Stitching method based on dual quaternion for cylindrical mirrors.

In this study, a stitching method based on dual quaternion is proposed. The application of a dual quaternion in sub-aperture stitching interferometry is analyzed in detail, and a calculation method for sub-aperture stitching based on a dual quaternion is deduced. The experimental results demonstrate the accuracy of the stitching method proposed in this study (residuals of overlapping area approximately 0.22 nm RMS). Finally, the residual differences of 0.79 nm RMS between the figure errors are acquired with a stitching by parts algorithm based on the dual quaternion and long trace profiler (FSP at HEPS). The high-accuracy and high-efficiency stitching method proposed in this study will expand its application in the metrology and manufacture of long cylindrical mirrors.