► High quality imaging spectroscopy data is useful for both military and civilian applications. ► State-of-the-art spectrometers incorporate spherically concentric, axially symmetric and telecentric optical design. ► However, these designs require a diffraction grating operating in reflection that is manufactured on a convex, spherical or possibility freeform surfaces, and thus traditional grating manufacturing methods limit modern designs and raise costs. ► Further, it is often desirable to manufacture such optics in a monolithic configuration aligning them and eliminating assembly. ► This paper explores the capability of new 5-axis ultra-precision machine tools for manufacturing diffraction gratings in simplified experiments aimed at progressing toward producing gratings on freeform surfaces and monolithic combined optical designs. ► The results show that it is likely possible to use multi-axis diamond machining to make components for imaging spectrometry.