DEVELOPMENT OF PHASE RETRIEVAL TECHNIQUES IN DISPLACEMENT AND DISPLACEMENT DERIVATIVES MEASUREMENT

Ph.DDOCTOR OF PHILOSOPH

Phase extraction of non-stationary signals produced in dynamic interferometry involving speckle waves

It is now widely acknowledged, among communities of researchers and engineers of very different horizons, that speckle interferometry (SI) offers powerful techniques to characterize mechanical rough surfaces with a submicronic accuracy in static or quasi-static regime, when small displacements are involved (typically several microns or tens of microns). The issue of dynamic regimes with possibly large deformations (typically several hundreds of microns) is still topical and prevents an even more widespread use of speckle techniques. This is essentially due to the lack of efficient processing schemes able to cope with non-stationary AM-FM interferometric signals. In addition, decorrelation-induced phase errors represent an hindrance to accurate measurement when such large displacements and classical fringe analysis techniques are considered. This work is an attempt to address those issues and to endeavor to make the most of speckle interferometry signals. Our answers to those problems are located on two different levels. First of all, we adopt the temporal analysis approach, i.e. the analysis of the temporal signal of each pixel of the sensor area used to record the interferograms. A return to basics of phase extraction is operated to properly identify the conditions under which the computed phase is meaningful and thus give some insight on the physical phenomenon under analysis. Due to their intrinsic non-stationary nature, a preprocessing tool is missing to put the SI temporal signals in a shape which ensures an accurate phase computation, whichever technique is chosen. This is where the Empirical Mode Decomposition (EMD) intervenes. This technique, somehow equivalent to an adaptive filtering technique, has been studied and tailored to fit with our expectations. The EMD has shown a great ability to remove efficiently the random fluctuating background intensity and to evaluate the modulation intensity. The Hilbert tranform (HT) is the natural quadrature operator. Its use to build an analytical signal from the so-detrended SI signal, for subsequent phase computation, has been studied and assessed. Other phase extraction techniques have been considered as well for comparison purposes. Finally, our answer to the decorrelation-induced phase error relies on the well-known result that the higher the pixel modulation intensity, the lower the random phase error. We took benefit from this result – not only linked to basic SNR considerations, but more specifically to the intrinsic phase structure of speckle fields – with a novel approach. The regions within the pixel signal history classified as unreliable because under-modulated, are purely and simply discarded. An interpolation step with the Delaunay triangulation is carried out with the so-obtained non-uniformly sampled phase maps to recover a smooth phase which relies on the most reliable available data. Our schemes have been tested and discussed with simulated and experimental SI signals. We eventually have developed a versatile, accurate and efficient phase extraction procedure, perfectly able to tackle the challenge of dynamic behaviors characterization, even for displacements and/or deformations beyond the classical limit of the correlation dimensions

Development and Characterization of a Dispersion-Encoded Method for Low-Coherence Interferometry

This Open Access book discusses an extension to low-coherence interferometry by dispersion-encoding. The approach is theoretically designed and implemented for applications such as surface profilometry, polymeric cross-linking estimation and the determination of thin-film layer thicknesses. During a characterization, it was shown that an axial measurement range of 79.91 µm with an axial resolution of 0.1 nm is achievable. Simultaneously, profiles of up to 1.5 mm in length were obtained in a scan-free manner. This marked a significant improvement in relation to the state-of-the-art in terms of dynamic range. Also, the axial and lateral measurement range were decoupled partially while functional parameters such as surface roughness were estimated. The characterization of the degree of polymeric cross-linking was performed as a function of the refractive index. It was acquired in a spatially-resolved manner with a resolution of 3.36 x 10-5. This was achieved by the development of a novel mathematical analysis approach

Integrated tactile-optical coordinate measurement for the reverse engineering of complex geometry

Complex design specifications and tighter tolerances are increasingly required in modern engineering applications, either for functional or aesthetic demands. Multiple sensors are therefore exploited to achieve both holistic measurement information and improved reliability or reduced uncertainty of measurement data. Multi-sensor integration systems can combine data from several information sources (sensors) into a common representational format in order that the measurement evaluation can benefit from all available sensor information and data. This means a multi-sensor system is able to provide more efficient solutions and better performances than a single sensor based system. This thesis develops a compensation approach for reverse engineering applications based on the hybrid tactile-optical multi-sensor system. In the multi-sensor integration system, each individual sensor should be configured to its optimum for satisfactory measurement results. All the data measured from different equipment have to be precisely integrated into a common coordinate system. To solve this problem, this thesis proposes an accurate and flexible method to unify the coordinates of optical and tactile sensors for reverse engineering. A sphere-plate artefact with nine spheres is created and a set of routines are developed for data integration of a multi-sensor system. Experimental results prove that this novel centroid approach is more accurate than the traditional method. Thus, data sampled by different measuring devices, irrespective of their location can be accurately unified. This thesis describes a competitive integration for reverse engineering applications where the point cloud data scanned by the fast optical sensor is compensated and corrected by the slower, but more accurate tactile probe measurement to improve its overall accuracy. A new competitive approach for rapid and accurate reverse engineering of geometric features from multi-sensor systems based on a geometric algebra approach is proposed and a set of programs based on the MATLAB platform has been generated for the verification of the proposed method. After data fusion, the measurement efficiency is improved 90% in comparison to the tactile method and the accuracy of the reconstructed geometric model is improved from 45 micrometres to 7 micrometres in comparison to the optical method, which are validated by case study

Compressive phase retrieval

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 129-138).Recovering a full description of a wave from limited intensity measurements remains a central problem in optics. Optical waves oscillate too fast for detectors to measure anything but time{averaged intensities. This is unfortunate since the phase can reveal important information about the object. When the light is partially coherent, a complete description of the phase requires knowledge about the statistical correlations for each pair of points in space. Recovery of the correlation function is a much more challenging problem since the number of pairs grows much more rapidly than the number of points. In this thesis, quantitative phase imaging techniques that works for partially coherent illuminations are investigated. In order to recover the phase information with few measurements, the sparsity in each underly problem and ecient inversion methods are explored under the framework of compressed sensing. In each phase retrieval technique under study, diffraction during spatial propagation is exploited as an effective and convenient mechanism to uniformly distribute the information about the unknown signal into the measurement space. Holography is useful to record the scattered field from a sparse distribution of particles; the ability of localizing each particles using compressive reconstruction method is studied. When a thin sample is illuminated with partially coherent waves, the transport of intensity phase retrieval method is shown to be eective to recover the optical path length of the sample and remove the eect of the illumination. This technique is particularly suitable for X-ray phase imaging since it does not require a coherent source or any optical components. Compressive tomographic reconstruction, which makes full use of the priors that the sample consists of piecewise constant refractive indices, are demonstrated to make up missing data. The third technique, known as the phase space tomography (PST), addresses the correlation function recovery problem. Implementing the PST involves measuring many intensity images under spatial propagation. Experimental demonstration of a compressive reconstruction method, which finds the sparse solution by decomposing the correlation function into a few mutually uncorrelated coherent modes, is presented to produce accurate reconstruction even when the measurement suers from the 'missing cone' problem in the Fourier domain.by Lei Tian.Ph.D