A method for the in situ determination of Abbe errors and their correction

Abstract

Often Abbe errors are the most important uncertainty sources in dimensional metrology applications aiming for measurement uncertainties of only a few nanometres. Abbe errors are caused by the angle deviations of relative translations between measurement object and sensing device—either in moving object or moving sensing device configuration—and the offset between the measurement axes of the machine and the measurement point of the structure localization device or the displacement sensor under investigation. The angle deviations of the motion stage can usually be determined, e.g. by an electronic autocollimator with sufficient accuracy. Unfortunately, in many cases, the Abbe offset cannot be estimated with sufficient accuracy or varies over the measurement range. In order to reduce the influence of the Abbe error many length measuring machines are equipped with control loops to reduce the angle deviations. However, in order to specify the uncertainty contribution of the residual Abbe errors, the Abbe offsets are still required. In these cases, in principle, an in situ determination of the Abbe errors is possible by the following method. First the measurement is conducted in the common way. Then two further measurements are performed during which one angle, consecutively the yaw and the pitch angle, is scanned by the angle actuators and measured by the angle sensors of the control loop. The differences of these two measurements from the first should reflect the influence of the Abbe errors and the dependence of the length measurement results on the angles can be determined. This predication was tested during the measurements of a high resolution encoder with the Nanometer Comparator. Contrary to the classical perception, the observed dependence of the Abbe error on the angle variation applied was nonlinear. However, using a polynomial of third order it is possible to correct the artificially introduced Abbe errors of up to 20 nm almost down to the noise level.