High-resolution tunable spectrograph for x-ray laser linewidth measurements with a plane varied-line-spacing grating

We describe a spectrograph for x-ray laser linewidth measurements in the range 100-220 A. The design employs a plane varied-line-spacing grating operating in the convergent light produced by imaging of the entrance slit with a concave spherical mirror. By the appropriate choice of the linear term in the grating-spacing variation, two separate wavelengths can be focused at the same image distance. As a result all wavelengths within the range of interest are focused at or near the same distance. The spectrograph can be tuned by rotation of the grating to bring any wavelength within the range to the center of the focal plane, and the spectra are dispersed on a surface that is erect or practically flat and perpendicular to the principal ray. This allows the use of a planar detector. With a streak camera used as a detector, the instrument obtained time-resolved linewidth data on x-ray lasers with a resolving power of 1 x 10(4) to 2 x 10(4). This paper presents the design methods used to optimize the varied-line-spacing grating, the design of the tunable spectrograph, and the results from the instrument in operation.