Two characterization methods of ripple errors for the large square aperture

The specification and characterization of mid-spatial-frequency (MSF) ripples for the large-square-aperture optical elements, typically used in high-power laser systems, have received considerable critical attention. It is necessary to resort to a simple and robust way to characterize error surfaces for facilitating prediction of performance degradation and guiding the fabrication and tolerance settings. In this paper, we characterize residual periodic surface undulations called ripple errors for the large square aperture generated from modern subapertures and deterministic optical fabrication techniques through two methods, taking a step from qualitative judgment to quantitative analysis. The cross artifact reduction technology, instead of traditional windowed preprocessing, is introduced into power spectral density to suppress spectrum leakage while retaining the information about the part. An efficient algorithm to generate Legendre moments for two-dimensional Legendre polynomials is proposed to quantify ripple errors. This work contributes to understanding the optical degradation caused by MSF errors and associating the design and performance index with surface parametric description.