Patent ID: 7420736

Claim:
A method of determining a set of grating parameters for the production of a diffraction grating for a vacuum-ultraviolet spectrometer whereby the parameters are the small radius and the large radius of a toroidal grating substrate (ρ and R), the two distances (r c and r d ) of two holographic illumination points from the grating center, the angular positions (γ and δ) of the holographic illumination points to grating normals and the laser wavelength ((λ L ) for the holographic illumination and whereby the method comprises the following steps: a) establishing the wavelength range to be observed, b) determining the height and width of the detector of the spectrometer, c) determining the starting parameters for the following spectrometer parameters: d) the width and height of the inlet gap, e) the distance L A from the inlet gap to the center point of the grating, f) the incident angle α of the light with respect to a grating normal, g) the width and height of the diffraction grating, h) the distance r so from the grating center point to the meridional focus of zero order, and i) the angular setting of the detector, j) determining the laser wavelength λ L for the holographic exposure of the grating substrate, k) determining the greater radius of curvature R of the grating substrate, l) iteratively determining the smaller radius of curvature ρ of the grating substrate, the line density G at the center point of the grating and the wavelength at the detector center point, m) determining the position of the detector and the angle at which the light of the first order from the grating falls upon the detector, n) of the remaining four variables including the distances (r c and r d ) of the two holographic illumination points from the grating center point and their angular positions γ and δ with respect the grating normals, eliminating one of the two angles γ based upon the mean line count of the grating, o) determining the minimum of the magnitude Δλ iteratively as a function of the three remaining variables (spacings r c , r D and angle δ), whereby a set of variables r C , r D and δ are obtained as a solution for which the Δλ is an absolute minimum.