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Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
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Local and global surface errors evaluation using Ronchi test, without both approximation and integration.

Alberto Cordero-Dávila1, Jorge González-García, Carlos Ignacio Robledo-Sánchez

  • 1Facultad de Ciencias Físico Matemáticas (FCFM), Benemérita Universidad Autónoma de Puebla (BUAP), Av. San Claudio y Río Verde s/n Col. San Manuel, Puebla, Apartado Postal 1152, C. P. 72570, Mexico. acordero@fcfm.buap.mx

Applied Optics
|August 23, 2011
PubMed
Summary

This study presents a novel method for accurately measuring conic surface errors using Ronchigrams. By avoiding integration and employing cubic splines with genetic algorithms, the technique enhances precision in optical surface evaluation.

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Area of Science:

  • Optical engineering
  • Metrology
  • Surface analysis

Background:

  • Optical shops commonly use Ronchigrams to assess surface errors.
  • Evaluating conic surfaces requires precise measurement of curvature radius and conic constant.
  • Traditional methods may face challenges with integration and local error reproduction.

Purpose of the Study:

  • To quantitatively reproduce and enhance the technique for evaluating surface errors from Ronchigrams.
  • To accurately determine the curvature radius and conic constant of conic surfaces.
  • To avoid issues associated with numerical or polynomial integration in error function calculation.

Main Methods:

  • Quantitative reproduction of optical shop techniques for Ronchigram analysis.
  • Evaluation of conic surfaces using Ronchigrams with varying fringe numbers.
  • Error function calculation without integration, utilizing cubic splines.
  • Application of genetic algorithms for optimal reproduction of experimental Ronchigrams.

Main Results:

  • Successful quantitative evaluation of surface errors from experimental and simulated Ronchigrams.
  • Accurate determination of curvature radius and conic constant for conic surfaces.
  • Superior local error reproduction using cubic splines compared to polynomial descriptions.
  • Optimized reproduction of experimental Ronchigrams through genetic algorithms.

Conclusions:

  • The developed method provides a robust and accurate approach for evaluating conic surface errors.
  • Avoiding integration and using cubic splines significantly improves error function description.
  • Genetic algorithms enhance the fidelity of experimental Ronchigram reproduction, leading to more reliable measurements.