Angle measurement accuracy requirement analysis for the relative angle determinable stitching interferometry (RADSI)

The relative angle determinable stitching interferometry (RADSI) is widely used for testing X-ray mirrors. However, the required angle measurement accuracy for a specific mirror with determined length and accuracy requirements is not clear. To this end, simulations were conducted to clarify the influence of different order terms of angular measurement errors (AME) on the RADSI measurement error. Using practical AME repeatability data as the input error, the stitching parameters including sub-aperture length and overlap ratio for obtaining higher RADSI measurement accuracy were optimized. Further, the required AME for a typical 300 mm length X-ray flat mirror with radius of curvature (Roc) toleration test accuracy better than 60 km and residual form (i.e., without 2^nd order term) measurement accuracy better than 1 nm peak-to-valley (PV) was analyzed. The requirement on linear term of AME should be better than 940 nrad/h PV and AME without linear term should be better than 96 nrad/5 h PV. Finally, some strategies on reducing the AME are proposed by analyzing the sensitivity of the different order terms of AME on the RADSI measurement accuracy and the coefficients of different order terms of the practical AME. The proposed method is promising to offer a framework for analyzing the required AME for guaranteeing the measurement accuracy posed by specific X-ray mirrors.