Absolute interferometric shift-flip method for measuring X-ray mirrors

The absolute interferometric shift-flip method is proposed to perform absolute measurements for measuring X-ray mirrors. The shift-flip method includes the primary position, two shifts, and one flip, determining four interferometric relative measurements. According to four measurements, the surface shape matrix corresponding to the point-by-point is obtained. The optimized least squares method is further used to reconstruct the absolute surface shapes of the interferometer reference (REF) mirror and the measured X-ray mirror surface under test (SUT). With well-organized measurement procedures, the positional alignment ensures that the measurement area after the flipped X-ray mirror is the same as the initial benchmark position. We implemented absolute testing experiments using a Fizeau interferometer and an X-ray mirror and then verified the validity of the proposed method using a self-check method. The experimental results show that the proposed method effectively obtains the absolute surface shape of the X-ray mirror.