Statistical Engineering Division Seminar

Nadia Machkour Deshayes
Manufactering Metrology Division
NIST
Statistical Engineering Division Seminar
Teusday July 11, 2006, 10:30-11:30 AM
Lecture Room C

Abstract

The National Institute of Standards and Technology (NIST) is developing the Geometry Measuring Machine (GEMM) for free-form and aspheric surface metrology. While optical interferometry is a general, simple, and accurate method for form metrology of flat and spherical surfaces, interferometers are not well suited to testing objects with complex shapes. The reason is that, unlike flat and spherical optics, a reference wavefront for a complex surface is difficult to generate. The idea behind GEMM is to reconstruct the 3D-shape or the 2D-profile of a surface under test from its local curvature measurements. In Euclidean space, curvature is an intrinsic property of an object's shape; and is invariant under Euclidean motions, which means curvature can define a curve regardless of the part's position and angular orientation. The 2D-profile of a test part is given by solving a second-order differential equation involving curvature, but the 3D-shape reconstruction uses a model derived from Zernike polynomials. To realize this differential geometry theory, there remain challenging engineering and signal processing hurdles to overcome.