High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating

Laser diffractometer constructed at MIKES for calibration of pitches of 1D and 2D gratings is based on the Littrow configuration. The grating is rotated by a rotary table. In order to obtain optimal beam quality a fibre-coupled frequency-doubled stabilized Nd:YAG laser is used as a light source and a CCD without internal reflections is used to detect the diffracted beam position. The angle corresponding to the Littrow null position is calculated using a linear fit to equidistantly spaced angles around the null position, which reduces the effect of nonlinearity of the angle encoder scale. Pitch is calculated as a weighted average of the diffraction orders. Novel use of an uncalibrated 1D grating applied to classical error separation methods for angle calibration by full-circle subdivision is described. Diffraction angle measurements are repeated in many sample holder alignments rotated relative to the absolute angle scale. The sequences overlap so that the full circle of the angle scale is covered with multiple evenly distributed sequences, needed for circle-subdivision metrology. The average grating pitch over all sequences is used to separate angle scale errors and a correction table for the rotary table is calculated. The method was verified using a calibrated polygon and an autocollimator. Uncertainty estimates for the grating pitch calibration are given, e.g. the standard uncertainty of 9 pm for 2 µm grating.