Hyperspectral imaging as an instrument for obtaining a wide range of information on the world around us is a fast developing area of modern technology. In such systems, the desired information is obtained via the processing of stored spectral information of a measured scene. One of the main advantages of hyperspectral imaging over conventional imaging methods is the use of a broad spectral range, which is not restricted to just the visible range but can extend to adjacent regions and further, for example, deeply into the infrared region. The main element in such hyperspectral systems is the spectral separating system, which can be based on a wide variety of spectral dependent physical processes - birefringence, refraction, diffraction, etc. In this contribution, we would like to present the design and fabrication process of such a spectral separating system based on diffraction grating. The main requirements for this system were - operation in the long-wavelength infrared region (LWIR, 7-14 um), the highest possible diffraction efficiency in this spectral region with respect to the black body radiation of a temperature of 350 K, and the avoidance of restrictions inherent to fabrication. The design was carried out with the use of Scalar theory of transmission gratings, which is based on the idea of thin grating. The obtained results were compared to the designs produced via the Rigorous coupled wave theory (RCWA) and Finite Element Method (FEM). Fabrication of the designed grating was done in germanium with the use of single-point diamond turning.