Tomographic measurement of all orthogonal components of three-dimensional displacement fields within scattering materials using wavelength scanning interferometry

Experimental mechanics is currently contemplating tremendous opportunities of further advancements thanks to a combination of powerful computational techniques and also fullfield non-contact methods to measure displacement and strain fields in a wide variety of materials. Identification techniques, aimed to evaluate material mechanical properties given known loads and measured displacement or strain fields, are bound to benefit from increased data availability (both in density and dimensionality) and efficient inversion methods such as finite element updating (FEU) and the virtual fields method (VFM). They work at their best when provided with dense and multicomponent experimental displacement (or strain) data, i.e. when all orthogonal components of displacements (or all components of the strain tensor) are known at points closely spaced within the volume of the material under study. Although a very challenging requirement, an increasing number of techniques are emerging to provide such data. In this Thesis, a novel wavelength scanning interferometry (WSI) system that provides three dimensional (3-D) displacement fields inside the volume of semi-transparent scattering materials is proposed. Sequences of two-dimensional interferograms are recorded whilst tuning the frequency of a laser at a constant rate. A new approach based on frequency multiplexing is used to encode the interference signal corresponding to multiple illumination directions at different spectral bands. Different optical paths along each illumination direction ensure that the signals corresponding to each sensitivity vector do not overlap in the frequency domain. All the information required to reconstruct the location and the 3-D displacement vector of scattering points within the material is thus recorded simultaneously in a single wavelength scan. By comparing phase data volumes obtained for two successive scans, all orthogonal components of the three dimensional displacement field introduced between scans (e.g. by means of loading or moving the sample under study) are readily obtained with high displacement sensitivity. The fundamental principle that describes the technique is presented in detail, including the correspondence between interference signal frequency and its associated depth within the sample, depth range, depth resolution, transverse resolution and displacement sensitivity. Data processing of the interference signal includes Fourier transformation, noise reduction, re-registration of data volumes, measurement of the illumination and sensitivity vectors from experimental data using a datum surface, phase difference evaluation, 3-D phase unwrapping and 3-D displacement field evaluation. Experiments consisting of controlled rigid body rotations and translations of a phantom were performed to validate the results. Both in-plane and the out-of-plane displacement components were measured for each voxel in the resulting data volume, showing an excellent agreement with the expected 3-D displacement.