### SX calibration

Interaction matrix for SX:

**20180222_153225**
The Tip and Tilt in the Interaction Matrix with KL_v18 on SX side look different respect than we expect. The application of Tip or Tilt should generate on Shack-Hartmann WFS constant values in all the subapertures, instead the results obtained is showed in figure below. Figures show that the slopes over the pupils are not constant.

The procedure to build the LGS reconstructor from the interaction matrix expect to remove from the higher modes the contribution of the Tip/Tilt because when the system is acquiring the interaction matrix the telescope is vibrating, injecting a Tip/Tilt disturbance. If recorded Tip/Tilt are the combination of different modes than every higher modes will be affect; the results is that there will be a contamination between modes. For example a pure Tip/Tilt produce a constant signal in all the subapertures, if we multiply a vector of constant slopes (all slopes=k) for this mixed rec we reconstruct not only Tip/Tilt but also higher modes. With the Reconstructor on SX we measure a contamination near the 10% on the two astigmatism.

The problem seem to be related to the KL_v18 because the LGS WFS is able to measure properly. To get a good measure of Tip/Tilt modes (with different orientation respect to ASM Shell tip/tilt) we use the hexapod.

The function "argos.arbitrator.correctHexapodPointing(Pointing.fromNumPyArray(np.array([tipInArcsec,tiltInArsec])))" move the hexapod.
We used the function and we record snapshot for Tip:

Hexapod offset in arcsec |
TN |

0.2, 0.0 |
20180222_235933 |

0.0, 0.0 |
20180222_235836 |

and Tilt:

Hexapod offset in arcsec |
TN |

0.0, 0.0 |
20180222_234006 |

0.0, 0.4 |
20180222_234526 |

The differences between average slopes of snapshots, divided by a scale factor angleInArcsec/4e-6, give a good interaction matrix for Tip and Tilt. We cannot use this interaction matrix to produce a reconstructor for the ASM but we used to remove the Tip/Tilt contribution from the higher (>2) modes of the Interaction Matrix. The new interaction matrix for Tip/Tilt has constant values in the entire pupils.

We replace from the IM 20180222_153225 the tip/tilt columns with the new interaction matrix produced with the hexapod.

The new IM is :

**20180223_004400**
LGSW Rec made with the new IM:

**20180223_004000**
The ARGOS reconstructor for night time use the FLAO rec for Tip/Tilt. The new Combined RECs are:

Bin2 + LGSW:

**20180223_004600**
Bin4 + LGSW:

**20180223_004700**
Figure below shows the measure of higher modes when slopes are constant. The measures is nm rms when slopes are constant and equal to 1. The 20170303_221100 is the LGSW REC used on sky in the previous runs. All old recs produce similar results.

The new Reconstructor doesn't solve totally the problem. In CL every time a Tip/Tilt command is applied also a spurious astigmatism is applied, but the system should be able to correct it. With the old reconstructor every vibration (that produce pure Tip/Tilt) was injecting higher modes in the AO loop; with the new reconstructor this should not be true any more.