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# Control Loops

## LGS loop

This is the heart of the MCAO correction. This loop (also called high-order loop) controls the 3 DMs shape based on the measurements from the 5 LGS WFSs. We are using a tomographic algorithm process, that optimally finds the best shape to apply to each DM, in order to have the best performance. This reconstructor is updated on the fly depending on the atmospheric conditions (seeing, wind speed, etc...)

## NGS loop

#### Tip-Tilt and Plate Scales modes

This loop controls the Tip-Tilt and Plate Scale (anisoplanatism) modes. It is well known that the position of the LGS WFS can not be trusted on the sky. This is called the "tilt indetermination problem" and is basically due to the fact that the laser beam uplink tip-tilt is unknown. Thus, we need NGSs to provide this part. In classical, one LGS AO systems, the only modes we care about are tip and tilt. Here with MCAO, because we want to correct not only on axis but also off-axis on a extended field (that is, we correct for anisoplanatism), we need -in addition to tip and tilt- to correct for Tip and Tilt anisoplanatism. These anisoplanatism modes are plate scales modes. Then, from the 3 TT WFS, we can deduce the following:
• Global (average) Tip and Tilt (2 modes)
• Plate scale modes (global shrinking of the image, or stretching in X and shrinking in Y, or same rotated 45 degrees = 3 modes)
• Image rotation (1 "mode")

Below is an animation of these 5 modes on an star field:

 Tip Tilt Focus Astigmatism 0 Astigmatism 45 Rotation

These plate scale modes are not produced by the TT mirror, but by the DMs. It turns out that by combining a Defocus D0 on DM9 and the opposite defocus -D0 on DM0, one can control plate scale in the output focal plane. Note that rotation does not corresponds to anything that is correctable with the DMs. It is not a mode which can be induced by any physically possible phase aberration. It can only be a rotation, and thus need to be corrected by a element that can induce a rotation. The only such element is the Cassegrain rotator. Thus this fifth TTWFSs measurement will be low pass filtered and send to the Cassegrain Rotator as an error term, that has to be added to the current target.
The NGS can be located anywhere in the 2 arcmin Canopus input field (defined by the canopus mechanical input port), but should preferentially be as widely spread as possible. At first approximation, the field inside the area defined by the 3GS triangle will be best corrected, and the correction will degrade outside this area.

#### Slow Focus Sensor (SFS)

The range (the altitude) of a Laser Guide Stars depends on the altitude of the Sodium Layer. When looking at zenith, this altitude is ~90km. As we are using the LGS to compensate for atmospheric focus, we cannot disentangle any changes in the sodium layer altitude from real atmospheric focus changes. In other word, if the altitude of the LGS varies (by a few hundreds of meters) we will interpret this as focus, and the DMs will compensate for it. As a matter of fact, the image appear out of focus in the science instrument. To cope with this effect, we need a "truth focus sensor" which monitor the true focus on an NGS. This is done by the SFS, with a 2x2 Shack-Hartmann sensor that uses 30% of the light of one of the NGS probes. This error focus signal is sent to the LGSWFS zoom, as offsets around the best focus position.

#### LGS Tip-Tilt stabilization

The natural TT only have little to do with the position of the LGS. The position of the LGS on the LGS WFS will also be a result of the laser beam direction, LLT flexures, etc... This overall spot centering of the LGSs on the LGS WFS need therefore to be somehow compensated, otherwise they will slowly drift and eventually get out of the LGS WFS subapertures field of view. To achieve this, we use the LGS WFS derived Tip-Tilt signal to drive the BTO Field Steering Array (one small TT mirror per beam). In effect, the FSA move the laser beams on the sky (independantly for each beam), and thus allow to recenter them on each LGS WFS. The average motion of the FSA is offloaded to the Poiting/Centering Mirror. The average rotation of the constellation is offloaded to the K-Mirror.

By default, PWFS1 will not be used together with GeMS . PWFS2 can not be used, as it occupies the same physical space as the AO fold (flat that sends the light into Canopus). Therefore, we are running "open loop" on the primary mirror figure, only using a LUT after the night initial setup. There might be, and probably will be, some drift, as the LUT are not perfect. In particular, astigmatism is likely to drift slowly. Correcting these slow drifts of the primary mirror figure is not a problem for the AO system, except for the fact that it will eat up some dynamical range from the DMs (more precisely, DM0). To avoid this, we offload at a low rate (typically every 10sec) the low order spatial modes of DM0 to M1 (typically 6-10 modes).

Similarly, we do not use a tracker. Thus, if the open-loop telescope tracking is imperfect, this will slowly build up on the TT mirror. In a similar fashion as for the M1 offload, we offload the TTM average position to M2. In fact, because M2 accept commands up to 200Hz, we do the offload at this rate, albeit with a very low gain, which in effect means offloading only the very lowest temporal frequencies.

#### Elevation LUT to LGS WFS zoom

Following simple geometric considerations, the distance from the telescope to the sodium layer (and thus the physical LGS) vary with the telescope elevation. The average sodium layer altitude is 90km. Hence the range to the LGS is 90km at zenith, but it becomes 180km when looking down at zenith angle = 60 degrees. The LGS WFS zoom is a device that allows to maintain the LGS in focus on the LGS WFS themselves, to accommodate for this large LGS range variation. Because the main term in the LGS WFS zoom position is a (predictable) geometric term driven by elevation, this is taken in to account with a LUT.

#### Flexure Guide Star

There will be flexure of the science instrument vs. GeMS . For instance, flexure of the CANOPUS output optics (AOP2 and fold), or flexure of the science fold, or of the science instrument internal optics. Flexure of the CANOPUS TTWFS will also induce unwanted motion of the output beam, through the AO close loop. To avoid image motion on the science detector, the best approach is to actively sense its position on the science detector itself, or as close as possible to it. In GSAOI, we have the possibility to have On-Detectors Guide Windows (ODGW), that measure the position of a star on the detector. The error signal, if any, will be used to drive the TTWFSs probe position (probe#3 will move, #1 and #2 will move along with it, being positioned on top of #3), to compensate for possible flexure.

#### Non Common Path Aberrations Correction

An AO system can compensate for optical aberrations, but only the one that it can sees with the WFS. All the optics that are after the WFS can introduce aberrations that will reduce the image quality on the science detector. On the other hand, all the aberrations that only exists in the WFS path will be compensate, when they are not supposed to be, degrading the IQ as well. The combination of all of these reduces significantly the static performance (when there's no atmospheric turbulence) and the Strehl Ratio we get are of the order of 20% in H-band. But as these aberrations are static, we can pre-compensate for them by adding a static shape on the DMs. To define this static shape, we optimize the image quality on the science detector. This is done by using focal plane wave-front sensing technique such as phase diversity. But for GeMS , this has been generalized to tomography.