Detection and correction of mosaic grating errors based on optical vortex phase-shifting interference

The mosaic grating technique is currently an enabling technique for facilitating large-size gratings. A method for the detection and correction of mosaic grating errors for the fabrication of large-size gratings is proposed based on dual-wavelength optical vortex polarization phase-shifting interference. A dedicated mosaic error detection system is designed accordingly. Within this system, an optical vortex beam serves as the reference beam. The reference beam interferes with the plane beam diffracted from the mosaic gratings, which contains information about the mosaic errors of the mosaic gratings. Mosaic errors are quantified by computationally fitting the interference fringe patterns generated between the vortex reference beam and the diffracted plane beam, and a dual-wavelength algorithm is utilized for the extension of the translational alignment error (Δ<i>z</i>) measurement range. Key steps for correcting these mosaic errors are outlined, and an accuracy analysis for the detection system itself is performed. Experimental validation demonstrates that the measurement resolutions achieved for angular alignment errors (Δ<i>θ</i>_<i>x</i> and Δ<i>θ</i>_<i>y</i>) are approximately 1'', while the resolutions for translational alignment errors (Δ<i>z</i> and Δ<i>x</i>) are approximately 2 nm. The proposed method offers an extended measurement range, high accuracy, and robust stability. This study provides a novel and general approach for the detection and correction of mosaic grating errors.