AO PSF determination

Images obtained from optical instruments results from a convolution between the intensity distribution of the observed object with the optical response of the system, the PSF. Consequently, in order to measure the astrophysical metrics of interest (astrometry, photometry, velocity, topology, ...), one must usually have a model or priors on the PSF.

For instance, the estimation of astrometry and photometry on images of globular clusters is degraded in the presence of strong sources confusion due to noise and crowding, and having an accurate model of the PSF allows to improve the source disentanglement. Also, in order to obtain highly resolved images, one must use deconvolution algorithms that are designed to suppress the PSF contribution to unveil the real intensity distribution of the object.

Adaptive-optics (AO) instruments enable diffraction-limited observations but introduce complex features in the PSF that are not well represented with classical models (Gaussian, Moffat, ...). Furthermore, AO introduce strong PSF variability across time, which prevents to offset the telescope to accurately calibrate the PSF from the image of a bright star. Moreover, AO come with spatial variability of the PSF due to anisoplanatism or tomography. Figure 3 illustrates on simulations of galactic center observations that not accounting for this variability can significantly degrade the photometry accuracy [Beltramo-Martin et al., AO4ELT6, 2019].

Figure 3 : (top) simulated images of the galactic center observed with NIRC2 in K-band. (right) Corresponding photometric error (mag) obtained from Starfinder with a shift-invariant or variable PSF model.

The estimation of the AO PSF is a hot topic for decades. There is a zoo of methods that can be sorted into three main categories :

Focal-plane based techniques : all methods that use astronomical images to identify the PSF, that is the input is a PSF or an extended object convolved by a PSF. Extraction and best-fitting methods are the most common techniques, thanks to their flexibility and the absence of AO expertise needed. They rely usually on a four-part process that consists of (i) correct frames from dark, backgrounds, flat field and distorsions (ii) detect stars and extract PSFs from the entire field or sub-fields to account forPSF spatial variations (iii) adjust a parametric model over extracted images or stack them to estimate a PSF function (iv) use the PSF model for science post-processing (deconvolution, photometry/astrometry,...). However, these methods are sensitive to the image noise and source confusion and require the presence of a point-like source within the scientific field, calling for consideration of model-fitting instead.
- PSF fitting/interpolation : extract point sources images and calibrating a PSF model to either deblend sources that overlap or provide a PSF at any position in the field/spectrum.
- PSF marginal estimation and deconvolution : retrieve the PSF from the image of an extended object assuming some priors on the object (and the PSF).
- PSF classification : estimate the PSF from classification methods, such as PCA, supervised classification, and machine-learning/deep-learning -based approaches generally.
Pupil-plane based techniques : all methods that use wavefront measurements and/or models of wave-front propagation. The input is a time-series of wavefront measurements or integrated parameters derived from wavefront measurements.
- PSF simulation : end-to-end simulations based on integrated atmospheric and system parameters.They allow to include any non-linear effects and rely on wavefront propagation theory. Powerful tools have been developed such as OOMAO, COMPASS, DASP, PASSATA, SOAPY, YAO, OCTOPUS and many others.
- PSF analytical models : from integrated parameters derived from the AO telemetry, one may use analytical models to infer the PSF as well as the PSF spatial variations due to the anisoplanatism for instance
- PSF reconstruction : estimation of the PSF using AO control loop data or integrated parameters estimated from those. PSF reconstruction involves several approximations to derive the PSF from the residual phase power spectrum density.
Hybrid techniques : all methods that uses jointly astronomical images, wavefront measurements and analytical models.

Figure 4 shows an application of the recently developed analytical model PSFAO19 [Beltramo-Martin et al., A&A 2020, Fétick et al., A&A, 2019] that was validated over 4,800 images obtained from 7 different instruments. Thanks to the accuracy of flexibility of this model, optimized post-processing tools (PSF-fitting/deconvolution) for AO-corrected images can be envisioned.

Figure 4 : Two dimensional comparison in log scale and over 64× 64 pixels of (top) observed PSFs and (middle) fitted PSFAO19 model for multiple types of AO systems and instruments working in either visible or NIR wavelengths. From left to right: SPHERE/ZIMPOL, SPHERE/IRDIS with the apodizer and the Lyot stop (no focal plane mask), Keck AO/NIRC2, SOUL/LUCI, CANARY/CAMICAZ in MOAO mode, GALACSI/MUSE NFM, and GEMS/GSAOI. All PSFs have been normalized to the sum of pixels.Comparison (log scale) of observed PSFs and the model PSFAO19 fitted on the image on 7 different instruments.

In this context, I work on the development and validation of advanced PSF model and post-processing techniques for AO-corrected images processing.