optical elements in soft X-ray monochromators. As the resolution of beamlines in synchrotron radiation sources continuously increases, diffraction grating has become a key optical element affecting the resolution. Therefore, VLS grating needs to be accurately tested before being installed in beamlines. To achieve high energy resolution for some beamlines in new generation of synchrotron light sources, not only high precision VLS grating is required, but also more accurate methods of measuring the corresponding line density distributions are necessary.For the positions of the grating overlapping with those of the grating in the first step, it is assumed that the line densities of the overlapping positions are equal to each other. In this way, the incidence angle for the overlapping positions can be calculated, which is the same as that of the un-overlapping positions of the second segment. Using the inverted incidence angle, the improved line density of the un-overlapping positions can be obtained. Repeating the above two steps, the linear density of the entire grating can be calculated with improved precision.Results and Discussions The key point of the method is to calculate the mean value of the incident angle using all sampling points in the overlapping area. This not only eliminates positioning errors in the deflector, but also suppresses random and drift errors, reduces the transfer of measurement errors from a single sampling point to adjacent segments and improves the accuracy of the test results. The effect of positioning errors in the rotary table can be eliminated. During the measurement process, the position offset of the measurement spot is corrected in time and the environmental stability is improved to further reduce the error. In this paper, by using a data processing method that accurately inverts the incident angle of each segment, the repeatability of the measurement of the line density of the VLS grating can be compared between the two methods, with a repeatability of 9.55×10^-7 (RMS), which is much better than that of the previous method [2.12×10^-5 (RMS)]. This paper also conducted four groups of comparison experiments with overlapping rates of 2.4%, 26.8%, 51.2%, and 75.6%. The consistency of the coefficients N₁ and N₂ in the fitted equations of the line density for the four groups were ΔN₁/N₁≤8.49×10^-5 and ΔN₂/N₂≤1.67×10^-3, respectively, The beamline requires an accuracy of around 0.5% and 5% for N₁ and N₂ of the grating. The accuracy of the test at different overlapping rates meets the test requirements. This result demonstrates the high repeatability and consistency of this method for measuring the linear density of VLS grating.

Since its development in the last century, the performance of synchrotron light sources has been-increasingly improved, providing a new and efficient platform for research in many fundamental disciplines such as physics, chemistry, materials science, and life sciences, and helping to achieve many cutting-edge results. In synchrotron light sources and X-ray free electron laser devices, grating monochromators and spectrometers are crucial for both beamlines and experimental stations. Monochromators variable-line-spacing (VLS) grating is simple and easily achieve high spectral resolution and transmission efficiency. Thus, VLS gratings have become the dominant

The main methods for measuring grating line densities include interferometry, diffraction, and long trace profiler (LTP) methods. These methods have their advantages and disadvantages. To meet the need of measuring line density of VLS grating, LTP with stitched data is used. In order to complete the Hefei Light Source photoelectron spectral beam line maintenance project, the Hefei Light Source independently developed a VLS grating. In order to characterize the line density more precisely, this paper proposes an improved stitching measurement method using LTP. In particular, the incident angle of each segment is inverted to improve based on the proposed stitching measurement method of LTP. In fact, for previous stitching methods, the angle of incidence at the central of each segment was determined from the angle of the deflector and the relative diffraction angle within each segment, which was based on the angle value given by the LTP detector. However, the angular error of the deflector is not negligible. In this method, first, taking the midpoint of the VLS grating as a reference point, the line density and incidence angle of the reference point is determined. Moreover, with the data of the reference point, the line densities of other positions of this segment are measured. Second, it is to measure the line density distribution of the next segment.

The LTP stitching measurement method is used to test VLS grating parameters using a segmented overlapping data processing method, which avoids angular errors in the deflector and provides a significant improvement in repeatability. The consistency of the test results is better than 1.13×10^-6 (RMS) for the same VLS grating using different overlapping rates, and the PV value of the repeatability deviation of the test data decreases significantly with increasing overlapping rate. Therefore, a reasonable selection of step length and the overlapping ratio of two adjacent segments can improve measurement accuracy while suppressing splicing errors and ensuring a certain level of measurement efficiency. However, due to the relative accuracy of the turntable, the deviation of the absolute value of the central density is about 0.1 lp/mm, which needs to be improved by using the relative calibration method. This will be followed by an experimental approach to investigate the effect of central line density error measurements on variable-line-spacing grating parameters and experimental verification.