Measuring and calibrating non-common path aberrations in adaptive optics assisted image-slicer based spectrographs
Keywords: integral field spectrograph
spectrographs
machine learning
image slicers

HARMONI is the first-light, visible and near-IR integral field spectrograph for ESO’s Extremely Large Telescope (ELT), which promises to revolutionise observational astrophysics with its high spatial resolution, offering quasi-diffraction-limited performance from a ground-based observatory. The performance of Adaptive Optics assisted instruments such as HARMONI is hindered by the presence of differential aberrations between the AO wavefront sensing and science optical paths, known as NonCommon Path Aberrations (NCPA). These aberrations, which primarily affect the spatial point spread function (PSF) in HARMONI, cannot be sensed directly due to the absence of phase information in focal plane intensity measurements, so special techniques are needed to calibrate and pre-compensate them.
This is particularly problematic in high-contrast observations aimed at detecting and characterising exoplanets, as NCPA give rise to quasi-static speckles that resemble planetary signals and severely limit the contrast. Although extensive research has been devoted to developing NCPA calibration techniques for AO systems and coronagraphic instruments, these have not been demonstrated in the context of integral field spectrographs like HARMONI that contain an image slicer. This optical component, made out of a stack of thin mirrors, slices a 2D field of view into slitlets and re-arranges them into a long pseudo-slit that can be dispersed by a spectrograph. The effects of an image slicer on light propagation could have a negative impact on the behaviour of state-of-the-art techniques for NCPA calibration, and require modifications to account for these effects to ensure they could be applied to instruments such as HARMONI.
This DPhil thesis makes several novel contributions to this field of research. First of all, I have investigated the impact of an image slicer on light propagation and characterised its effects on the PSF following two approaches: a theoretical one, using a mathematical framework crossvalidated with simulations based on optical models of the HARMONI sub-systems; and an experimental one, for which I have designed and conducted an experiment with the engineering model of the SWIFT instrument image slicer.
Secondly, given that image slicers can affect the relationship between phase aberrations and focal plane intensity, and the unproven behaviour of traditional techniques, I decided to explore alternative approaches that could circumvent this drawback. I have developed a novel technique for NCPA calibration that relies on machine learning methods to estimate the aberrations directly from PSF images. I have demonstrated that this technique can discriminate between features from image slicers and features caused by aberrations in the system. I have thoroughly characterised its response to multiple sources of uncertainty and shown how it can be successfully applied to HARMONI.
Lastly, I have developed the capability to create and analyse End-toEnd Monte Carlo models of HARMONI that aggregate the different subsystems to form a realistic representation of how the as-built instrument would behave. This has been used to support our calibration efforts in multiple ways: to characterise the expected level of NCPA in the system and its major contributors, to define requirements for NCPA calibration accuracy based on the intrinsic limitation of field-dependent aberrations, and to train the machine learning calibration models with realistic wavefront maps that reproduce the typical NCPA that we will encounter in HARMONI.
All of these efforts shed light on the question of how NCPA can be calibrated in instruments that contain image slicers, and will pave the way for its future application in HARMONI. The only missing piece of the puzzle is the thorough characterisation of how image slicers impact the behaviour of traditional methods like Phase Diversity and how they could be adapted to account for such effects. Due to time constraints, this could not be fully explored and will be the subject of future research.