Dynamic Coherence Scanning Interferometry to Characterise the Einstein Telescope Prototype Mirror under Cryogenic Conditions

This work describes the development of a new concept of Coherence Scanning Interferometer to measure local changes in topography and local low-frequency out-of-plane vibrations of a mirror during cryogenic operation. The metrology instrument incorporates a novel optical phase mask and a microlens array, enabling the acquisition of the full white light interference pattern at multiple local points on the mirror under characterisation within a single camera frame. This contrasts with traditional interferometers, which require multiple camera frames and a translation stage to reconstruct the full interferogram. We design the optical phase mask as a combination of steps of different thicknesses, so each step introduces a different optical path difference to the rays. The local interference patterns recorded in each camera frame provide real-time information about the mirror's local surface topography, therefore, enabling an instantaneous 3D scan of the mirror's surface. In this context, surface topography refers to the spatial distribution of the mirror surface height measured along the optical axis, with particular emphasis on its low-spatial-frequency component corresponding to the optical surface figure. The displacement of the interference patterns between consecutive frames enables measurement of local out-of-plane vibrations below 10 Hz. Such vibrations may originate from thermo-mechanical effects associated with cryogenic cooling, mechanical coupling within the suspension or support structure, or external environmental disturbances. Theoretical analysis, numerical simulations, and experimental validation on a custom-built optical bench in the laboratory support the instrument's working principle. The metrology instrument is developed within the framework of the E-TEST prototype for the third-generation gravitational-wave observatory, Einstein Telescope, to characterise its mirrors, which operate at extremely low temperatures to reduce thermal noise.