HARMONI at ELT: Modelling the optical performance of a diffraction limited integral field spectrograph

HARMONI is the first light visible and near-IR integral field spectrograph for the ELT. It covers a large spectral range from 470 nm to 2450 nm with resolving powers from 3300 to 18000 and spatial sampling from 60 mas to 4 mas. It can operate in two Adaptive Optics modes - SCAO (including a High Contrast capability) and LTAO - or with NOAO. To model the optical performance we include manufacturing and alignment tolerances alongside other static and dynamic effects. Diffraction of both image and pupil become significant when the spectrograph slit width matches the diffraction limited point spread function. A set of Zemax OpticStudio macros and Python scripts are used to bring together the subsystem models that make up HARMONI and combine them to include all these effects. We present an overview of our approach to modelling this complex instrument and key results predicting the optical performance of HARMONI.