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Statistical measurement of mid-spatial frequency defects of large optics

A statistical method is proposed to measure the power-spectral density (PSD) of the mid-spatial frequency defects of large optics. The method measures the geometrical defects of large optics by a large-aperture low-resolution interferometer, and then measures the mid-spatial frequency defects of every subregion in large optics by a small-aperture high-resolution interferometer. Statistical theory shows that the PSD of mid-spatial frequency defects in large optics approximately equals the weighted average of that in every subregion. Simulation and experiment demonstrate the effectiveness and feasibility of the proposed method. The proposed statistical method is not sensitive to the translation stage's error and thus is more appropriate for measurement of the mid-spatial frequency defects of large optics than the traditional sub-aperture stitching interferometry.