Hilbert transform (HT) is widely used in temporal speckle pattern interferometry, but errors from low modulations might propagate and corrupt the calculated phase. A spatio-temporal method for phase retrieval using temporal HT and spatial phase unwrapping is presented. In time domain, the wrapped phase difference between the initial and current states is directly determined by using HT. To avoid the influence of the low modulation intensity, the phase information between the two states is ignored. As a result, the phase unwrapping is shifted from time domain to space domain. A phase unwrapping algorithm based on discrete cosine transform is adopted by taking advantage of the information in adjacent pixels. An experiment is carried out with a Michelson-type interferometer to study the out-of-plane deformation field. High quality whole-field phase distribution maps with different fringe densities are obtained. Under the experimental conditions, the maximum number of fringes resolvable in a 416×416 frame is 30, which indicates a 15λ deformation along the direction of loading.
A modified Michelson interferometer for spatial phase shifting speckle shearography is presented. The interferometer consists of one slit aperture, one beam splitter, and two spherical mirrors. Spatial carrier frequency and shear are both generated by one translated spherical mirror. The slit aperture controls the speckle size. These arrangements make the system simple and easy to align. The shear is proportional to the translation of the spherical mirror. Shear distortion due to the rotated mirror in a traditional Michelson interferometer is avoided as well. The carrier frequency is proven to be constant in image plane and can be conveniently adjusted by translating the spherical mirror without changing imaging setup. Fourier analysis method is applied to accurately calibrate carrier frequency. Finally, experimental dynamic deformation results of a center loaded metal plate using the proposed method are provided.