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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 7 — Jul. 1, 2007
  • pp: 2003–2013

Design considerations in projection phase-shift moiré topography based on theoretical analysis of fringe formation

Jan A.N. Buytaert and Joris J.J. Dirckx  »View Author Affiliations


JOSA A, Vol. 24, Issue 7, pp. 2003-2013 (2007)
http://dx.doi.org/10.1364/JOSAA.24.002003


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Abstract

Moiré topography is a well-established optical technique to measure the shape of three-dimensional surfaces, based on the geometric interference between an optical grid and its image deformed by an object surface. The technique produces fringes that represent contours of equal height, and from the recordings of several phase-shifted topograms surface height coordinates can be calculated. To perform these calculations, it is assumed that object height variation is small in comparison with the measurement setup dimensions, and this approximation leads to systematic errors in measurement accuracy. We present the mathematical description of the fringe formation process in projection moiré topography, and on the basis of these equations we establish the relation between setup geometry and upper limits of the systematic measurement errors. We derive the equations that determine design specifications needed to reduce the effects of approximations to be below the measurement resolution of the setup. It is shown that setup geometry should be adapted to the gray-scale measurement resolution of the imaging system. We show that, using an iterative correction from one fringe order to the next, measurement accuracy can be maintained over the entire object depth.

© 2007 Optical Society of America

OCIS Codes
(080.2740) Geometric optics : Geometric optical design
(110.2990) Imaging systems : Image formation theory
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.2830) Instrumentation, measurement, and metrology : Height measurements

ToC Category:
Geometrical Optics

History
Original Manuscript: November 27, 2006
Manuscript Accepted: January 14, 2007
Published: June 13, 2007

Citation
Jan A. N. Buytaert and Joris J. J. Dirckx, "Design considerations in projection phase-shift moiré topography based on theoretical analysis of fringe formation," J. Opt. Soc. Am. A 24, 2003-2013 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-7-2003

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