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Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces

Optical aspherical lenses with high surface quality are increasingly demanded in several applications in medicine, synchrotron, vision, etc. To reach the requested surface quality, most advanced manufacturing processes are used in closed chain with high precision measurement machines. The measured d...

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Autores principales: Chiboub, Amine, Arezki, Yassir, Vissiere, Alain, Mehdi-Souzani, Charyar, Anwer, Nabil, Alzahrani, Bandar, Bouazizi, Mohamed Lamjed, Nouira, Hichem
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8703870/
https://www.ncbi.nlm.nih.gov/pubmed/34947735
http://dx.doi.org/10.3390/nano11123386
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author Chiboub, Amine
Arezki, Yassir
Vissiere, Alain
Mehdi-Souzani, Charyar
Anwer, Nabil
Alzahrani, Bandar
Bouazizi, Mohamed Lamjed
Nouira, Hichem
author_facet Chiboub, Amine
Arezki, Yassir
Vissiere, Alain
Mehdi-Souzani, Charyar
Anwer, Nabil
Alzahrani, Bandar
Bouazizi, Mohamed Lamjed
Nouira, Hichem
author_sort Chiboub, Amine
collection PubMed
description Optical aspherical lenses with high surface quality are increasingly demanded in several applications in medicine, synchrotron, vision, etc. To reach the requested surface quality, most advanced manufacturing processes are used in closed chain with high precision measurement machines. The measured data are analysed with least squares (LS or L(2)-norm) or minimum zone (MZ) fitting (also Chebyshev fitting or L(∞)-norm) algorithms to extract the form error. Performing data fitting according to L(∞)-norm is more accurate and challenging than L(2)-norm, since it directly minimizes peak-to-valley (PV). In parallel, reference softgauges are used to assess the performance of the implemented MZ fitting algorithms, according to the F1 algorithm measurement standard, to guarantee their traceability, accuracy and robustness. Reference softgauges usually incorporate multiple parameters related to manufacturing processes, measurement errors, points distribution, etc., to be as close as possible to the real measured data. In this paper, a unique robust approach based on a non-vertex solution is mathematically formulated and implemented for generating reference softgauges for complex shapes. Afterwards, two implemented MZ fitting algorithms (HTR and EPF) were successfully tested on a number of generated reference pairs. The evaluation of their performance was carried out through two metrics: degree of difficulty and performance measure.
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spelling pubmed-87038702021-12-25 Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces Chiboub, Amine Arezki, Yassir Vissiere, Alain Mehdi-Souzani, Charyar Anwer, Nabil Alzahrani, Bandar Bouazizi, Mohamed Lamjed Nouira, Hichem Nanomaterials (Basel) Article Optical aspherical lenses with high surface quality are increasingly demanded in several applications in medicine, synchrotron, vision, etc. To reach the requested surface quality, most advanced manufacturing processes are used in closed chain with high precision measurement machines. The measured data are analysed with least squares (LS or L(2)-norm) or minimum zone (MZ) fitting (also Chebyshev fitting or L(∞)-norm) algorithms to extract the form error. Performing data fitting according to L(∞)-norm is more accurate and challenging than L(2)-norm, since it directly minimizes peak-to-valley (PV). In parallel, reference softgauges are used to assess the performance of the implemented MZ fitting algorithms, according to the F1 algorithm measurement standard, to guarantee their traceability, accuracy and robustness. Reference softgauges usually incorporate multiple parameters related to manufacturing processes, measurement errors, points distribution, etc., to be as close as possible to the real measured data. In this paper, a unique robust approach based on a non-vertex solution is mathematically formulated and implemented for generating reference softgauges for complex shapes. Afterwards, two implemented MZ fitting algorithms (HTR and EPF) were successfully tested on a number of generated reference pairs. The evaluation of their performance was carried out through two metrics: degree of difficulty and performance measure. MDPI 2021-12-14 /pmc/articles/PMC8703870/ /pubmed/34947735 http://dx.doi.org/10.3390/nano11123386 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Chiboub, Amine
Arezki, Yassir
Vissiere, Alain
Mehdi-Souzani, Charyar
Anwer, Nabil
Alzahrani, Bandar
Bouazizi, Mohamed Lamjed
Nouira, Hichem
Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
title Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
title_full Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
title_fullStr Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
title_full_unstemmed Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
title_short Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
title_sort generation of reference softgauges for minimum zone fitting algorithms: case of aspherical and freeform surfaces
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8703870/
https://www.ncbi.nlm.nih.gov/pubmed/34947735
http://dx.doi.org/10.3390/nano11123386
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