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## Fringe pattern processing using modified fast adaptive bidimensional empirical mode decomposition algorithm

### Paweł Piotr Gocłowski

#### Abstract

This engineering thesis is dedicated to fringe pattern pre-processing using the empirical mode decomposition (EMD) algorithm. This method allows to separate image components of different spatial frequencies (modes) in order to eliminate unwanted background and noise from the fringe pattern. Empirical mode decomposition algorithms are currently commonly used in fringe pattern analysis due to its effectiveness and speed. The goal of the thesis is to improve this method of the fringe pattern pre-processing by modifying the algorithm, taking locally variable fringe period into account during mode extraction. Theoretical part of the thesis contains basic description of interference and its applications, particularly in optical metrology. Selected methods of fringe pattern analysis are presented, such as: temporal phase shifting, spatial-carrier phase-shifting and Fourier transform method. Several drawbacks and limitations of these methods are pointed out, particularly in case of low quality interferogram analysis. Subsequently principles of empirical mode decomposition method and historical evolution of this family algorithms are presented. The end of theoretical part describes imperfections of the latest version of the 2D EMD algorithm showing potential perspectives of improvement. In the experimental part of the thesis novel and original methods for fringe pattern envelope generation are proposed. These new functions eliminated some errors of the latest version of the 2D EMD algorithm. Next the most important problem of mode-mixing phenomena was eliminated. Normally fringe component with phase information is stored in several different modes and merging some of them together to reconstruct the fringe term is time-consuming and cumbersome task (there is a risk of losing information and noise transfer). Adaptive decomposition aided by the adaptive fringe density map was proposed as an original solution of mode-mixing problem. Fringe density map was computed locally based on the derivative of the phase and was used to guide the filter size used in the decomposition, previously set globally. It was verified to allow to contain complete fringe information in single first mode (even in case of highly variable local fringe period) – without necessity of reconstruction process. The idea proved to be successful and the results of comprehensive study are satisfactory but access to phase map is not granted in experimental reality. Novel original fringe density map computing method was proposed, which does not require any a priori knowledge of the phase function. The quality of the new method was tested using simulated fringe pattern and by computing RMS (Root Mean Square) parameter of the difference between the first mode and the cosine of the phase (reference fringe pattern). The thesis contains careful RMS analysis in relation with such parameters as density of fringes, background illumination amplitude and noise level. The method was also tested on fringe patterns originated from the laboratory measurements corroborating its experimental usefulness and unique features highlighted by numerical simulations. As a result, the new fast fringe pattern pre-processing method with incredibly low error rate is proposed. Extraction of the first mode from fringe pattern using the new method provides effective background elimination. Further improvements of the algorithm should be related to noise elimination (proposed algorithm does not provide noise extraction, most of noise component is included in the first mode) and reducing the time needed to extract the first mod from fringe pattern.
Diploma type
Engineer's / Bachelor of Science
Diploma type
Engineer's thesis
Author
Paweł Piotr Gocłowski (FM) Paweł Piotr Gocłowski,, Faculty of Mechatronics (FM)
Title in Polish
Przetwarzanie obrazów prążkowych zmodyfikowanym algorytmem szybkiej adaptacynej dwuwymiarowej dekompozycji modów empirycznych
Supervisor
Maciej Trusiak (FM/IMPh) Maciej Trusiak,, The Institute of Micromechanics and Photonics (FM/IMPh)Faculty of Mechatronics (FM)
Certifying unit
Faculty of Mechatronics (FM)
Affiliation unit
The Institute of Micromechanics and Photonics (FM/IMPh)
Study subject / specialization
, Mechatronika
Language
(pl) Polish
Status
Finished
Defense Date
07-05-2019
Issue date (year)
2019
Reviewers
Maciej Trusiak (FM/IMPh) Maciej Trusiak,, The Institute of Micromechanics and Photonics (FM/IMPh)Faculty of Mechatronics (FM) Adam Styk (FM/IMPh) Adam Styk,, The Institute of Micromechanics and Photonics (FM/IMPh)Faculty of Mechatronics (FM)
Keywords in Polish
polowa metrologia optyczna, interferometria, analiza obrazów prążkowych, przetwarzanie obrazu
Keywords in English
field optical metrology, interferometry, fringe pattern analysis, image processing
Abstract in Polish
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Local fields
Identyfikator pracy APD: 33986

Uniform Resource Identifier
https://repo.pw.edu.pl/info/bachelor/WUT00510590e77540979a568edaf1b60958/
URN
urn:pw-repo:WUT00510590e77540979a568edaf1b60958

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