Establishing an optical flatness standard

Methods proposed by the authors to establish a flatness standard without using a liquid mirror are proved in practice and extended. The extension is performed by a development of methods for the determination and compensation of random and systematic measuring errors by means of condition equations which must be satisfied by the measured sums of deviations from absolute planeness. Linear errors of these sums of deviations which can lead to ambiguities and errors of planeness deviations can be discovered and completely eliminated. Also nonlinear errors, for example, as a result of temperature differences or of mechanical stress, can be recognized without repeating the interference photography procedure. The deviations from absolute planeness of three fused silica plates were determined along seven diameters (angular distance 2pi/14) with an accuracy of lambda/500 (mean square error). This was performed by evaluating two sets of four different interference photographs, each with contour plane distances of lambda/50 (from fringe to fringe).