Monte Carlo simulations: a tool to assess complex measurement systems

Abstract

In the metrology of aspheres and freeforms, missing reference surfaces are a big challenge. The evaluation of the performance of measurement systems is currently done by round robin tests. Since the true form of the used specimens are unknown, the question still remains: who is right? This problem is also faced during the assessment of the performance of the Tilted Wave Interferometer. For both the calibration and measurement complex algorithms are applied. They calculate the system model parameters or the surface error from phaseshifting data. The analytical evaluation of different configurations or the influence of certain errors is impossible. The GUM (Guide to the Expression of Uncertainty in Measurement) proposes Monte Carlo simulations as an option for uncertainty evaluations. They are applicable for complex relationships between a measurand and the system’s input quantities. By repeatedly setting the input quantities to random values within a given range and evaluating the system response, statistically relevant data can be generated. In this contribution we present a Monte Carlo based simulation environment for the performance assessment of non-null interferometric measurements. By using the presented simulation tool, virtual experiments can be executed, including the calibration of the setup. They provide simulated measurement data - in the case of the Tilted Wave Interferometer simulated phase data – taking a number of possible errors, like interferometer errors, stage errors and errors of the reference spheres, into account. On this basis, complete calibration procedures and measurements on given samples can be simulated. Its result can be compared with the simulated truth, since all parameters and errors are known, and a statement about the performance can be made. This tool also proves useful for investigations on effects of measurement parameters such as misalignments of the sample.