The AO PSF

Description of the AO-PSF.

Let us start with a description of the AO-PSF. The 2D (x,y) AO-PSF formed at the focal plane of the scientific instrument is a function of wavelength, time (t) and field position (r). To first order, it can be described by the convolution of three contributors: the telescope, the AO and the science instrument:

Telescope PSF: The first term includes all the telescope specificities, the first one being the diffraction pattern imposed by the telescope aperture. For circular apertures, this would be the well-known Airy pattern, with a FWHM equal to Lambda/D, where D is the telescope diameter. This first term also includes the effect of central obstruction, spiders and all the telescope aberrations that will not (or partially) be corrected by the AO system, as for instance vibrations, windshake, field aberrations or phasing errors in case of segmented mirrors. Those aberrations are field, time and wavelength dependent and may affect all the PSF focal positions (i.e. all x,y – see Figure above).

Atmosphere/AO PSF: The second term depends on the atmospheric and AO system characteristics. To first order, the AO system can be seen as a transfer function filtering the atmospheric perturbations. If there were no atmosphere, this PSF contributor would become a Dirac, and the resulting PSF would be independent of the AO system characteristics. This is the case for space missions, where the final PSF only depends on the telescope and instrument aberrations. At the other end of the range of the limiting cases, if the AO system is turned-off, this PSF becomes seeing-limited with a FWHM equal to Lambda/r₀, where r₀ (Fried parameter) encodes the atmospheric turbulence strength. Typical values of r₀ are on the order of tens of centimeter, therefore, this atmospheric PSF is fully dominating the final PSF shape when compared to the telescope PSF (Figure – 2^nd inset). The seeing-limited PSF is strongly time dependent, with variations faster than seconds, and with FWHM variations spanning ~0.3 to 2arcsecs for typical astronomical sites.

The AO system partially compensates for the aberrations induced by the atmosphere and the telescope. It is first important to understand that, because of the limited number of actuators on the AO deformable mirror, only a limited number of spatial frequencies can be corrected by the AO system. For instance, if the AO system would be perfectly correcting all the aberrations within the range of its deformable mirror, the final PSF would be the combination of the Airy function near the optical axis, and remains of the extended seeing-limited wings for focal positions above the correction range (Figure - middle inset). In reality, the AO system is not perfect and suffers from measurement noise, temporal or aliasing errors among others. Those error terms impact the PSF shape within the correction range and strongly depend on wavelength, field position and time (Figure, 4^th inset).

Instrument PSF: This last term includes all the instrument characteristics, the first one being the sampling of the PSF by the detector pixels (Figure – right inset). But the scientific instruments may also carry their own aberrations, called NCPA (for Non-Common Path Aberrations). As for the telescope aberrations, part of those NCPA can be compensated by the AO system, and if these aberrations are static, they can be calibrated during day-time. A particular case applies for IFSs, which can produce differential aberrations over the wavelength range, and for which the NCPA compensation can only be performed for a specific wavelength.

Back in 1997, Véran et al. [ref26] proposed a PSF Reconstruction (PSF-R) method allowing one to estimate the “Atmosphere/AO” PSF, solely based on the AO data (WFS measurements and deformable mirror shapes - also called telemetry).

This seminal work, proposed already 20 years ago, initiated an effort in the AO community to provide the astronomers with PSF models associated with their observations. However, and even if the efforts have been continuously progressing (e.g 140papers on Astro-ph since 1997), the lack of scientific applications is a clear sign of the complexity of the whole process, and may be explained by a few factors:

The impact of the telescope and instrument PSF, not encoded in the telemetry, plays a major role in the final PSF shape. In particular, the calibration of instrumental NCPA, in conditions as close as possible as the actual observations has been one of the main challenges. For instance, Keck developed a strategy to capture those aberrations on-sky, but the need of sky time for instrument/telescope calibration discourages the observers from using it.

• The AO-PSF reconstruction assumes a perfectly calibrated AO system while operational constraints (temperature, gravity, local turbulence, mis-alignments) may modify the working point of the adaptive telescopes. This mis-calibration information is not (or only partially) captured by the telemetry.
• Generalization of PSF-R algorithm to multi-LGS systems remains a challenge.
• So far, the PSF-R efforts have been mostly driven by AO specialists, with only a weak connection with astronomers. As a result, even when a PSF can be delivered to the users, they would either not know how to use it, nor trust its validity and accuracy. A critical missing step has been to couple the AO-PSF with specific data reduction tools commonly used by astronomers. There is an on-going effort toward this direction at Keck, and now with the ESO MUSE instrument, and those initiatives should be encouraged and consolidated.

A good summary of the situation can be extracted from the Keck experience (Ragland et al. – ref28), as they developed the most advanced PSF estimation facility so far, “The expectation was that the telescope and the AO system were performing optimally and the telemetry from AO and the telescope is adequate to define the AO PSF at a given instance. We have been learning that PSF-R is more of a systems science problem, where understanding the limits of the telescope, AO and science become necessary to overcome the challenge”.