Multiple Shear-Shift Absolute Calibration of Reference Surface for White-Light Interferometers

With advantages for testing midfrequency form error and strong curved surfaces, the white-light interferometers (WLIs) have been widely used for testing advanced X-ray surfaces with subnanometer accuracy. The calibration of the reference error is the prerequisite. The commonly utilized random averaging method requires a flat with high form accuracy and the information of the correlation length of the test flat, which can hardly be known ahead. For calibrating the reference surface with the accuracy required by most advanced X-ray surfaces, a multiple shear-shift (MSS) absolute test method for WLIs is proposed. The MSS method is conducted by performing multiple sets of measurements on a test surface. Each set involves one measurement at the original position and two measurements with the test surface translated along the two orthogonal directions with different distances of integer pixels, respectively. The mathematical model of reference retrieval is known; however, the result is sensitive to environment disturbance and shear-shift errors. The influence of these source of errors is evaluated, and the optimal acquisition parameters are determined. The reference surface of a $1\times $ objective lens with 8.6-mm square view field was calibrated. We could achieve the repeatability of peak-to-valley (PV) 0.18 nm and root mean squares (rms) 0.03 nm with a normal accuracy test surface and the optimal acquisition parameters. The accuracy is PV 0.23 nm and rms 0.03 nm by comparing the calibration results that obtained by random averaging method utilizing a flat with extreme form accuracy. By comparisons, the repeatability and accuracy drop to unaccepted level with inappropriate acquisition parameters. The proposed method offers a new reference surface calibration strategy with determined model for guaranteeing the absolute measurement accuracy of X-ray surfaces utilizing WLIs.