Loughborough University
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Development of temporal phase unwrapping algorithms for depth-resolved measurements using an electronically tuned Ti:Sa laser

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posted on 2017-01-31, 09:21 authored by Christos A. Pallikarakis
This thesis is concerned with (a) the development of full-field, multi-axis and phase contrast wavelength scanning interferometer, using an electronically tuned CW Ti:Sa laser for the study of depth resolved measurements in composite materials such as GFRPs and (b) the development of temporal phase unwrapping algorithms for depth re-solved measurements. Item (a) was part of the ultimate goal of successfully extracting the 3-D, depth-resolved, constituent parameters (Young s modulus E, Poisson s ratio v etc.) that define the mechanical behaviour of composite materials like GFRPs. Considering the success of OCT as an imaging modality, a wavelength scanning interferometer (WSI) capable of imaging the intensity AND the phase of the interference signal was proposed as the preferred technique to provide the volumetric displacement/strain fields (Note that displacement/strain fields are analogous to phase fields and thus a phase-contrast interferometer is of particular interest in this case). These would then be passed to the VFM and yield the sought parameters provided the loading scheme is known. As a result, a number of key opto-mechanical hardware was developed. First, a multiple channel (x6) tomographic interferometer realised in a Mach-Zehnder arrangement was built. Each of the three channels would provide the necessary information to extract the three orthogonal displacement/strain components while the other three are complementary and were included in the design in order to maximize the penetration depth (sample illuminated from both sides). Second, a miniature uniaxial (tensile and/or compression) loading machine was designed and built for the introduction of controlled and low magnitude displacements. Last, a rotation stage for the experimental determination of the sensitivity vectors and the re-registration of the volumetric data from the six channels was also designed and built. Unfortunately, due to the critical failure of the Ti:Sa laser data collection using the last two items was not possible. However, preliminary results at a single wavelength suggested that the above items work as expected. Item (b) involved the development of an optical sensor for the dynamic monitoring of wavenumber changes during a full 100 nm scan. The sensor is comprised of a set of four wedges in a Fizeau interferometer setup that became part of the multi-axis interferometer (7th channel). Its development became relevant due to the large amount of mode-hops present during a full scan of the Ti:Sa source. These are associated to the physics of the laser and have the undesirable effect of randomising the signal and thus preventing successful depth reconstructions. The multi-wedge sensor was designed so that it provides simultaneously high wavenumber change resolution and immunity to the large wavenumber jumps from the Ti:Sa. The analysis algorithms for the extraction of the sought wavenumber changes were based on 2-D Fourier transform method followed by temporal phase unwrapping. At first, the performance of the sensor was tested against that of a high-end commercial wavemeter for a limited scan of 1nm. A root mean square (rms) difference in measured wavenumber shift between the two of ∼4 m-1 has been achieved, equivalent to an rms wavelength shift error of ∼0.4 pm. Second, by resampling the interference signal and the wavenumber-change axis onto a uniformly sampled k-space, depth resolutions that are close to the theoretical limits were achieved for scans of up to 37 nm. Access of the full 100 nm range that is characterised by wavelength steps down to picometers level was achieved by introducing a number of improvements to the original temporal phase unwrapping algorithm reported in ref [1] tailored to depth resolved measurements. These involved the estimation and suppression of intensity background artefacts, improvements on the 2-D Fourier transform phase detection based on a previously developed algorithm in ref [2] and finally the introduction of two modifications to the original TPU. Both approaches are adaptive and involve signal re-referencing at regular intervals throughout the scan. Their purpose is to compensate for systematic and non-systematic errors owing to a small error in the value of R (a scaling factor applied to the lower sensitivity wedge phase-change signal used to unwrap the higher sensitivity one), or small changes in R with wavelength due to the possibility of a mismatch in the refractive dispersion curves of the wedges and/or a mismatch in the wedge angles. A hybrid approach combining both methods was proposed and used to analyse the data from each of the four wedges. It was found to give the most robust results of all the techniques considered, with a clear Fourier peak at the expected frequency, with significantly reduced spectral artefacts and identical depth resolutions for all four wedges of 2.2 μm measured at FWHM. The ability of the phase unwrapping strategy in resolving the aforementioned issues was demonstrated by successfully measuring the absolute thickness of four fused silica glasses using real experimental data. The results were compared with independent micrometer measurements and showed excellent agreement. Finally, due to the lack of additional experimental data and in an attempt to justify the validity of the proposed temporal phase unwrapping strategy termed as the hybrid approach, a set of simulations that closely matched the parameters characterising the real experimental data set analysed were produced and were subsequently analysed. The results of this final test justify that the various fixes included in the hybrid approach have not evolved to solve the problems of a particular data set but are rather of general nature thereby, highlighting its importance for PC-WSI applications concerning the processing and analysis of large scans.


EPSRC and Loughborough University, Wolfson School of Mechanical and Manufacturing Engineering.



  • Mechanical, Electrical and Manufacturing Engineering


© Christos Antoniou Pallikarakis

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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.


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