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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
  • 34 Downloads

Abstract

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.

Keywords

Conical mirror Deflectometry Geometric control Optical geometrical form measurement Roundness 

Notes

Acknowledgements

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

References

  1. 1.
    Pfeifer T (2002) Production metrology. De Gruyter Oldenbourg, Munich; Reprint 2015 ed. edition (21 Aug 2002)Google Scholar
  2. 2.
    VDI – The Association of German Engineers. VDI/VDE 2601 (1991) Requirements on the surface structure to cover function capability of surfaces manufactured by cutting; list of parametersGoogle Scholar
  3. 3.
    International Organization for Standardization (2012) ISO 1101: geometrical product specifications (GPS)—geometrical tolerancing—tolerances of form, orientation, location and run-out, 3rd edn. ISO, GenevaGoogle Scholar
  4. 4.
    Humienny Z et al (2001) Geometrical product specifications: course for technical universities. Warsaw University of Technology Printing House, WarsawGoogle Scholar
  5. 5.
    Smith GT (2002) Industrial metrology: surfaces and roundness, 1st edn. Springer, LondonCrossRefGoogle Scholar
  6. 6.
    International Organization for Standardization (2011) ISO 12181-1: geometrical product specifications (GPS)—roundness—part 1: vocabulary and parameters of roundness, 1st edn. ISO, GenevaGoogle Scholar
  7. 7.
    International Organization for Standardization (2011) ISO 12181-2: Geometrical product specifications (GPS)—roundness—part 2: specification operators, 1st edn. ISO, GenevaGoogle Scholar
  8. 8.
    Albertazzi A, Dal Pont A (2005) Preliminary measurement performance evaluation of a new white light interferometer for cylindrical surfaces. Am J Phys US 13:28–31Google Scholar
  9. 9.
    Albertazzi A, Dal Pont A (2006) A white light interferometer for measurement of external cylindrical surfaces. In: Osten W (ed) Fringe 2005. Springer, Berlin.  https://doi.org/10.1007/3-540-29303-5_85 CrossRefGoogle Scholar
  10. 10.
    Viotti MR, Albertazzi A, Fantin AV, Dal Pont A (2008) Comparison between a white-light interferometer and a tactile formtester for the measurement of long inner cylindrical surfaces. Opt Lasers Eng 46(5):396–403.  https://doi.org/10.1016/j.optlaseng.2007.12.004 CrossRefGoogle Scholar
  11. 11.
    Viotti MR, Albertazzi A, Dal Pont A, Fantin AV (2007) Evaluation of a novel algorithm to align and stitch adjacent measurements of long inner cylindrical surfaces with white light interferometry. Opt Lasers Eng 45(8):852–859.  https://doi.org/10.1016/j.optlaseng.2007.02.003 CrossRefGoogle Scholar
  12. 12.
    Albertazzi A, Viotti MR, Miggiorin RM, Dal Pont A (2008) Applications of a white light interferometer of wear measurement of cylinders. Proc SPIE 7064(2008):70640B–1–70640B–10.  https://doi.org/10.1117/12.796058 CrossRefGoogle Scholar
  13. 13.
    Albertazzi A, Viotti MR; Dal Pont A (2006) A white-light interferometer for inner cylindrical surfaces. In: Interferometry XIII: applications 62930F, 13 Aug 2006. SPIE, pp 1–8. http://dx.doi.org/10.1117/12.678050
  14. 14.
    Weckenmann A, Bruning J, Patterson S, Knight P (2001) Grazing incidence interferometry for high precision measurements of cylindrical form deviations. Cirp Ann Oxf 50(1):381–384.  https://doi.org/10.1016/s0007-8506(07)62145-3 CrossRefGoogle Scholar
  15. 15.
    Chen F, Brown GM, Song MM (2000) Overview of three-dimensional shape measurement using optical methods. Opt Eng 39(1):10–22CrossRefGoogle Scholar
  16. 16.
    Bothe T, Li W, von Kopylow C, Jüptner W (2004) High-resolution 3 D shape measurement on specular surfaces by fringe reflection. Proc SPIE 5457:411–422CrossRefGoogle Scholar
  17. 17.
    Huang L, Idir M, Zuo C, Asundi A (2018) Review of phase measuring deflectometry. Opt Lasers Eng 107:247–257.  https://doi.org/10.1016/j.optlaseng.2018.03.026 CrossRefGoogle Scholar
  18. 18.
    Pérard D, Beyerer J (1997) Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique. Proc SPIE 3204-11:74–80CrossRefGoogle Scholar
  19. 19.
    Höfer S, Heizmann M, Werling S (2011) Deflectometry for the inspection of specular surfaces. Workshop on “non-destructive inspection technologies”, Zurich: [s.n.]Google Scholar
  20. 20.
    Häusler G, Faber C, Olesch E, Ettl S (2013) Deflectometry vs. interferometry. Proc SPIE 8788:13–16Google Scholar
  21. 21.
    Yang F, Wang Z, Wen Y, Qu W (2015) Two-dimensional phase unwrapping algorithms for fringe pattern analysis: a comparison study. In: Proceedings of SPIE, vol 9302, no 93023FGoogle Scholar
