HARMONI at ELT: line spread functions in a diffraction limited spectrometer

HARMONI is the first light, adaptive optics assisted, near-IR integral field spectrograph for the ELT. It covers a spectral range from 800~nm to 2450~nm with resolving powers from 3000 to 7000 and spatial sampling of 25~mas and 6~mas. It can operate in two adaptive optics modes - SCAO (including a high contrast capability) and MCAO. The project is resuming its final design phase after a rescope design phase in 2025. Diffraction of the pupil becomes significant in a spectrograph where the slit width is comparable to the diffraction limited PSF. When the spatial coherence due to the narrow slit is considered, the resulting line spread function can be narrower than the geometric width of the input slit, with a non-linear dependence on the size of the pupil aperture after the slit. We outline the impact of these diffraction and spatial filtering effects on the line spread function of HARMONI and identify parameters that should be considered when designing a diffraction limited spectrograph.