Synchronous triple-optical-path digital speckle pattern interferometry with fast discrete curvelet transform for measuring three-dimensional displacements

• Simultaneous 3D digital speckle pattern interferometry method is proposed.
• A pre-filtering method based on fast discrete curvelet transform is presented.
• An improved threshold function in fast discrete curvelet transform is conceived.

Digital speckle pattern interferometry (DSPI) is a well-established and widely used optical measurement technique for obtaining qualitative as well as quantitative measurements of objects deformation. The simultaneous measurement of an object's surface displacements in three dimensions using DSPI is of great interest. This paper presents a triple-optical-path DSPI based method for the simultaneous and independent measurement of three-dimensional (3D) displacement fields. In the proposed method, in-plane speckle interferometers with dual-observation geometry and an out-of-plane interferometer are optimally combined to construct an integrated triple-optical-path DSPI system employing the phase shift technique, which uses only a single laser source and three cameras. These cameras are placed along a single line to synchronously capture real-time visible speckle fringe patterns in three dimensions. In addition, a pre-filtering method based on the fast discrete curvelet transform (FDCT) is utilized for denoising the obtained wrapped phase patterns to improve measurement accuracy. Finally, the simultaneous measurement of the 3D displacement fields of a simple beam and a composite laminated plate respectively subjected to three-point and single-point bend loading are investigated to validate the feasibility and effectiveness of the proposed method.