Large-size ultra-smooth mirrors remain essential for focusing and deflecting X-rays. As the demand for higher mirror surface accuracy increases in advanced light sources, such as hard X-ray free electron laser facilities, optical metrology with precision in the range of a few nanometers for peak-to-valley (PV) and sub-nanometer root mean square (RMS) values is required. Commonly used techniques include the long trace profiler (LTP) and the nanometer optical component measuring machine (NOM), both of which measure surface slope and derive height through mathematical conversion. In addition, the Fizeau interferometer combined with stitching is widely used for 2D surface height measurements. However, X-ray mirrors, such as elliptical cylinders, parabolic cylinders, and cylindrical surfaces, present challenges due to the limited accuracy imposed by reference mirrors in Fizeau interferometry. To address this, we employ highly precise displacement sensors with picometer-level resolution and sub-millimeter spot size. In this paper, we report a three-sensor measurement system that demonstrates repeatable nanometer-level accuracy, showing its effectiveness in X-ray mirror surface metrology.

The system consists of three displacement sensors, a scanning stage, and two mirrors. The sensors are mounted on an aluminum alloy beam, which is rigidly connected to the scanning stage. This configuration ensures that the sensors and stage move as a rigid body. One sensor measures the surface under test (SUT), while the other two measure the reference mirror surface (REF) to compensate for motion errors from the scanning stage. Sensor measurements include not only the mirror surface height but also motion errors from the stage. These errors are categorized as straightness errors and angular errors. Straightness errors affect all three sensors equally, while angular errors cause varying displacements among them. According to Euler’s theorem, the displacement caused by angular errors can be derived by analyzing the angles in the x, y, and z directions. A linear relationship exists between the displacements caused by angular errors in the three sensors. Thus, the surface height can be determined by compensating for the motion errors using this linear relationship.

The results of single-point measurements show an average PV of 10 nm and an average standard deviation (STD) of 2 nm within 1 h (Fig. 6), indicating the feasibility of using interferometric displacement sensors for surface shape measurement. The correlation analysis between temperature and displacement shows a negligible effect (Figs. 7 and 8), indicating that temperature fluctuations can be disregarded. The surface profile of the mirror is measured (Fig. 9), with five repeated measurements conducted to evaluate repeatability. The average standard deviation of the difference between individual measurements and their mean is 2.69 nm, demonstrating excellent repeatability. The results closely match those obtained with the Fizeau interferometer, demonstrating a correlation coefficient of 0.804 and validating the accuracy of the three-sensor system (Fig. 10).

In this paper, we propose a three-sensor displacement measurement system integrated with a scanning stage for accurate mirror surface profiling. Theoretical analysis demonstrates that there is a linear relationship between the displacements due to stage angular errors, which can be effectively compensated. Single-point measurements show the system’s capability, while temperature tests verify that environmental factors have minimal influence. The system demonstrates a repeatability of 2.69 nm in measurements and shows high agreement with Fizeau interferometer results. Our findings demonstrate that the system effectively compensates for motion error and reliably measures mirror surfaces with nanometer-level precision. In conclusion, the three-sensor measurement system shows great promise for measuring high-precision mirror surfaces. In future research, we aim to further enhance the accuracy of these measurements.