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

Phase-shift shadow-moire topography is a noncontact optical technique for m easuring the shapes of surfaces. Artifactual bands resembling isoheight sur face contours are observed during measurement of small changes in shape by use of this technique. The shape-reconstruction algorithm used in shadow-mo ire topography is based on a mathematical model of the fringe patterns gene rated 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 simul ating 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 su rface is reconstructed from fringe patterns simulated with a model containi ng the height-dependent terms. Shape-error curves are computed as a functio n of the surface height by the subtraction of the reconstructed shape from the known shape. Simulated shape-error curves agree with experimental measu rements in that they show an increase in error with surface height, and bot h the experimental and the simulated shape-error curves contain ripples. Al though the errors are small in comparison with the dimensions of the surfac e and are negligible in shape measurements and in most deformation measurem ents, they may show up as noticeable bands in images of small deformations. (C) 2000 Optical Society of America. OCIS codes: 120.4120, 000.4430, 050.5 080.