https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Sun, 07 Jun 2026 14:32:20 GMT 2026-06-07T14:32:20Z http://hdl.handle.net/10985/8635 Fast B-Spline 2D Curve Fitting for unorganized Noisy Datasets EL HAYEK, Nadim; DAMAK, Mohamed; NOUIRA, Hichem; ANWER, Nabil; NYIRI, Eric; GIBARU, Olivier In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98]. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8635 2014-01-01T00:00:00Z EL HAYEK, Nadim DAMAK, Mohamed NOUIRA, Hichem ANWER, Nabil NYIRI, Eric GIBARU, Olivier In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98]. http://hdl.handle.net/10985/8646 Reconstruction of freeform surfaces for metrology EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8646 2014-01-01T00:00:00Z EL HAYEK, Nadim NOUIRA, Hichem ANWER, Nabil DAMAK, Mohamed GIBARU, Olivier The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces. http://hdl.handle.net/10985/8946 A newly conceived cylinder measuring machine and methods that eliminate the spindle errors VISSIERE, Alain; NOUIRA, Hichem; DAMAK, Mohamed; GIBARU, Olivier; DAVID, Jean-Marie Advanced manufacturing processes require improving dimensional metrology applications to reach a nanometric accuracy level. Such measurements may be carried out using conventional highly accurate roundness measuring machines. On these machines, the metrology loop goes through the probing and the mechanical guiding elements. Hence, external forces, strain and thermal expansion are transmitted to the metrological structure through the supporting structure, thereby reducing measurement quality. The obtained measurement also combines both the motion error of the guiding system and the form error of the artifact. Detailed uncertainty budgeting might be improved, using error separation methods (multi-step, reversal and multi-probe error separation methods, etc), enabling identification of the systematic (synchronous or repeatable) guiding system motion errors as well as form error of the artifact. Nevertheless, the performance of this kind of machine is limited by the repeatability level of the mechanical guiding elements, which usually exceeds 25 nm (in the case of an air bearing spindle and a linear bearing). In order to guarantee a 5 nm measurement uncertainty level, LNE is currently developing an original machine dedicated to form measurement on cylindrical and spherical artifacts with an ultra-high level of accuracy. The architecture of this machine is based on the ‘dissociated metrological technique’ principle and contains reference probes and cylinder. The form errors of both cylindrical artifact and reference cylinder are obtained after a mathematical combination between the information given by the probe sensing the artifact and the information given by the probe sensing the reference cylinder by applying the modified multi-step separation method. Sun, 01 Jan 2012 00:00:00 GMT http://hdl.handle.net/10985/8946 2012-01-01T00:00:00Z VISSIERE, Alain NOUIRA, Hichem DAMAK, Mohamed GIBARU, Olivier DAVID, Jean-Marie Advanced manufacturing processes require improving dimensional metrology applications to reach a nanometric accuracy level. Such measurements may be carried out using conventional highly accurate roundness measuring machines. On these machines, the metrology loop goes through the probing and the mechanical guiding elements. Hence, external forces, strain and thermal expansion are transmitted to the metrological structure through the supporting structure, thereby reducing measurement quality. The obtained measurement also combines both the motion error of the guiding system and the form error of the artifact. Detailed uncertainty budgeting might be improved, using error separation methods (multi-step, reversal and multi-probe error separation methods, etc), enabling identification of the systematic (synchronous or repeatable) guiding system motion errors as well as form error of the artifact. Nevertheless, the performance of this kind of machine is limited by the repeatability level of the mechanical guiding elements, which usually exceeds 25 nm (in the case of an air bearing spindle and a linear bearing). In order to guarantee a 5 nm measurement uncertainty level, LNE is currently developing an original machine dedicated to form measurement on cylindrical and spherical artifacts with an ultra-high level of accuracy. The architecture of this machine is based on the ‘dissociated metrological technique’ principle and contains reference probes and cylinder. The form errors of both cylindrical artifact and reference cylinder are obtained after a mathematical combination between the information given by the probe sensing the artifact and the information given by the probe sensing the reference cylinder by applying the modified multi-step separation method. http://hdl.handle.net/10985/8944 Concept and architecture of a new apparatus for cylindrical form measurement with a nanometric level of accuracy VISSIERE, Alain; NOUIRA, Hichem; DAMAK, Mohamed; GIBARU, Olivier; DAVID, Jean-Marie In relation to the industrial need and to the progress of technology, Laboratoire National de M´etrologie et d’Essais (LNE) would like to improve the measurement of its primary pressure standards, spherical and flick standards. The spherical and flick standards are, respectively, used to calibrate the spindle motion error and the probe, which equip commercial conventional cylindricity-measuring machines. The primary pressure standards are obtained using