This paper extends Digital Speckle Pattern Interferometry into three dimensions. A Wavelength Scanning Interferometry (WSI) system is proposed which provides displacement fields inside the volume of semi-transparent scattering materials with high spatial resolution and three-dimensional displacement sensitivity. The main driver to develop such a system is the need to determine constitutive parameters (mainly elastic constants) of materials such as polymers and biological tissues so that their behavior can be modeled computationally. The sample is illuminated by three non-coplanar collimated beams around the observation direction. Sequences of two-dimensional interferograms are recorded while the frequency of the laser is tuned at a constant rate. Each pixel thus records and intensity signal which temporal frequency encodes the optical path difference between the illumination and reference beams for a particular point on the sample. Fourier transformation along the time axis reconstructs the magnitude and phase of the material's microstructure. Different optical paths along each illumination direction are required in order to separate or multiplex, in the frequency domain, the signals corresponding to each sensitivity vector. In this way, all the information required to reconstruct the location and the 3D displacement vector of scattering points within the volume in the material is recorded simultaneously. A controlled validation experiment is performed, which confirms the ability of the technique to provide three dimensional displacement distributions inside semitransparent scattering materials
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