At the foundation of the problem of light propagation through optical turbulence is the classical Obukhov-Kolmogorov theory. It rests in the requirement that the refractive index fluctuations should be homogeneous and isotropic. These, with other necessary assumptions, lead to the very well-known -11/3-power exponent spectrum on the inertial range; although departures have been found, they are usually associated with partially developed turbulence or its intrinsic intermittency. Recently, in optics, the interest in anisotropic fluctuations of the refractive index has gained attention. These studies are mostly theoretical, and reduce anisotropic effects to a dilatation along a coordinate direction in the three-dimensional wavenumber space. Few experimental works exists, but all of them employ simulated turbulence. In this Letter, we describe an experiment to produce anisotropic turbulence under controlled conditions; moreover, we observe anisotropy by studying the spectral power exponent of a temporal series of laser beam wandering.

This work shows the design and training of a convolutional neural network to improve the linear response of a modulated pyramid wavefront sensor, allowing to estimate and compensate for the optical gain in real time.

The deep learning wavefront sensor (DLWFS) allows the direct estimate of Zernike coefficients of aberrated wavefronts from intensity images. The main drawback of this approach is related to the use of massive convolutional neural networks (CNNs) that are lengthy to train or estimate. In this paper, we explore several options to reduce both the training and estimation time. First, we develop a CNN that can be rapidly trained without compromising accuracy. Second, we explore the effects given smaller input image sizes and different amounts of Zernike modes to be estimated. Our simulation results demonstrate that the proposed network using images of either 8 × 8 , 16 × 16 , or 32 × 32 will dramatically reduce training time and even boost the estimation accuracy of Zernike coefficients. From our experimental results, we can confirm that a 16 × 16 DLWFS can be quickly trained and is able to estimate the first 12 Zernike coefficients–skipping piston, tip, and tilt–without sacrificing accuracy and significantly speeding up the prediction time to facilitate low-cost, real-time adaptive optics systems.

No abstract

In this work, we evaluate a especially crafted deep convolutional neural network to provide with estimations of the wavefront aberration modes directly from pyramidal wavefront sensor (PyWFS) images. Overall, the use of deep neural networks allow to improve the estimation performance as well as the operational range of the PyWFS, especially when considering cases of strong turbulence or bad seeing ratios D 0 /r 0 . Our preliminary results provide with evidence that by using neural nets, instead of the classic linear estimation methods, we can obtain a low modulation sensitivity response while extending the linearity range of the PyWFS, reducing the residual variance by a factor of 1.6 when dealing with a r 0 as low as a few centimeters.