pressure balances equipped with rotary pistons. To reach a relative uncertainty of 10−6 in the pressure measurement, it is necessary to know the diameters of both the piston and the cylinder with an uncertainty of 5 nm for a piston diameter of 10 mm. Conventional machines are not able to reach such an uncertainty level. That is why the development of a new machine is necessary. The purpose of this paper is to present the concepts and the architecture adopted in the development of the new equipment dedicated to cylindricity measurement at a nanometric level of a accuracy. The choice of these concepts is based on the analysis of the uncertainty sources encountered in conventional architectures. The architecture of the new ultra-high equipment as well as the associated calibration procedures will be described and detailed. Sun, 01 Jan 2012 00:00:00 GMT http://hdl.handle.net/10985/8944 2012-01-01T00:00:00Z VISSIERE, Alain NOUIRA, Hichem DAMAK, Mohamed GIBARU, Olivier DAVID, Jean-Marie In relation to the industrial need and to the progress of technology, Laboratoire National de M´etrologie et d’Essais (LNE) would like to improve the measurement of its primary pressure standards, spherical and flick standards. The spherical and flick standards are, respectively, used to calibrate the spindle motion error and the probe, which equip commercial conventional cylindricity-measuring machines. The primary pressure standards are obtained using pressure balances equipped with rotary pistons. To reach a relative uncertainty of 10−6 in the pressure measurement, it is necessary to know the diameters of both the piston and the cylinder with an uncertainty of 5 nm for a piston diameter of 10 mm. Conventional machines are not able to reach such an uncertainty level. That is why the development of a new machine is necessary. The purpose of this paper is to present the concepts and the architecture adopted in the development of the new equipment dedicated to cylindricity measurement at a nanometric level of a accuracy. The choice of these concepts is based on the analysis of the uncertainty sources encountered in conventional architectures. The architecture of the new ultra-high equipment as well as the associated calibration procedures will be described and detailed. http://hdl.handle.net/10985/8653 3D Measurement and Characterization of Ultra-precision Aspheric Surfaces EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; BOURDET, Pierre; GIBARU, Olivier Aspheric surfaces have become widely used in various fields ranging from imaging systems to energy and biomedical applications. Although many researches have been conducted to address their manufacturing and measurement, there are still challenges in form characterization of aspheric surfaces considering a large number of data points. This paper presents a comparative study of 3D measurement and form characterization of an aspheric lens using tactile and optical single scanning probing systems. The design of the LNE high precision profilometer, traceable to standard references is presented. The measured surfaces are obtained from the aforementioned system. They are characterized with large number of data points for which a suitable process chain is deployed. The form characterization of the aspheric surfaces is based on surface fitting techniques by comparing the measured surface with the design surface. A comparative study of registration methods and non-linear Orthogonal Least-Squares fitting Methods is presented. Experimental results are analyzed and discussed to illustrate the effectiveness of the proposed approaches. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8653 2014-01-01T00:00:00Z EL HAYEK, Nadim NOUIRA, Hichem ANWER, Nabil DAMAK, Mohamed BOURDET, Pierre GIBARU, Olivier Aspheric surfaces have become widely used in various fields ranging from imaging systems to energy and biomedical applications. Although many researches have been conducted to address their manufacturing and measurement, there are still challenges in form characterization of aspheric surfaces considering a large number of data points. This paper presents a comparative study of 3D measurement and form characterization of an aspheric lens using tactile and optical single scanning probing systems. The design of the LNE high precision profilometer, traceable to standard references is presented. The measured surfaces are obtained from the aforementioned system. They are characterized with large number of data points for which a suitable process chain is deployed. The form characterization of the aspheric surfaces is based on surface fitting techniques by comparing the measured surface with the design surface. A comparative study of registration methods and non-linear Orthogonal Least-Squares fitting Methods is presented. Experimental results are analyzed and discussed to illustrate the effectiveness of the proposed approaches. http://hdl.handle.net/10985/8647 A new method for aspherical surface fitting with large-volume datasets EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8647 2014-01-01T00:00:00Z EL HAYEK, Nadim NOUIRA, Hichem ANWER, Nabil DAMAK, Mohamed GIBARU, Olivier In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods. http://hdl.handle.net/10985/23488 Modelling and characterisation of geometric errors on 5-axis machine-tool VIPREY, Fabien; NOUIRA, Hichem; LAVERNHE, Sylvain; TOURNIER, Christophe This research work deals with the geometric modelling of 5-axis machine tool