SPLATT-Simulations

The simulation toolkit is composed by three main parts: the DM, the PWFS and the closedloop. The DM is segmented and replicates the JWST geometry, with hexagonal segments on a hexagonal grid with 3 rings, within a circular outer mask. The segments alignment modes (piston and tip/tilt) are the system degrees of freedom (DoF) and are simulated by producing the associated shapes on the pupil mask. The PWFS and closedloop code are part of the PASSATA toolkit, that has been used intensively for the simulation, design, and performance evaluation of the FLAO, ERIS, GMT, MAVIS AO system. In particular, PASSATA was adopted to simulate the WF sensing and control strategy (including the segments piston) for the GMT. The first stage of the simulation, after importing the DM, is to calibrate the PWFS. This is done in two steps: as first the system mask is created by selecting those pixel with an illumination level above a user-defined threshold. As a second step, the PWFS interaction matrix is calibrated by measuring the PWFS signal when the DoF of the simulated DM are excited individually. The measurement is differential according to the push-pull technique: the commands are applied sequentially with positive, then negative amplitude, and the difference of the corresponding signals is taken. The command amplitude shall be chosen carefully to calibrate the system within its linear range. Our test model is composed by a segmented DM with 19 hexagonal segments and a circular mask, whose degrees of freedom are the local alignment modes, namely segment piston and tip/tilt; the PWFS images the DM on a 36x36 to 76 x76 pixel grid (per sub-pupil), in order to test the effect of a better resolution versus a lower photon signal per pixel. The WFS camera is the CCD39 (the one used for the FLAO16 AO system at the Large Binocular Telescope), which has a known noise characteristic and is consistent with a worst case scenario (it is a quite old camera with important read-out noise and a quantum efficiency lower than 35 %).

Closed loop result

We tested closing the loop for a demonstration test case. We created an initial DM offset by scrambling the segments with piston and tip/tilt; such initial surface error is 50 nm RMS and is consistent with a preliminary co-alignment and co-phasing performed with a different device (the PWFS at low sensitivity or the scientific camera to identify and pre-adjust the single segments). We then closed the PWFS loop with the parameters reported in Tab. 1, in particular the guide star magnitude was 10 and the loop frequency was 10 Hz. The loop frequency is the PWFS frame rate; we must then consider that with a 0.1 gain the effective loop speed is 1 Hz. We are interested in the stability of the WF correction, which is related to the sensitivity of the PWFS. We therefore evaluated the loop performances by computing the dispersion of the DM surface error during the loop, after the initial convergence stage. We basically computed the residual DM surface error versus time: we then calculated the standard deviation of the plot, as an estimation of the WF stability. The result (see Fig. 11) is very promising since we computed a sub-nanometer stability (or sensitivity) compared to a significantly fast loop speed and faint star magnitude. We are currently (summer 2022) running simulations to further asses these results, for instance by evaluating the loop performances at different guide star magnitudes and PWFS sampling, i.e. the number of pixel on each sub-pupil of the pyramid CCD.

Discussion

Some points descending from the PWFS sensitivity need here to be discussed. As first, it would be possible to push the limit for the guide star magnitude toward the faint end. This implies a large sky coverage with the scientific target to be used also as a reference for the WFS. The case of the extended object shall be addressed to understand the possible limitations. The relatively fast frame rate implies that the open-loop stability of the DM (and of the entire system) can be limited to a sub-minute time scale. We could also consider another scenario (following a virtual adaptive optics approach) where the PWFS doesn’t actually drive the DM, but its fast cadence readings are used for an enhanced data processing.

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