Deflectometry in cylindrical coordinates using a conical mirror: principles and proof of concept

  • Marcos José Ferreira CarvalhoEmail author
  • Celso Luiz Nickel Veiga
  • Armando Albertazzi
Technical Paper


Engineering applications for precision cylindrical parts have required increasingly tight geometric tolerances to guarantee their correct functionality. In addition to demanding better machine tools and manufacturing processes, it is also important to have the means to verify if the qualities of precision cylindrical components meet the requirements. Optical measurement techniques are excellent options for this task since they are contactless, fast and precise. This paper proposes the concept of deflectometry in cylindrical coordinates for measuring roundness in precision cylindrical parts. Deflectometry is an optical technique that indirectly measures the shape deviations of a mirror-like surface from the distortions in reflected images by the measured surface. Flat or smooth surfaces with good surface finishes are among the main applications. Measurement uncertainties of a few nanometers have been reported in the literature. The new concept presented in this paper uses deflectometry through a 45° conical mirror. The conical mirror turns the cylindrical surface into a planar image by an optical transformation, making possible to measure the geometric deviations using deflectometry. This paper presents the proposed optical configuration, the required sequence of fringes to be reflected, measurement and reconstruction algorithms and the results of proof-of-concept experiments. The preliminary results show very good performance for roundness measurements of cross sections. However, it was not possible to measure efficiently the cylinder generatrix straightness. The concept presented here may give rise to a new family of optical roundness measurement machines.


Conical mirror Deflectometry Geometric control Optical geometrical form measurement Roundness 



The authors would like to express thanks to PHOTONITA for the technical support and for the development of this research.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Brazilian Military Engineering Institute – IMERio De JaneiroBrazil
  2. 2.Federal University of Santa Catarina – UFSCFlorianópolisBrazil

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