Out-of-plane displacement field measurement by shearography

• We report an out-of-plane displacement measurement method by shearography.
• The method is based on the improved shearography system and two step integration.
• The method relaxes the environmental stability requirement.
• The boundary conditions are unnecessary for the method.
• Relative out-of-plane displacement field of object surface is obtained.

Existing shearography systems measuring out-of-plane displacements suffer from boundary-constraint or reference surface requirements. Therefore, we propose an accurate non-uniform out-of-plane displacement field measurement method based on a modified shearography system and two-step integration method. The proposed method combines high-resolution interferometry with the advantage of relaxing the environmental stability requirements. The modified shearography system adopts three beam splitters and two switches when compared with conventional optical configurations. The three beam splitters are used to construct a modified Michelson interferometer that shears the image along two orthogonal directions, and the shearing direction can be switched by the two hardware switches between the orthogonal directions. With phase shifting performed on the recorded images, the out-of-plane displacement gradients along the orthogonal directions are extracted sequentially. In general, without boundary restrictions on the object surface, it is difficult to directly extract out-of-plane displacement from a single displacement gradient field. Accordingly, the two-step integration method is proposed and applied to the orthogonal displacement gradients to extract the relative out-of-plane displacement field without any boundary conditions of the object surface provided. Experiments are performed on a clamped circular plate with uniform loading, and the results are compared with electronic speckle pattern interferometry (ESPI) results to validate the proposed method.