Wavefront reconstruction

^Figure 2 : Illustration of the Shack-Hartmann wavefront sensor concept : the micros-lens array allows to form several spots in the focal-plane, whose positions depends on the local 1st order derivative of the wavefront.

> Figure 3 : Illustration of the correlation of measurements obtained from two 7x7 Shack-Hartmann WFS pointing at two different stars. The presence of turbulent layers in the atmosphere introduces a peak of correlation at a distance that depends on the pupil diameter and the layer altitude.

Figure 3 shows that the presence of atmospheric turbulent layers introduces peaks in the spatial correlation of Shack-Hartmann WFSs measurements. The location of this peak depends on the pupil diameter and the altitude, and the amplitude of the correlation linearly depends on the strength of the layer as well, i.e. the Cn2 value at this specific altitude. Regarding this, one may tomographically reconstruct the wavefront in any direction from the Cn2 profile and a model of the spatial covariance.

Wavefront sensing is the heart of Adaptive Optics (AO) systems and consists in estimating the phase of the electric field, usually in the instrument pupil plane.

Several devices exist to perform the wavefront sensing, such as the Shack-Hartmann wavefront sensor (WFS), the curvature WFS or Fourier-filtering sensors (pyramid, axicon, ZELDA,...) that have an intermediate focal-plane in which is place the optical element. Regardless the WFS technology, the optical elements is crucial to transform incoming phase fluctuations into a signal whose amplitude linearly (hopefully) depends on the phase fluctuations and can be measured with the detector.

Figure 2 illustrates the principle of the well known Shack-Hartmann WFS that relies on a micro-lens array to form spots whose displacements linearly depends on the local 1st order derivative of the phase.

Wide-field AO systems rely on multiple WFSs that measure the incoming wavefront in different directions in the field. In order to compensate for the atmospheric turbulence in a large field of view (larger than the isoplanatic patch), such systems combine those multiple measurements to command the DM. There is a trade-off between uniformity of the field and correction efficiency: Ground Layer AO (GLAO) systems are designed to provide a uniform correction over a wide-field (~1') but quite poor (improvement of the FWHM by a factor 2 from seeing-limited images), while Laser Tomography AO (LTAO) systems optimize the correction in a small field (~10''). Multi-conjugated AO (MCAO) allow to meet both uniformity and efficiency by including several DMs in the optical path, but at the cost of an increasing of the system complexity and control.

In this context, I'm specializing in supervised neural networks, especially in Convolutionnal Neural Networks (CNNs) to perform the wavefront reconstruction and the atmospheric tomography. Figure 4 illustrates the architecture that is currently under study to perform atmospheric tomography on CANARY. In the presence of noise (detector, shot noise, background), the CNN performs 15% better than a classical feedforward architecture, which is already 20% better than the MMSE approach.

Figure 4 : CNN architecture (VGGnet) deployed for performing atmospheric tomography from the 3 NGS Shack-Hartmann WFSs of the CANARY instrument. The CNN is designed and trained in with simulated data to estimate the on-axis WFS slopes (72 measurements) from the set of three images.

In this context, I work on the development and validation of supervised neural networks for wavefront reconstruction with Fourier-filtering WFSs (MAWSER project) and atmospheric tomography (CARMEN).