Pablo D. Ruiz

Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography.

We describe a system for measuring sub-surface displacement fields within a scattering medium using a phase contrast version of spectral Optical Coherence Tomography. The system provides displacement maps within a 2-D slice extending into the sample with a sensitivity of order 10 nm. The data for a given deformation state is recorded in a single image, potentially allowing sub-surface displacement and strain mapping of moving targets. The system is based on low cost components and has no moving parts. The theoretical basis for the system is presented along with experimental results from a simple well-controlled geometry consisting of independently-tilting glass sheets. Results are validated using standard two-beam interferometry. A modified system was used to measure through-the-thickness phase changes within a porcine cornea due to displacements produced by an increase in the intraocular pressure.

Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping

We demonstrate in both simulated and real cases the effect that undersampling of a three-dimensional (3D) wrapped phase distribution has on the geometry of phase singularity loops and their branch cut surfaces. The more intuitive two-dimensional (2D) problem of setting branch cuts between dipole pairs is taken as a starting point, and then branch cut surfaces in flat and ambiguous 3D loops are discussed. It is shown that the correct 2D branch cuts and 3D branch cut surfaces should be placed where the gradient of the original phase distribution exceeded pi rad voxel(-1). This information, however, is lost owing to undersampling and cannot be recovered from the sampled wrapped phase distribution alone. As a consequence, empirical rules such as finding the surface of minimal area or methods based on the wrapped phase gradient will fail to find the correct branch cut surfaces. We conclude that additional information about the problem under study is therefore needed to produce correct branch cut surfaces that lead to an unwrapped phase distribution with minimum local errors. An example with real data is provided in which downsampled phase contrast magnetic resonance imaging data are successfully unwrapped when the position of the vessel walls and the physical properties of the flowing blood are taken into account.

Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry

We show, for the first time to our knowledge, how wavelength-scanning interferometry can be used to measure depth-resolved displacement fields through semitransparent scattering surfaces. Temporal sequences of speckle interferograms are recorded while the wavelength of the laser is tuned at a constant rate. Fourier transformation of the resultant three-dimensional (3-D) intensity distribution along the time axis reconstructs the scattering potential within the medium, and changes in the 3-D phase distribution measured between two separate scans provide the out-of-plane component of the 3-D displacement field. The principle of the technique is explained in detail and illustrated with a proof-of-principle experiment involving two independently tilted semitransparent scattering surfaces. Results are validated by standard two-beam electronic speckle pattern interferometry.

Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps

Inasmuch as current fringe analysis techniques used in digital speckle-pattern interferometry (DSPI) yield a phase map modulo 2pi, phase unwrapping is the final step of any data evaluation process. The performance of a recently published algorithm used to unwrap DSPI phase maps is investigated. The algorithm is based on a least-squares minimization technique that is solvable by the discrete cosine transform. When phase inconsistencies are present, they are handled by exclusion of invalid pixels from the unwrapping process through the assignment of zero-valued weights. Then the weighted unwrapping problem is solved in an iterative manner by a preconditioned conjugate-gradient method. The evaluation is carried out with computer-simulated DSPI phase maps, an approach that permits the generation of phase fields without inconsistencies, which are then used to calculate phase deviations as a function of the iteration number. Real data are also used to illustrate the performance of the algorithm.

Unwrapping of digital speckle-pattern interferometry phase maps by use of a minimum L 0 -norm algorithm

The performance of a minimum L(0)-norm unwrapping algorithm is investigated by use of synthetic digital speckle-pattern interferometry (DSPI) wrapped phase maps that simulate experimentally obtained data. This algorithm estimates its own weights to mask inconsistent pixels. Particular features usually included in DSPI wrapped phase distributions, such as shears, speckle noise, fringe cuts, object physical limits, and superimposed phase maps, are analyzed. Some adequate approaches to solving these features are discussed. Finally, it is shown that a complex case in which shears and fringe cuts coexist in the wrapped phase cannot be solved satisfactorily with the minimum L(0)-norm algorithm by itself. To cope with this problem, we propose a new scheme.

