaging under different loadings (e.g. thermal cycling, electrical current stressing and etc). The miniaturization of the microelectronic packaging calls for the operation of MI at a level with higher sensitivity and better resolution. The proposed operation of MI combines two novel methods in the interferometry, phase shifting (PS) and continuous wavelet transform (CWT) to achieve a 164 nm/pixel spatial resolution. The entire operation procedure is completed automatically by computer programs. A two-level zooming system is designed and implemented in MI to give a high spatial resolution. The idea of combination of CWT and PS here is to put both spatial phase calculation and temporal phase calculation together. By introducing both the spatial and temporal redundancy, the authors show that the hybrid methods take the advantages from both of them. Furthermore, the direct calculation of the spontaneous spatial frequency of the interferogram is carried out using the property of the maximum power ridge of CWT. This method doesn't require unwrapping and differentiation, which avoid the possible numerical noise introduced in these two steps. In the proposed system, pixel by pixel in-plane strain tensors can be calculated from the intensity map of interferograms using phase-based method for MI in contrast with the traditional fringe counting. The resulting strain tensor can be used to model constitutive relationship or compare with finite element analysis results. A thermal experiment on BGA packaging is used to demonstrate the advantages of the proposed new design.