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Adaptive Optics Facility
Calibrations

Calibration Issues for the Adaptive Optics Facility

Purpose of work:	AO Facility DSM calibrations
Studies conducted by:	Sylvain Oberti (soberti@eso.org)
Project Manager AOF:	Robin Arsenault (rarsenau@eso.org)
Location:	N/A
Status:	Preliminary Studies & Simulations

Calibration Requirements

A fundamental limitation of AO systems based on an adaptive secondary mirror like the VLT M2 is that there is no intermediate focus before the deformable mirror. Therefore, it is not possible to install an artificial calibration source, seen by the DM and the Interaction Matrix (IM) measurement in a conventional way is not possible. An extensive program has been initiated at ESO to study this limitation and explore alternatives.

AdSec vs Conventional
Figure 1: Left a Adaptive secondary scheme; there is no intermediate focus where an artificial star can be located upstream from the DSM. This is the case for an conventional AO system (right) where a re-imaging optics system is inserted before the final corrected focus.

Several solutions are being envisioned for the IM measurement. First, Synthetic (simulated) IM using measured influence functions of the DSM in the laboratory and calibration of the WFS optical path and second several different methods of performing on-sky IM measurements.

Even if the synthetic IM is the most seductive solution (noiseless, simplicity, no calibration time required), it still has to be demonstrated that the accuracy of the models (DM and WFS) can be high enough to ensure the expected performances.

Regarding the experimental estimation of the IM, novel techniques are investigated in order to deal with the new issues that we have to face:

There is turbulent noise either because the calibration is performed on sky or because of the telescope internal turbulence.
The calibration time might dramatically increased because of the larger number of degrees of freedom.
Several methods are being investigated through simulations and laboratory tests as well as on sky tests when possible. The different schemes aim at minimizing the noise and bias on the measurement in order to optimize the quality of the reconstructor.

Using various modal bases (zonal, Hadamard, system modes/mirror modes, Zernike or Karhuenen-Loeve), several techniques are foreseen and being compared:

Open loop fast DM actuation, which allows freezing the disturbances between modal push and pull and thus minimize turbulent noise as well as any low frequency effect.
Open loop DM modulation and demodulation by FFT detection. The stimulus power is concentrated on a single frequency beyond the modal atmospheric bandwidth. Low frequency effects are cancelled out and it allows for multiplexing. This way, several modes can be measured at the simultaneously, reducing the total calibration time.
Closed loop calibration. Dynamic bias is applied as offset on the WFS signal. The DM command is measured as a response to this bias and therefore the reconstruction matrix (or control matrix) is measured directly.

Furthermore, there is a key issue related to calibration. A pupil offset may have a strong impact on the system performance and must be addressed properly. Indeed, for high order AO systems such as VLT with DSM, the tolerance is very tight. Dynamical pupil alignment is envisioned to minimize this effect.

Modal Basis

The choice of the modal basis to activate the DM actuator is extremely important. Hadamard modes have the property to maximize the WFS signal for a low voltage actuation of each electrode. A mathematical matrix operation allows to recover the individual DM Influence function. The figure 2 provides a comparison for the MACAO-VLTI 60 elements curvature systems of the IM betwen zonal (one actuator at a time) and Hadamard modes.
Zonal vs Hadamard

Figure 2: Zonal IM versus Hadamard IM. The Hadamard matrix have the property to exhibit the largest determinant for a matrix made of 1 and -1. This reflects in the highest WFS signal for a given voltage actuation.

Fast DM Actuation

Another ingredient to a high S/N ratio IM is a fast actuation of the DM electrode. This has the advantage of freezing the turbulence and therefore making the process independant of time dependant variations (like turbulence). Care must be taken to leave a short delay after actuation (by a square wave for instance) to let the DM stabilize (in case of overshoot and/or vibration after actuation). The measurement is repeated several time and measurement averaged.

The use of the above technique have proven very promising on MACAO-VLTI where an interaction matrix has been obtained on the sky (August 2004) in moderate seeing conditions and used to close the loop and correct turbulence. The result is shown on figure 3.
IM on sky

Figure 3: IM obtained conventionally on artificial star (left) and IM obtained on sky on a turbulent source (right). The image on the right has been obtained after AO correction using the IM obtained on sky.

Modulation Technique

This is a classical technique in optics and telecommunications. It consists in modulating the input signal with a sinusoidal wave. The demodulation is obtained by multiplying by the same function. The useful signal is folded to DC, a low pass filter (averager) retrieves signal amplitude and averaging cancels out the white noise term.

Synthetic IM

The advantage of this technique is that it is independant of noise and bias such as turbulent noise, photon noise, read noise, telescope drifts and deformable mirror limitation (hysterisis, creep, non-linearity...).
On the other hand it doesn't account for realistic effects like optical mis-alignment and its effect on static aberration (and/or pupil misregistration). A very accurate DM model is required and WFS as well; the calibrations or definition of the model is a critical and not obvious process.

MAD for test bed

Conclusions

Various techniques have been investigated to tackle the calibration issues in the AO facility case
This study is of major importance for ELT AO as well
The most promising solutions are synthetic and modulation techniques
They have been validated in the low order case
Simulations, the HOT experiment (+1000 actuators) and later ASSIST will allow addressing the high order case

More Details...

The following work led by S. Oberti (AOD) has been presented to the SPIE meeting Orlando (May 2006). It represents the most up-to-date approaches and strategy for accurate calibration of high order AO system like the AO Facility and its DSM.
"Large DM AO systems: synthetic IM or calibration on sky?"

Adaptive Optics Facility Calibrations