The  object  of  the  invention  is  to  provide manufacturing parameters for a  holographic  diffraction  grating  on  a  concave  or  toroidal  surface,  which  is used as the single optical element in a VUV spectrometer with a flat detector. The spectrometer geometry is also defined alongside the diffraction grating parameters. The invention from the research center Juelich (Germany) consists of a proprietary software  code  which  uses  various  numerical  methods  to  determine  the  optimal  grating parameters, with the aim of producing such gratings for VUV spectrometers with  a  minimal  line  width  for  a  pre-­‐defined  wavelength  and  at  the  same  time  achieving high spectrometer efficiencies.