Copernicus, the European Union's programme for observing and monitoring the Earth, represents one of the most successful space programmes coordinated and managed by the European Commission in partnership with ESA, the Member States and Agencies. 2020 marked a major step of the Copernicus expansion programme with the selection of six missions to enter into B2CD implementation, namely CHIME, LSTM, CO2M, CRISTAL, ROSE-L, and CIMR. The CHIME mission (Copernicus Hyperspectral Imaging Mission for the Environment) space segment was awarded to an industrial consortium led by Thales Alenia Space (FR), as Mission Prime, and OHB (DE), as Instrument Prime. Within the instrument team, the responsibility of the design and development of the spectrometer system (SPS) have been assigned to AMOS (BE). The SPS is the centrepiece of the CHIME instrument, ensuring the accurate spectral dispersion of the imaged ground swath over wide focal planes. The SPS consists of three identical spectrometer units drawn from the compact de-magnifying freeform Offner optical solution developed at AMOS. Its throughput is guaranteed by a broadband convex diffraction grating, while the image quality and distortion control are enabled using freeform mirrors. This paper describes the mathematical modelling and prototyping activities, including manufacturing and testing of grating samples, carried by AMOS raising the maturity of the CHIME diffraction grating achieving Technology Readiness Level 6 (TRL6).