Hyperspectral-grating-based imaging spectrometer systems with F/3 and covering the visual-near-infrared (420-1000 nm) spectral range are investigated for monitoring Earth's environmental changes. The systems have an entrance slit of 24 μm and a 6.5 nm spectral resolution. Both smile and keystone distortions are smaller than 20% of the pixel pitch. We benefit from the development in freeform technology and design 15 different systems with the help of off-axis aspheric and freeform surfaces. The potential of each system is explored with the help of nonspherical surfaces. Cross comparisons between different system types are summarized to give their advantages and disadvantages. In the end, detailed tolerancing of one selected system is presented to show the feasibility for fabrication.