Numerical and Experimental Modal Analysis Applied to an Optical Test System Designed for the Form Measurements of Metre-Scale Optics

Abstract

The work focuses on the structural design and performances of a unique optical test system (OTS) used for measuring metre-scale optical surfaces. The investigation was carried out through a modal analysis. Two sets of results are presented. Both modal analysis of the entire OTS and transmissibility function related to its use as an optical system are carried out and analysed. The OTS is used for the measurements of the form accuracy at nanometre level of metre-scale concave surfaces. The OTS is a four and half-metre-tall mechanical structure made of bolted aluminium profiles, two structural platens, two dedicated precision positioning supports, a test piece, and a state-of-the-art laser interferometer. The OTS was numerically modelled and fully instrumented with triaxial accelerometers. The results of the modal analysis highlight the natural modes of the entire OTS. Both numerical and experimental methods are designed. The investigation methods are iterative. Indeed, a preliminary numerical model is created using finite element analysis (FEA). FEA results enable the determination of the dynamic range and suitable locations of accelerometers that are mounted onto the OTS for the experimental validation of the FEA model and further to carry out the transmissibility study. Natural frequencies, damping ratios, and mode shape values are obtained and scrutinized. These results are used for refining the FEA model. In fact, the lack of symmetry and the use of feet are identified as the key design feature that affects the OTS. The correlation between experimental and numerical results is within five percent for the first four modes. The results of the transmissibility study highlight the specific natural modes that influence the OTS measurement capability. Overall, the study enables to guide engineers and researchers towards a robust design using a validated and methodical approach.