2.2 Wavefront Reconstruction Techniques
2.2.3 Mitigation of Vibrations in AO
described is due to the fact that the control matrices A and B in Equation 2.35 do not depend on the DM parameter which makes the model structurally simple and the choice of state-vector also allows an adaptation to more complex models and configurations (Kulcsár et al., 2012).
2.2.3 Mitigation of Vibrations in AO
The LQG AO control described in Section 2.2.2 doesn’t immediately account for telescope vibrations. However by inserting in the model additional states corre- sponding to spring-mass subsystems, this observer-based control can also filter out and/or compensate for telescope vibrations. This can be achieved by defining a global phase, φglob
k , which includes the turbulent phase and also a phase perturba-
tion, φvib
k , due to vibrations,
φglobk = φturk + φvibk . (2.38)
This allows the additive vibrations to be straightforwardly included as perturba- tions in the state vector and estimated in the same way as the turbulence (Petit et al., 2008); the models then only need to be modified to explicitly describe the impact of vibrations on the phase. The vibrations can be modelled as a dampened oscillatory signal generated by a forcing function at the natural frequency of the vibrations to be compensated for, as described in Petit et al. (2008). This then leads to a a second order auto-regressive model, AR(2),
φvibk = a1φvibk−1+ a2φvibn−2+ Ξk, (2.39)
where the coefficients a1 and a2 are given by,
a1 = 2e−Kω0Tcos(ω0T
p
1 − K2), a
2.2.3. Mitigation of Vibrations in AO
where K is the damping coefficient, ω0 = 2πfvibis the natural vibration frequency, T
is the sampling period and Ξkis the, in general unknown, forcing function modelled
simply as Gaussian white noise.
This vibration induced phase profile can then be included in the state space model with a modified state space vector given by,
xk =
φvibk t φvibk−1t φturk t φturk−1t uk−1t uk−2t t
, (2.41)
and the measurement equation, Equation 2.19, now takes into account the global phase so that it becomes,
yk = Dφresk−1+ wk = D(φturk−1− φcork−1) + wk⇒ yk= D(φglobk−1− φcork−1) + wk. (2.42)
The state space model matrices, A, B, C etc, as shown in Equation 2.35 can easily be modified for this new vector and the estimation of the vibration and turbulence is still provided by an equation of the form of Equation 2.36. Correction is also performed similarly, by projecting both the turbulent phase and the phase perturbation caused by vibrations onto the DM (Petit et al., 2008).
The most popular alternative methods for vibration rejection are the H2 and H∞
frequency based approaches which have been shown to perform similarly to LQG (Guesalaga et al., 2013). It has been demonstrated by simulation (Kulcsár et al., 2006) that the LQG control described here, without vibration mitigation, has been able to increase the SR of a PSF to 71% from the 69% obtained using the classical techniques. Other laboratory simulations (Petit et al., 2008) have shown that LQG vibration mitigation has been able to increase an 81% SR, measured without vibra- tion mitigation, up to 90% with an equivalent vibration free measurement of 91%.
H2 synthesis has been demonstrated (Guesalaga et al., 2013) to give reductions of
up to 50% in the variance of residuals in off-line runs and also an improvement of around 30% in on-line runs, although the on-line results are inconclusive. LQG
2.2.3. Mitigation of Vibrations in AO
control has also demonstrated benefits in wide-field AO control (Kulcsár et al., 2012) with test bench results giving LQG control an 81% SR for a an off-axis star with relative separation of 20% compared to the 34% SR obtained for the same star with classical AO control.
These results show the potential for LQG and H2/H∞ control to improve the reso-
lution of seeing limited observations and also to allow for the characterisation and mitigation of telescope vibrations. Further research and study into these methods is currently being conducted with the aim of producing an AO control system suit- able for Extremely Large Telescopes for which vibrations are expected to play a large role in the perturbations of the detected wavefront.
Chapter
3
Many-core CPU RTC and
ELT-scale Optimisations
3.1
Current RTCs and their Suitabilty for ELT-scale
As described in Section 1.2 current AO RTCs are implemented on multiple hard- ware types and running different implementations of RTC software. One of the most widely used RTC systems is the European Southern Observatory (ESO) Stan- dard Platform for Adaptive optics Real Time Applications (SPARTA, Fedrigo et al., 2006) platform, which is a set of tools and definitions which can be used to build AO RTC systems. The hardware defined by SPARTA uses FPGAs for the wave- front processing and DSPs for the reconstruction step. Section 1.2 discusses how both FPGAs and DSPs are generally more complex to work with than CPUs and therefore more time is required in the initial development, and it makes it difficult for further modifications to the RTC algorithms to be made. There is also the problem of the limited processing power per device with these technologies and so scaling such a system to the ELT-scale as described in Section 1.1.4.2 becomes very difficult.
Other current AO RTC implementations will use either GP-GPU technologies or standard CPU systems. However the data transfer from host to accelerator makes