The Need for the PSF

The success of scientific AO-assisted astronomical programs depends on meeting highly challenging levels of accuracy (see below for quantitative examples). In order to disentangle the instrument contribution from the intrinsically faint signature of the astrophysical signal in the observed data, one requires a precise knowledge of the instrumental response (so-called Point Spread Function - PSF). AO systems increase the energy concentration of the PSF but the PSF delivered by AO systems suffers from a complex shape, with spatial, spectral and temporal variability. The lack of knowledge for this PSF variability often represents the main limitation when analyzing AO data.

In order to get an accurate AO-PSF model, a first naive approach would be to use any point sources located in the field. Unfortunately, this simple method quickly fails for extragalactic fields that are usually empty of reference stars, or dense stellar fields for which crowding prevents the extraction of an isolated PSF. Moreover, the situation is particularly critical for IFS, as their fields of view are generally too small to contain any point source that could act as PSF calibrator, and the PSF strongly varies across their wavelength range.

The main challenge for the AO PSF comes from the stochastic effects induced by the environment, the first one being the atmospheric turbulence. By nature, the strength and spatial structure of the atmospheric turbulence is constantly evolving, on time scales faster than seconds. As a consequence, a PSF calibrator acquired with the same instrument setting before or after the science exposure can be completely uncorrelated to the actual PSF. An alternative approach may be to simultaneously acquire an off-axis reference field that would contain PSF calibrators. This is the case for instance for OSIRIS, an AO-assisted IFS at Keck which is equipped with a 20 arcseconds off-axis imager. However, because of the vertical distribution of the atmospheric turbulence (anisoplanatism), the perturbations seen by the IFS and by the reference star may again be decorrelated.

Adaptive Optics has been very successful in the observations of solar systems objects. Indeed, AO allows observations of a large number of targets, and their follow-up across time. With the spatial resolution achieved by the ELTs, the observations of the solar system small- bodies from the ground represent an attractive complement to space missions. An appropriate data processing in this case is deconvolution, with the aim to enhance low contrast features in the data, removing the characteristic broad AO PSF halo that dilutes them (see figure above, first inset).

Standard deconvolution methods require a PSF model. The accuracy of the deconvolved image directly depends on the accuracy of this PSF model. For example, using a database of 20 observations of asteroids, we showed that the standard way of getting a reference PSF by observing calibration stars before or after the science observations leads to unacceptable errors in more than 50% of the cases [Fetick et al.]. For those observations, the deconvolution resulted in strong artefacts at the asteroid edges, highlighted by the presence of a bright corona (see figure above, second inset). This situation clearly is the consequence of inaccurate reference stars, differing from the actual PSF. By developing and using an analytical PSF model, and by empirically adjusting the PSF parameters (e.g. using MISTRAL), it is possible to partially recover the situation (3^rd image in Figure): the largest craters (>30km) and geological characteristics can be exploited. This is still a factor 2 to 3 above the theoretical limit, and the smallest craters (< 15km) remain unresolved because of the PSF inaccuracy (4^th image in Figure).

The main challenges for extragalactic observations are two-fold. First, extragalactic observations require long exposures, over the course of different nights. The PSF variability over the whole observations can potentially be significant (more than 100% over several nights). At the same time, cosmological fields are usually devoid of point-sources that can be used to monitor this variability. PSF variations then becomes a major limitation in kinematics or morphological analyses of distant galaxies. In this case, analytical PSF models are sufficient and a better knowledge of the PSF is not critical, as the accuracy of the analysis is limited by the morpho-kinematical model and/or signal-to-noise.

An additional requirement comes from the possibility to extrapolate the PSF to other wavelengths as several physical parameters are extracted from emission lines ratios. For instance, resolved metallicity gradients in individual galaxies, which can only be extracted from IFS data, are used to probe the role of gaseous accretion in governing galaxy assembly history. Current IFS studies of high-z galaxies have shown a wide range of metallicity gradients, and it has been difficult to attribute whether this is due to the inhomogeneous sample or beam smearing due to the PSF. Being able to predict the PSF shape over the entire wavelength range would solve this degeneracy

For stellar science, knowledge of the spatial shape of source images is critical to deblend the overlapping images of adjacent stars and to optimally extract the photometry, astrometry and spectrum of each star. For instance, the search for IMBHs is based on the detection of kinematic signatures in the central region of globular clusters, such as the rise of the central velocity dispersion. But the accuracy required (of the order of 1 - 3km/s) is extremely challenging because of the rather low velocities involved and the high stellar densities. Even though a large number of point sources are present in the field, extracting an empirical PSF from the science image itself remains a challenge. For such crowded fields, systematics (biases) in the radial velocity measurement of less than 2km/s may be reached only if the FWHM of the PSF is determined to an accuracy of < 2%. Current state-of-the art methods to extract an analytical PSF shape model directly from the data (e.g. PampelMuse) are typically a factor 2 worse than this requirement for the FWHM, and up to a factor 5 worse for the modelling of the PSF wings, leading to velocity biases up to 10km/s. As a consequence of this PSF modeling inaccuracy, observational evidence for the existence of IMBHs in globular clusters is still scant, or even contradictory in some cases. Improving the PSF model accuracy, and consequently remove radial velocity biases, would bring unambiguous proofs of the existence of IMBHs, and precise constraints on their mass and physical origins.