based on a standard-ised parameterisation of geometric errors with the aim to decrease the volumetric error in the workspace. The identification of the model's parameters is based on the development of a new standard thermo-invariant material namely the Multi-Feature Bar. Thanks to its calibration and a European intercom-parison, it now provides a direct metrological traceability to the SI metre for dimensional measurement on machine tool in a hostile environment. The identification of three intrinsic parameters of this standard , coupled with a measurement procedure ensures a complete and traceable identification of motion errors of linear axes. An identification procedure of location and orientation errors of axes is proposed by probing a datum sphere in the workspace and minimising the time drift of the structural loop and the effects of the previously identified motion errors. Finally, the developed model partially identified, allows the characterisation of 95% of the measured volumetric error. Therefore, the mean volumetric error not characterised by the model only amounts to 8 µm. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/23488 2019-01-01T00:00:00Z VIPREY, Fabien NOUIRA, Hichem LAVERNHE, Sylvain TOURNIER, Christophe This research work deals with the geometric modelling of 5-axis machine tool based on a standard-ised parameterisation of geometric errors with the aim to decrease the volumetric error in the workspace. The identification of the model's parameters is based on the development of a new standard thermo-invariant material namely the Multi-Feature Bar. Thanks to its calibration and a European intercom-parison, it now provides a direct metrological traceability to the SI metre for dimensional measurement on machine tool in a hostile environment. The identification of three intrinsic parameters of this standard , coupled with a measurement procedure ensures a complete and traceable identification of motion errors of linear axes. An identification procedure of location and orientation errors of axes is proposed by probing a datum sphere in the workspace and minimising the time drift of the structural loop and the effects of the previously identified motion errors. Finally, the developed model partially identified, allows the characterisation of 95% of the measured volumetric error. Therefore, the mean volumetric error not characterised by the model only amounts to 8 µm. http://hdl.handle.net/10985/8649 Comparison of tactile and chromatic confocal measurements of aspherical lenses for form metrology EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier Both contact and non-contact probes are often used in dimensional metrology applications, especially for roughness, form and surface profile measurements. To perform such kind of measurements with a nanometer level of accuracy, LNE (French National Metrology Institute (NMI)) has developed a high precision profilometer traceable to the SI meter definition. The architecture of the machine contains a short and stable metrology frame dissociated from the supporting frame. It perfectly respects Abbe principle. The metrology loop incorporates three Renishaw laser interferometers and is equipped either with a chromatic confocal probe or a tactile probe to achieve measurements at the nanometric level of uncertainty. The machine allows the in-situ calibration of the probes by means of a differential laser interferometer considered as a reference. In this paper, both the architecture and the operation of the LNE’s high precision profilometer are detailed. A brief comparison of the behavior of the chromatic confocal and tactile probes is presented. Optical and tactile scans of an aspherical surface are performed and the large number of data are processed using the L-BFGS (Limited memory-Broyden-Fletcher-Goldfarb-Shanno) algorithm. Fitting results are compared with respect to the evaluated residual errors which reflect the form defects of the surface. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10985/8649 2014-01-01T00:00:00Z EL HAYEK, Nadim NOUIRA, Hichem ANWER, Nabil DAMAK, Mohamed GIBARU, Olivier Both contact and non-contact probes are often used in dimensional metrology applications, especially for roughness, form and surface profile measurements. To perform such kind of measurements with a nanometer level of accuracy, LNE (French National Metrology Institute (NMI)) has developed a high precision profilometer traceable to the SI meter definition. The architecture of the machine contains a short and stable metrology frame dissociated from the supporting frame. It perfectly respects Abbe principle. The metrology loop incorporates three Renishaw laser interferometers and is equipped either with a chromatic confocal probe or a tactile probe to achieve measurements at the nanometric level of uncertainty. The machine allows the in-situ calibration of the probes by means of a differential laser interferometer considered as a reference. In this paper, both the architecture and the operation of the LNE’s high precision profilometer are detailed. A brief comparison of the behavior of the chromatic confocal and tactile probes is presented. Optical and tactile scans of an aspherical surface are performed and the large number of data are processed using the L-BFGS (Limited memory-Broyden-Fletcher-Goldfarb-Shanno) algorithm. Fitting results are compared with respect to the evaluated residual errors which reflect the form defects of the surface.