Phase reconstruction of phase shifted moire interferograms using continuous wavelet transforms

A method to accurately reconstruct detailed deformation from moiré interferometry is proposed in this dissertation. A phase shifting moiré interferometer is designed and implemented. Image processing algorithms based on continuous and discrete wavelet transforms are developed. Although the improvement made was derived from perfecting moiré interferometry, the proposed method can be extended to virtually any type of interferometries and thus benefits a wide range of applications.; Moiré interferometer has been widely applied to the reliability study of electronic packaging industry due to its high sensitivity for in-plane deformation measurements. The most commonly used moirE interferometer has a measurement sensitivity of 417 nm/fringe. However, such discrete deformation measurement represented by fringe spacing can no longer meet the requirements of rapidly developing package designs. Higher sensitivity is required to measure very small deformation and/or obtain localized deformation. Although it can be implemented with finer diffraction grating, it is unlikely to be applied to the industry in near future because of the difficulty of precisely manufacturing such grating and maintaining high diffraction efficiency. Fortunately, utilizing the existing phase information contained in interferograms becomes an economic and convenient alternative.; In this dissertation, phase shifting moiré interferometer is designed and implemented to calculate a phase map of an interferogram. Additional phase shifts are introduced with translations of a diffraction grating. A program that coordinates the grating translations with the interferogram acquisitions is developed, such that the effects of environmental vibration on the accuracy of phase calculation are minimized. However, even with the minimization of phase shift errors, intensity errors still cannot be suppressed.; An image processing technique based on wavelet transform is then developed to precisely remove irregular localized noises in interferograms to ensure an accurate reconstruction of a phase map. A continuous wavelet based technique calculates the correlation between an interferometer signal and single-tone functions with different frequencies. The ridge of the correlation map provides a smoothly varying local frequency curve, and thus can be used to eliminate localized noise and to reconstruct interferometer signal. A detection algorithm based on optimizing a carefully designed cost function is proposed to ensure an accurate noise removal for low SNR interferograms. The limitation of CWT algorithm is overcome by introducing carrier phase when the algorithm is applied to phase shifting moiré interferograms. Furthermore, a discrete wavelet based filtering technique is developed in this dissertation to smooth the derivative of the reconstructed phase and thus provides accurate in-plane strain maps. The proposed algorithms are demonstrated to be effective and are applied to an actual BGA packages under thermal cycling.