Fringe projection is an optical method of measuring the surface profile of a part. Most basic fringe projection processes require an initial calibration step to determine components of coordinate transformation matrices before the surface point coordinates can be measured. Calibration typically involves estimation of transformation matrix components by least-squares regression of a linearized system of equations. However, the presence of uncertainty in both the observations vector and the components matrix complicates the calculation of uncertainty in the transformation matrix components. Because the transformation matrix components are inputs upon which the surface point coordinate measurement relies, the uncertainty in the final measurement is a non-trivial determination. Thus, the uncertainty analysis does not involve calculation of transformation matrix component values and their associated uncertainties. Rather, estimates for transformation matrix components are left in equation form and substituted into the measurement equations. This allows uncertainty in measurement to be determined symbolically following procedures outlined in the Guide to the Expression of Uncertainty in Measurement. Use of computational mathematical software allows such a large scale problem to be solved and also allows several parameters of the problem to be varied, revealing output sensitivities.
Proceedings Title: Proceedings of the American Society for Precision Engineering 2009 Summer Meeting
Conference Dates: July 7-8, 2009
Conference Location: Peoria, IL
Pub Type: Conferences