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Applied Optics

Applied Optics


  • Vol. 39, Iss. 19 — Jul. 1, 2000
  • pp: 3266–3275

Systematic errors in small deformations measured by use of shadow-moiré topography

Hanif M. Ladak, Willem F. Decraemer, Joris J. J. Dirckx, and W. Robert J. Funnell  »View Author Affiliations

Applied Optics, Vol. 39, Issue 19, pp. 3266-3275 (2000)

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Phase-shift shadow-moiré topography is a noncontact optical technique for measuring the shapes of surfaces. Artifactual bands resembling isoheight surface contours are observed during measurement of small changes in shape by use of this technique. The shape-reconstruction algorithm used in shadow-moiré topography is based on a mathematical model of the fringe patterns generated on the surface to be measured. We hypothesize that the observed bands reflect systematic errors caused by ignoring height-dependent terms in the mathematical model of the fringe patterns. We test the assumption by simulating the fringe patterns for a virtual test surface by using a model that contains height-dependent terms and one term that is idealized by ignoring these terms. Small systematic errors in shape are observed only when the surface is reconstructed from fringe patterns simulated with a model containing the height-dependent terms. Shape-error curves are computed as a function of the surface height by the subtraction of the reconstructed shape from the known shape. Simulated shape-error curves agree with experimental measurements in that they show an increase in error with surface height, and both the experimental and the simulated shape-error curves contain ripples. Although the errors are small in comparison with the dimensions of the surface and are negligible in shape measurements and in most deformation measurements, they may show up as noticeable bands in images of small deformations.

© 2000 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.5080) Diffraction and gratings : Phase shift
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques

Original Manuscript: October 8, 1999
Revised Manuscript: April 4, 2000
Published: July 1, 2000

Hanif M. Ladak, Willem F. Decraemer, Joris J. J. Dirckx, and W. Robert J. Funnell, "Systematic errors in small deformations measured by use of shadow-moiré topography," Appl. Opt. 39, 3266-3275 (2000)

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