Gaia needs an almost diffraction-limited optical quality throughout the field of view of each telescope to provide exquisite astrometry. The key metrics is the Cram´er-Rao image sharpness2,3 which for a given LSF is expressed as:
(1)
ση = 1 � � � �
n−1
(S′ k)2
�
r2 + b + Sk
k=0
where Sk, the LSF, is the number of electrons collected from the star, binned Across Scan (AC), for Along Scan (AL) pixel coordinate k, where k ∈[0, n−1]. S′ k is the derivative of Sk with respect to the pixel coordinate, r the read-out noise (in electrons) and b the homogeneous sky background (in electrons). The units of ση are pixels. ση is a measure of the astrometric information present in a given LSF: it is the maximum centroiding precision that an optimum maximum-likelihood method can achieve. If only bright stars are considered, b is subtracted and ση is normalised by the photon noise:
� � � �
n−1
�
Cramer −Raonormalised = ση
(2)
Sk = ση �
Ne− k=0
which is independent of the stellar brightness, and can be averaged over the whole focal plane. Fig. 2 shows the evolution of the Cram´er-Rao image sharpness throughout the mission. Several things are apparent. First, the image quality is very good, being always around 1.0, as expected for the nearly diffraction-limited and slightly undersampled Gaia PSF. Second, telescope 1 provides better AL image quality.3 Third, decontamination is always beneficial in terms of image quality, although small focus adjustments are typically needed afterwards to regain optimum performance. Fourth, the focus has never been stable, although the degradation slope becomes shallower as the mission evolves. The root cause has not been identified, although a number of hypothesis have been postulated: glue shrinkage, hysteresis, water contamination, etc.
These rare but important focus adjustments are the only times the M2 Movement Mechanisms (M2MM) are operated.4 Basically, they provide five degrees of freedom (three translations and two rotations) control over the secondary mirrors, which has been sufficient to obtain a superb image quality. Two WaveFront Sensors (WFS) provide key information to avoid blind exploration of the 5-D actuation parameter space. The pre-launch preparations and its use during early commissioning are described in5.3 Basically, they were used in absolute mode, the zero wavefront reference being provided by a trio of reference fibres. These readings were essential to recover a reasonably sharp PSF after launch. See Fig. 3, adapted from,3 for an overview of the M2MM and a WFS pattern.
However, the WFS have a small number of microlenses (pupil sampling vs stellar brightness trade-off), which induces a small aliasing during the Legendre polynomial decomposition. In addition, the minimum wavefront point is just a good (and close) starting point for the optimum balanced configuration between all focal planes (astrometric, photometric and spectroscopic). The so-called “best focus” was a trade-off configuration iteratively obtained after all scientific data were analysed.3 Once an optimum configuration was defined, the WFS do not need to operate in absolute mode any more, but just determine the differences between the current situation and best focus. In addition, the most sensitive actuation is, of course, pure M2 z-axis focus. Therefore, the two focus corrections that have taken place during the nominal mission have been small pure z-axis focus adjustments (+2 µm in both cases).

[Figure: Figure 2. Focus evolution during the mission. The average Cram´er-Rao image sharpness metrics is plotted for each telescope from early commissioning (March 2014) to March 2016. Major payload decontaminations and telescope refocuses are indicated.]

[Figure: Figure 3. M2MM overview (left) and WFS sample pattern (right). The M2MM provides five degrees of freedom (three translations and two rotations) control over the Gaia telescope secondary mirrors. They are only operated during the rare refocusing events. Image: Airbus DS. Two Shack-Hartmann WaveFront Sensors (WFS) provide low-order sampling needed during the first focusing attempts in early commissioning and differential measurements for fine tuning during the nominal mission.]