Elastic stiffness characterization using three-dimensional full-field deformation obtained with optical coherence tomography and digital volume correlation

Abstract. This paper presents a methodology for stiffness identification from depth-resolved three-dimensional (3-D) full-field deformation fields. These were obtained by performing digital volume correlation on optical coherence tomography volume reconstructions of silicone rubber phantoms. The effect of noise and reconstruction uncertainties on the performance of the correlation algorithm was first evaluated through stationary and rigid body translation tests to give an indication of the minimum strain that can be reliably measured. The phantoms were then tested under tension, and the 3-D deformation fields were used to identify the elastic constitutive parameters using a 3-D manually defined virtual fields method. The identification results for the cases of uniform and heterogeneous strain fields were compared with those calculated analytically through the constant uniaxial stress assumption, showing good agreement.

Depth-resolved whole-field displacement measurement using wavelength scanning interferometry

We describe a technique for measuring depth-resolved displacement fields within a three-dimensional (3D) scattering medium based on wavelength scanning interferometry. Sequences of two-dimensional interferograms are recorded whilst the wavelength of the laser is tuned at a constant rate. Fourier transformation of the resulting 3D intensity distribution along the time axis reconstructs the scattering potential within the medium, and changes in the 3D phase distribution measured between two separate scans provide one component of the 3D displacement field. The technique is illustrated with a proof-of-principle experiment involving two independently controlled reflecting surfaces. Advantages over the corresponding method based on low-coherence interferometry include a depth range unlimited by mechanical scanning devices, and immunity from fringe contrast reduction when imaging through dispersive media.

Simultaneous measurement of in-plane and out-of-plane displacement fields in scattering media using phase-contrast spectral optical coherence tomography

The use of phase-contrast spectral optical coherence tomography to measure two orthogonal displacement components on a slice within a scattering medium is demonstrated. This is achieved by combining sequential oblique illumination of the object and recording two interferograms before plus two after the deformation. The proposed technique is illustrated with results from a sample undergoing simple shear. Depth-resolved out-of-plane and in-plane sensitivities of 0.14 and 4.2 microm per fringe are demonstrated up to a depth of 400 microm in a water-based polymer.

Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media

We describe a novel technique that we call tilt scanning interferometry to measure depth-resolved structure and displacement fields within semi-transparent scattering materials. The method differs significantly from conventional optical coherence tomography, in that only one wavelength is used throughout the whole measurement process. Temporal sequences of speckle interferograms are recorded while the illumination angle is tilted at constant rate. Fourier transformation of the resulting three-dimensional intensity distribution along the time axis reconstructs the scattering potential within the medium. Repeating the measurements with the object wave at equal and opposite angles about the observation direction results in two three-dimensional phase-change volumes, the sum of which gives the out-of-plane-sensitive phase volume and the difference between which gives the in-plane phase volume. From these phase-change volumes the in-plane and out-of-plane depth-resolved displacement fields are obtained. The theoretical framework for the technique is explained in detail and a practical optical implementation is described. Finally, results from proof-of-principle experiments involving a semi-transparent beam undergoing bending are presented.

Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints

Strain distributions within adhesively bonded double-lap shear joints under tensile load have been investigated experimentally using the complementary experimental techniques of neutron diffraction (ND) and moire interferometry (MI). ND provides three-dimensional strain values within the samples, whereas MI gives high-resolution maps of the in-plane strain components at the surface. The resulting comprehensive datasets obtained from both aluminium and steel joints were compared against finite element (FE) predictions. The importance of a range of factors (e.g. two-dimensional versus three-dimensional geometry, sample asymmetry, residual strains) was assessed through development of the FE model and detailed comparison with the experimental data. The main conclusions were that FEA can be used accurately to predict strains in the adherends of bonded lap joints and that many of the simplifications of the joints commonly used in the analysis of bonded joints are justified as including them results in relatively small differences compared with sample-to-sample variation and the safety factors used in designing bonded joints.