A method for determining a set of grating parameters for producing a diffraction grating for a vacuum-ultraviolet spectrometer, the parameters used being the small and large radius of the toroidal grating substrate, the two distances between the two holographic illumination points and the grating origin, the angular position of the holographic illumination points in relation to the grating normal, and the laser wavelength for the holographic illumination. The method determines respective optimum grating parameters on numeric iterative paths for a specific problem definition. The method thus advantageously enables the production of a VUV spectrometer having a diffraction grating that for a predetermined wavelength range produces a minimum line width on the detector with a large range.