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Spectroscopy is a key technique in astronomy and nowadays most major telescopes include at least one spectrograph in their instrument suite. The dispersive element is one of the most important components and it defines the pupil size, spectral resolution and efficiency. Different types of dispersive elements have been developed including prisms, grisms, VPH and echelle gratings. In this paper, we investigate the design and optimization possibilities offered by metallic freeform gratings using diamond machining techniques. The incorporation of power in a diffraction grating enables several functionalities within the same optical component, such as the combination of dispersion, focusing and field reformat. The resulting benefit is a reduction in the number of surfaces and therefore, an improvement in the throughput. Freeform surfaces are also interesting for their enhanced optical performance by allowing extra degree of freedom in the optimization. These degrees of freedom include the shape of the substrate but also additional parameters such as the pitch or the number of blaze angle. Freeform gratings used as single optical component systems also present some limitations such as the trade-off between optical quality versus field of view or the spectral range versus spectral resolution. This paper discusses the possibility offered by the design of freeform gratings for low to medium spectral resolution, in the visible and near-infrared, for potential applications in ultra-compact integral field spectrographs.
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