Development of a method for flat surface measurement of quasi-flat-bottomed plates using triple bonding

Zofia Sunderland

Abstract

This dissertation is devoted to flatness measurments of quasi-parallel plates taking advantage of three-beam interference. Method of analysis of the registered three-beam interferograms resulting in determination front and back surface flatness and optical thickness variation assuming homogeneous distribution of refractive index of the element under test is proposed. Processing paths using a single three-beam interferogram or a set of (at least two) three-beam interferograms with mutual phase shift is developed. The first case may be applied to images registered in Twyman-Green interferometer, the second case also in the Fizeau system. In both cases determination of plate parameters may be realized without interference into the optomechanical setup or the plate. Firstly, each of the proposed processing paths eliminates a fringe set Ifb from a three-beam interferogram. The set Ifb results from interference of the beams reflected from the tested element surfaces. It leads to intensity distribution containing sum of two fringe families coding plate front and back surface topography, which is further processed. In case of wedge plates, for which number of fringes in the Ifb map is greater than 5, furher processing relies on separating the fringe sets with the use of single-frame algorithms for interferogram analysis, for example two-dimensional continuous wavelet transform or Hilbert-Huang transform. Also, the Fourier transform,Wigner-Hough pseudotransform and phase-shifting digital moiré method was tested. In case of parallel plates more complex, multi-stage processing is conducted. Finally the methods lead to to the same results, i.e. to information on plate front surface shape and other plate parameters. There are a few ways to carry out the elimination of the fringe set Ifb from a three-beam interferogram: in the Twyman-Green interferometer by registration of the Ifb interferogram while the reference beam is blocked and its subtraction from the three-beam interferogram, and in the Fizeau setup by manipulating the reference beam intensity or subtracting two phase-shifted three-beam interferograms. All operations are described by formulas derived in this work. Accuracy of the methods was estimated using both computer-generated and experimental images. The accuracy of obtained phase maps was compared with reference methods.
Diploma typeDoctor of Philosophy
Author Zofia Sunderland (FM / IMPh)
Zofia Sunderland,,
- The Institute of Micromechanics and Photonics
Title in EnglishDevelopment of a method for flat surface measurement of quasi-flat-bottomed plates using triple bonding
Languagepl polski
Certifying UnitFaculty of Mechatronics (FM)
Disciplinemechanical engineering / (technology domain) / (technological sciences)
Defense Date08-02-2017
End date22-02-2017
Supervisor Krzysztof Patorski (FM / IMPh)
Krzysztof Patorski,,
- The Institute of Micromechanics and Photonics

Internal reviewers Wacław Urbańczyk - Wroclaw University of Science and Technology (PWr)
Wacław Urbańczyk,,
-
External reviewers Jan K. Jabczyński - Wojskowa Akademia Techniczna im. Jarosława Dąbrowskiego (WAT)
Jan K. Jabczyński,,
-
Pages121
Keywords in Englishthree-beam interference
Abstract in EnglishThis dissertation is devoted to flatness measurments of quasi-parallel plates taking advantage of three-beam interference. Method of analysis of the registered three-beam interferograms resulting in determination front and back surface flatness and optical thickness variation assuming homogeneous distribution of refractive index of the element under test is proposed. Processing paths using a single three-beam interferogram or a set of (at least two) three-beam interferograms with mutual phase shift is developed. The first case may be applied to images registered in Twyman-Green interferometer, the second case also in the Fizeau system. In both cases determination of plate parameters may be realized without interference into the optomechanical setup or the plate. Firstly, each of the proposed processing paths eliminates a fringe set Ifb from a three-beam interferogram. The set Ifb results from interference of the beams reflected from the tested element surfaces. It leads to intensity distribution containing sum of two fringe families coding plate front and back surface topography, which is further processed. In case of wedge plates, for which number of fringes in the Ifb map is greater than 5, furher processing relies on separating the fringe sets with the use of single-frame algorithms for interferogram analysis, for example two-dimensional continuous wavelet transform or Hilbert-Huang transform. Also, the Fourier transform,Wigner-Hough pseudotransform and phase-shifting digital moiré method was tested. In case of parallel plates more complex, multi-stage processing is conducted. Finally the methods lead to to the same results, i.e. to information on plate front surface shape and other plate parameters. There are a few ways to carry out the elimination of the fringe set Ifb from a three-beam interferogram: in the Twyman-Green interferometer by registration of the Ifb interferogram while the reference beam is blocked and its subtraction from the three-beam interferogram, and in the Fizeau setup by manipulating the reference beam intensity or subtracting two phase-shifted three-beam interferograms. All operations are described by formulas derived in this work. Accuracy of the methods was estimated using both computer-generated and experimental images. The accuracy of obtained phase maps was compared with reference methods.
Thesis file
rozprawa_doktorska_Zofia_Sunderland.pdf 12.1 MB

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