Measuring deformations with deflectometry

Phase-measuring deflectometry is a powerful method to measure reflective surfaces. It is relatively easy to extract slope and curvature information from the measured phase maps; however, retrieving shape information depends very sensitively on the calibration of the camera and the geometry of the measurement system. Whereas we have previously demonstrated shape uncertainties below 1 lam, the range below 100 nm is currently inaccessible to deflectometric shape measurement. On the other hand, the astounding sensitivity of deflectometry can be put to good use for deformation measurements. The evaluation of corresponding shape differences rather than absolute shapes is much less susceptible to system calibration errors and its resolution is given mostly by the measurement system's sensitivity. We give an overview of recent progress in difference deflectometry. Firstly we show results from solar mirror substrates under load to detect flaws with high sensitivity. Secondly we present a preliminary simulation study of achievable deformation-measurement uncertainties to assess the feasibility of deflectometric characterisation of actuator performance and gravity sag for the mirror segments of the European Extremely Large Telescope (E-ELT). Results for the relevant Zernike terms show reliable detection of Zernike coefficients at the 25 nm level. Random artefacts related to noise in the phase measurements are seen to translate into bogus Zernike terms, and we discuss possible mitigation techniques to enhance the sensitivity and accuracy further.