  22. 22.
    Knauer MC, Kaminski J, Häusler G (2004) Phase measuring deflectometry: a new approach to measure specular free-form surfaces. Proc SPIE 5457:366–376CrossRefGoogle Scholar
  23. 23.
    Sárosi Z et al (2011) Detection of surface defects on sheet metal parts using one-shot deflectometry in the infrared range. In: FLIR technical series: application note for research & science, Zurich, pp 1–10. http://www.flir.co.uk/WorkArea/DownloadAsset.aspx?id=50056. Accessed 6 Nov 2015
  24. 24.
    Zhang S (2010) Recent progresses on real-time 3D shape measurement using digital fringe projection techniques. Opt Lasers Eng 48(2):149–158.  https://doi.org/10.1016/j.optlaseng.2009.03.008 CrossRefGoogle Scholar
  25. 25.
    Yoshizawa T, Wakayama T (2009) Surface profilometry Handbook of optical metrology: principles and applications. CRC Press, Boca RatonCrossRefGoogle Scholar
  26. 26.
    Guo H, Feng P, Tao T (2010) Specular surface measurement by using least squares light tracking technique. Opt Lasers Eng 48(2):166–171.  https://doi.org/10.1016/j.optlaseng.2009.04.005 CrossRefGoogle Scholar
  27. 27.
    Xiao YL, Su X, Chen W, Liu Y (2012) Three-dimensional shape measurement of aspheric mirror based on fringe reflection photogrammetry. Appl Opt 51(4):457–464CrossRefGoogle Scholar
  28. 28.
    Srinivasan V, Liu HC, Halioua M (1984) Automated phase-measuring profilometry of 3-D diffuse objects. Appl Opt 23(18):3105–3108CrossRefGoogle Scholar
  29. 29.
    Zhang Q, Su X, Xiang L, Sun X (2012) 3-D shape measurement based on complementary gray-code light. Opt Lasers Eng 50(4):574–579.  https://doi.org/10.1016/j.optlaseng.2011.06.024 CrossRefGoogle Scholar
  30. 30.
    Li W, Bothe T, von Kopylow C, Jüptner W (2004) Evaluation methods for gradient measurement techniques. In: Optical metrology in production engineering, [s.l.]. SPIE, pp 300–311. http://dx.doi.org/10.1117/12.546002
  31. 31.
    Wu Y, Yue H, Yi J, Li M, Liu Y (2014) Single-shot three-dimensional shape measurement of specular surfaces by orthogonal color fringe pattern reflection technique. In: Optical metrology and inspection for industrial applications III, [s.l.]. SPIE, pp 1–9. http://dx.doi.org/10.1117/12.2072410
  32. 32.
    Southwell WH (1980) Wave-front estimation from wave-front slope measurements. J Opt Soc Am 70(8):998–1006CrossRefGoogle Scholar
  33. 33.
    Huang L, Asundi A (2012) Improvement of least-squares integration method with iterative compensations in fringe reflectometry. Appl Opt 51(31):7459–7465CrossRefGoogle Scholar
  34. 34.
    Harker M, O’Leary P (2015) Regularized reconstruction of a surface from its measured gradient field: algorithms for spectral, Tikhonov, constrained, and weighted regularization. J Math Imaging Vis N Y 51(1):46–70MathSciNetCrossRefGoogle Scholar
  35. 35.
    Zhang Z (1999) Flexible camera calibration by viewing a plane from unknown orientations. In: Proceedings of the seventh IEEE international conference on computer vision, 2012, vol 1(c), pp 0–7Google Scholar
  36. 36.
    Harker M, O’Leary P (2008) Least squares surface reconstruction from measured gradient fields. In: 2008 IEEE conference on computer vision and pattern recognition, [s.l.]. IEEE, pp 1–7Google Scholar
  37. 37.
    Harker M, O’Leary P (2011) Least squares surface reconstruction from gradients: direct algebraic methods with spectral, Tikhonov, and constrained regularization. In: CVPR 2011, [s.l.]. IEEE, pp 2529–2536Google Scholar
  38. 38.
    Harker M, O’Leary P (2013) Direct regularized surface reconstruction from gradients for industrial photometric stereo. Comput Ind Leoben 64(9):1221–1228CrossRefGoogle Scholar
  39. 39.
    Harker M, O’Leary P (2013) Computes the Global least squares reconstruction of a surface from its gradient field with spectral filtering, using either polynomial, cosine, or Fourier bases. http://www.mathworks.com/matlabcentral/fileexchange/authors/321598. Accessed 25 Jan 2016
  40. 40.
    Henzold G (2006) Geometrical dimensioning and tolerancing for design, manufacturing and inspection: a handbook for geometrical product specification using ISO and ASME standards, 2nd edn. Elsevier, LondonGoogle Scholar
  41. 41.
    Muralikrishnan B, Raja J (2009) Computational surface and roundness metrology. Springer, LondonGoogle Scholar
  42. 42.
    International Bureau of Weight and Measures (2008) Evaluation of measurement data: guide to expression of uncertainty in measurement. http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf. Accessed 15 July 2019

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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