Application of speckle interferometry to the mechanical characterization of a biopolymer sample.

In this work, we present an optical and mechanical characterization of the behavior of an inhomogeneous biopolymer sample through the use of an in-plane electronic speckle pattern interferometer with a pulling system along the $y$y direction. The characterization of the sample subjected to stress comprised the acquisition of speckle patterns for 1360 states. Displacement maps and their corresponding strain maps were computed for every state. Since the information of the maps changes with size due to the sample being pulled at the upper end while it is clamped at the lower end, a scaling method to relate the maps to each other, point-to-point, is presented. The method allows the correct evaluation of sequential strain maps, which depicts the mechanical evolution of the material. Upon managing to relate the strain maps, it is possible to extract strain values for zones of interest from every map in order to build the respective stress-strain curves. Three stress-strain curves associated with three zones in the sample (upper, middle, and bottom) are constructed. When sequential displacement and deformation maps are optically obtained by the interferometer, we present a full-field characterization, along with the obtention stress-strain curves associated with the three zones of strain maps. The curves represent the inhomogeneous performance of the sample. Three different elastic moduli (${E_u} = 2.59\;{\rm MPa}$Eu=2.59MPa, ${E_m} = 1.97\;{\rm MPa}$Em=1.97MPa, and ${E_{b}} = 1.67\;{\rm MPa}$Eb=1.67MPa), associated with three respective zones, were obtained. The experimental results for a biopolymer sample here presented show that the technique, in conjunction with the scaling method, is a novel proposal to characterize inhomogeneous materials.

Dynamic parallel phase-shifting electronic speckle pattern interferometer.

Methods for measuring variations in diffuse surfaces using electronic speckle pattern interferometry (ESPI) are widely used and well known. In this research, we present an out-of-plane ESPI system coupled to a Michelson configuration to generate simultaneous parallel interferograms with different phase shifts. The system uses circular polarization states to generate parallel phase shifted interferograms. Due to the polarization states, the fringes do not experience a contrast reduction, thus avoiding measurement errors that affect spatial or temporal phase-shifting in interferometry. The basic operating principle of polarization modulation is described, and results that represent the temporal evolution of an aluminum plate are presented. The generation of two simultaneous patterns allows one to track the dynamic performance of the plate.

Phase stepping through polarizing modulation in electronic speckle pattern interferometry.

We have demonstrated a speckle out-of-plane interferometer that employs phase-stepping procedures by means of polarization modulation. The system generates circular polarization states with opposite signs at each arm of the system, which overlap at the output of the interferometer, to generate phase shifts operating a conventional linear polarizer; the emerging polarization states have been analyzed to obtain the shifts needed to process the optical phase. The phase-stepping technique is demonstrated with a two-step algorithm to measure out-of-plane displacement on a flat metal plate.

Relative error in out-of-plane measurement due to the object illumination.

In this work the sensitivity vector is analyzed for collimated and divergent oblique illumination for an out-of-plane arrangement. In the case of collimated illumination, the variation of the sensitivity vector components was considered and a geometric model was proposed for its evaluation. The geometry of the optical setup used allowed us to find sensitivity mostly along the pulling direction; the other two components of the sensitivity vector were relatively small. We measured the displacement induced only along the pulling direction. Errors in the displacement measurement associated with divergent and collimated illumination can be predicted when the sensitivity vector is considered constant. Experimental and theoretical results are presented for the out-of-plane electronic speckle pattern interferometer. The analyzed object was an aluminum plate.