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## Processing and analysis of stripe images using Hilbert-Huang transformation for field optical measurement methods

### Maciej Trusiak

#### Abstract

The thesis is focused on expanding and advancing the Hilbert-Huang transform (HHT) method by creating innovative and versatile algorithmic solutions for optical metrology, especially very precise full-field measurement techniques for characterizing diverse technical and biomedical samples. The thesis consists of 14 papers published in JCR journals, 10 peer-reviewed conference proceedings and publication guide. The thesis encompasses two main areas of studies. First one consists in developing adaptive data analysis schemes based on the HHT method. Second layer comprises applications of HHT driven solutions for optical metrology either enabling the measurement or significantly minimizing its errors incorporating enhanced analysis of generated fringe patterns (with encoded information about the object under study). Continuous modification of the HHT based algorithmic solutions was naturally stimulated by the challenges encountered in real life applications. The goal was to create versatile numerical method able to successfully perform full path adaptive processing and the analysis of single low quality fringe pattern regardless the examined phenomenon and the full-field optical measurement technique used (i.e., interferometry, structured illumination, moiré, digital holographic microscopy etc.). Predefined aim was reached merging several cutting-edge algorithmic solutions motivated by real-life cumbersome aspects of optical metrology. The Hilbert-Huang transform consists of two stages – (1) empirical mode decomposition which dissects from the analyzed signal a set of components oscillating in various scales, and (2) the Hilbert transform for subsequent analytic signal generation and its straightforward instantaneous phase and amplitude demodulation. New accelerated bidimensional empirical mode decomposition technique was incorporated alongside with the original method for automatic selective reconstruction of high quality fringe pattern from a set of empirical modes derived from low quality fringe data. Moreover an inventive directional bidimensional empirical mode decomposition method was proposed. It is able to decouple a single fringe pattern from the multiple fringe set interferogram (encountered, e.g., in grating interferometry for displacement study in experimental mechanics). Next, three innovative techniques for precise phase demodulation were reported – (1) single-frame HHT-based method aided by the principal component analysis for local fringe direction map determination and two-frame methods based on (2) Gram-Schmidt orthonormalization process and (3) Lissajous figure technique with HHT driven pre-filtering. The set of created algorithms was augmented by the two-frame amplitude demodulation method to be applied for vibration studies of technical objects by time-averaged interferometry and volumetric optically-sectioned imaging of biomedical specimen by structured illumination microscopy used, e.g., for the cervical cancer cell visualization. Another proposed skillful algorithm utilized the HHT for wave front sensing by innovative Fresnel diffraction field multiple beam lateral shear grating interferometers. Original and versatile Hilbert-Huang phase microscopy for quantitative phase imaging of biomedical (e.g., red blood cells) and technical (i.e., polystyrene microbeads) samples completes the list of main achievements presented in the thesis. Numerical methods developed were comprehensively tested using simulated and experimental fringe patterns. Thoroughly conducted studies corroborated that proposed techniques compare favorably with common optical measurement schemes employing classical approaches for fringe analysis and in many cases are superior.
Record ID
Diploma type
Doctor of Philosophy
Author
Title in Polish
Przetwarzanie i analiza obrazów prążkowych z zastosowaniem transformacji Hilberta-Huanga na potrzeby polowych optycznych metod pomiaru
Title in English
Processing and analysis of stripe images using Hilbert-Huang transformation for field optical measurement methods
Language
(pl) Polish
Certifying Unit
Faculty of Mechatronics (FM)
Discipline
mechanical engineering / (technology domain) / (technological sciences)
Status
Finished
Start date
29-05-2013
Defense Date
21-06-2017
Title date
28-06-2017
Supervisor
External reviewers
Henryk Kasprzak, prof. Henryk Kasprzak, prof.,, Author's external affiliation: Wydział Podstawowych Problemów Techniki
Zbigniew Jaroszewicz Zbigniew Jaroszewicz,, External affiliation of publication: Institute of Applied Optics
Pages
335
Keywords in English
algorithms
Abstract in English
The thesis is focused on expanding and advancing the Hilbert-Huang transform (HHT) method by creating innovative and versatile algorithmic solutions for optical metrology, especially very precise full-field measurement techniques for characterizing diverse technical and biomedical samples. The thesis consists of 14 papers published in JCR journals, 10 peer-reviewed conference proceedings and publication guide. The thesis encompasses two main areas of studies. First one consists in developing adaptive data analysis schemes based on the HHT method. Second layer comprises applications of HHT driven solutions for optical metrology either enabling the measurement or significantly minimizing its errors incorporating enhanced analysis of generated fringe patterns (with encoded information about the object under study). Continuous modification of the HHT based algorithmic solutions was naturally stimulated by the challenges encountered in real life applications. The goal was to create versatile numerical method able to successfully perform full path adaptive processing and the analysis of single low quality fringe pattern regardless the examined phenomenon and the full-field optical measurement technique used (i.e., interferometry, structured illumination, moiré, digital holographic microscopy etc.). Predefined aim was reached merging several cutting-edge algorithmic solutions motivated by real-life cumbersome aspects of optical metrology. The Hilbert-Huang transform consists of two stages – (1) empirical mode decomposition which dissects from the analyzed signal a set of components oscillating in various scales, and (2) the Hilbert transform for subsequent analytic signal generation and its straightforward instantaneous phase and amplitude demodulation. New accelerated bidimensional empirical mode decomposition technique was incorporated alongside with the original method for automatic selective reconstruction of high quality fringe pattern from a set of empirical modes derived from low quality fringe data. Moreover an inventive directional bidimensional empirical mode decomposition method was proposed. It is able to decouple a single fringe pattern from the multiple fringe set interferogram (encountered, e.g., in grating interferometry for displacement study in experimental mechanics). Next, three innovative techniques for precise phase demodulation were reported – (1) single-frame HHT-based method aided by the principal component analysis for local fringe direction map determination and two-frame methods based on (2) Gram-Schmidt orthonormalization process and (3) Lissajous figure technique with HHT driven pre-filtering. The set of created algorithms was augmented by the two-frame amplitude demodulation method to be applied for vibration studies of technical objects by time-averaged interferometry and volumetric optically-sectioned imaging of biomedical specimen by structured illumination microscopy used, e.g., for the cervical cancer cell visualization. Another proposed skillful algorithm utilized the HHT for wave front sensing by innovative Fresnel diffraction field multiple beam lateral shear grating interferometers. Original and versatile Hilbert-Huang phase microscopy for quantitative phase imaging of biomedical (e.g., red blood cells) and technical (i.e., polystyrene microbeads) samples completes the list of main achievements presented in the thesis. Numerical methods developed were comprehensively tested using simulated and experimental fringe patterns. Thoroughly conducted studies corroborated that proposed techniques compare favorably with common optical measurement schemes employing classical approaches for fringe analysis and in many cases are superior.
Thesis file
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Trusiak_Rozprawa_DoWydruku.pdf
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Uniform Resource Identifier
urn:pw-repo:WUTff8c53833e0345a5817389a1c724ad47