Sensitivity analysis of tilted-wave interferometer asphere measurements using virtual experiments

The tilted-wave interferometer (TWI) was recently developed by the University of Stuttgart for the high-accuracy measurement of aspheres and freeform surfaces. The system works in a non-null measurement fashion and si­ multaneously uses several test beams with different tilts. Reconstruction of the specimen under test from TWI measurements is challenging and in order to correctly separate the real surface topography from systematic aberrations, the employed interferometer needs to be characterized. This characterization, as well as the recon­ struction of the specimen from TWI measurements, requires sophisticated data analysis procedures including ray tracing and the solution of an inverse problem. A simulation environment was developed at the Physikalisch-Technische Bundesanstalt (PTB) in order to inves­ tigate the accuracy and stability of TWI systems, and to explore possibilities and limitations of this promising measurement technique. Virtual experiments were carried out to quantify the sensitivity of the results with respect to the assumed linearity in the reconstruction procedure, positioning errors, and measurement noise. Our first results suggest that the mathematical TWI reconstruction technique basically allows highly accurate measurements with uncertainties down to a few nanometers, provided that calibration errors of the optical sys­ tems are kept small. The stability of the results and their accuracy can, however, depend significantly on the particular surface of the specimen and on the choice of experimental settings.