Absolute flatness testing by the rotation method with optimal measuring-error compensation

Abstract

The rotation method for the absolute testing of three flats by the evaluation of four interference patterns of pairs of these flats is developed further. Least-squares methods for determining and minimizing the effect of random measuring errors are fully applied. This application makes an optimal resolution in depth and an enhanced lateral resolution possible. The computational effort mainly consists of a repeated solution of a linear equation system with 3N unknowns if N diameters of each flat are to be evaluated. The rms error of determining a flatness deviation is calculated as a function of the rms measuring error, the desired lateral resolution, and the position on the surface. The algorithm is extended to the case of using square-grid detector arrays by a special interpolation method.