3D Measurement and Characterization of Ultra-precision Aspheric Surfaces☆

Abstract Aspheric surfaces have become widely used in various fields ranging from imaging systems to energy and biomedical applications. Although many research works 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.

[1]  Roland Siegwart,et al.  Comparing ICP variants on real-world data sets , 2013, Auton. Robots.

[2]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[3]  Nabil Anwer,et al.  Curvature-based Registration and Segmentation for Multisensor Coordinate Metrology , 2013 .

[4]  Martyn Hill,et al.  A new approach to characterising aspheric surfaces , 2010 .

[5]  Fengzhou Fang,et al.  Manufacturing and measurement of freeform optics , 2013 .

[6]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[7]  Xiangchao Zhang,et al.  Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology , 2010 .

[8]  Wenping Wang,et al.  Fast B-spline curve fitting by L-BFGS , 2011, Comput. Aided Geom. Des..

[9]  J. Nocedal Updating Quasi-Newton Matrices With Limited Storage , 1980 .

[10]  Héctor Aceves-Campos Profile Identification of Aspheric Lenses , 1998 .

[11]  Josef Hoschek,et al.  Global reparametrization for curve approximation , 1998, Comput. Aided Geom. Des..

[12]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[13]  A. B. Forbes,et al.  Generalised regression problems in metrology , 1993, Numerical Algorithms.

[14]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[15]  Min Zhang Discrete shape modeling for geometrical product specification : contributions and applications to skin model simulation , 2011 .

[16]  Ilhan Kaya,et al.  Comparative assessment of freeform polynomials as optical surface descriptions. , 2012, Optics express.

[17]  Craig M. Shakarji,et al.  Least-Squares Fitting Algorithms of the NIST Algorithm Testing System , 1998, Journal of research of the National Institute of Standards and Technology.

[18]  Nabil Anwer,et al.  Reconstruction of freeform surfaces for metrology , 2014 .

[19]  Qian Mi,et al.  Research of fitting algorithm for coefficients of rotational symmetry aspheric lens , 2009, International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT).

[20]  Zhengyou Zhang,et al.  Parameter estimation techniques: a tutorial with application to conic fitting , 1997, Image Vis. Comput..

[21]  Hyungjun Park,et al.  A solution for NURBS modelling in aspheric lens manufacture , 2004 .

[22]  Zbigniew Chuchro SOME COMMENTS ON REFERENCE DATA SET GENERATION IN PASSING , 2009 .

[23]  Peter Lancaster,et al.  Error analysis for the Newton-Raphson method , 1966 .

[24]  James P. Sethna,et al.  Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization , 2012, 1201.5885.

[25]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[26]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..