Measurements of groove density for concave gratings with the long trace profiler

A long trace profiler method has been developed to measure the groove density of concave gratings in National Synchrotron Radiation Laboratory recently. With the aid of large angular acceptance $\left(35\mathrm{mrad}\right)$ , it is suitable for precise measurement of concave or convex gratings with high curvatures. The effects of the slope variations along its substrate are discussed in detail. To eliminate the off-axis errors, which are the essential error sources in the measuring system based on rotating mounts of gratings, an error-reduced method is introduced consequently. A commercially available concave grating with a curvature radius of $998\mathrm{mm}$ is measured and the relative groove density error $\delta N∕N$ is about $4\times {10}^{-5}$ rms.