Standard FFT-based phase screen generation methods do not accurately model low-frequency turbulence characteristics. This paper introduces a new phase screen generation technique which uses low frequency subharmonic information to correct the problem. We compare our technique to two other subharmonic methods. The structure functions for this new method match very closely the structure functions of Kolmogorov turbulence theory.

/pdf/simulation-of-stellar-speckle-imaging-49uo34tw37.pdf

Simulation of stellar speckle imaging

The Phase Diverse Speckle (PDS) problem is formulated mathematically as Multi Frame Blind Deconvolution (MFBD) together with a set of Linear Equality Constraints (LECs) on the wavefront expansion parameters. This MFBD--LEC formulation is quite general and, in addition to PDS, it allows the same code to handle a variety of different data collection schemes specified as data, the LECs, rather than in the code. It also relieves us from having to derive new expressions for the gradient of the wavefront parameter vector for each type of data set. The idea is first presented with a simple formulation that accommodates Phase Diversity, Phase Diverse Speckle, and Shack--Hartmann wavefront sensing. Then various generalizations are discussed, that allows many other types of data sets to be handled.
Background: Unless auxiliary information is used, the Blind Deconvolution problem for a single frame is not well posed because the object and PSF information in a data frame cannot be separated. There are different ways of bringing auxiliary information to bear on the problem. MFBD uses several frames which helps somewhat, because the solutions are constrained by a requirement that the object be the same, but is often not enough to get useful results without further constraints. One class of MFBD methods constrain the solutions by requiring that the PSFs correspond to wavefronts over a certain pupil geometry, expanded in a finite basis. This is an effective approach but there is still a problem of uniqueness in that different phases can give the same PSF. Phase Diversity and the more general PDS methods are special cases of this class of MFBD, where the observations are usually arranged so that in-focus data is collected together with intentionally defocused data, where information on the object is sacrificed for more information on the aberrations. The known differences and similarities between the phases are used to get better estimates.

Multi-frame blind deconvolution with linear equality constraints

Because they have demonstrated very high visibility accuracies and have greatly simplified conventional interferometric recombination devices, single-mode fibers are being seriously considered in several optical interferometry projects. This paper deals with light coupling into single-mode fibers. An analytical expression of the coupling efficiency is derived for the monochromatic case. Then, the effect of purely static aberrations is considered. Finally, coupling in the presence of atmospheric turbulence is investigated for long exposure times. Using temporal sequencies of turbulent wavefronts, simulations are performed for a wide range of seeing conditions with both uncorrected turbulence and various levels of correction by an adaptive optics system.

A study of degraded light coupling into single-mode fibers

Context. The knowledge of the point-spread function compensated by adaptive optics is of prime importance in several image restoration techniques such as deconvolution and astrometric/photometric algorithms. Wavefront-related data from the adaptive optics real-time computer can be used to accurately estimate the point-spread function in adaptive optics observations. The only point-spread function reconstruction algorithm implemented on astronomical adaptive optics system makes use of particular functions, named U i j. These U i j functions are derived from the mirror modes, and their number is proportional to the square number of these mirror modes. Aims. We present here two new algorithms for point-spread function reconstruction that aim at suppressing the use of these U i j functions to avoid the storage of a large amount of data and to shorten the computation time of this PSF reconstruction. Methods. Both algorithms take advantage of the eigen decomposition of the residual parallel phase covariance matrix. In the first algorithm, the use of a basis in which the latter matrix is diagonal reduces the number of U i j functions to the number of mirror modes. In the second algorithm, this eigen decomposition is used to compute phase screens that follow the same statistics as the residual parallel phase covariance matrix, and thus suppress the need for these U i j functions. Results. Our algorithms dramatically reduce the number of U i j functions to be computed for the point-spread function reconstruction. Adaptive optics simulations show the good accuracy of both algorithms to reconstruct the point-spread function.

/pdf/new-algorithms-for-adaptive-optics-point-spread-function-6rwee5rrv3.pdf

New algorithms for adaptive optics point-spread function reconstruction

The vector vortex beams (VVB) possessing non-separable states of light, in which polarization and orbital angular momentum (OAM) are coupled, have attracted more and more attentions in science and technology, due to the unique nature of the light field. However, atmospheric transmission distortion is a recurring challenge hampering the practical application, such as communication and imaging. In this work, we built a deep learning based adaptive optics system to compensate the turbulence aberrations of the vector vortex mode in terms of phase distribution and mode purity. A turbulence aberration correction convolutional neural network (TACCNN) model, which can learn the mapping relationship of intensity profile of the distorted vector vortex modes and the turbulence phase generated by first 20 Zernike modes, is well designed. After supervised learning plentiful experimental samples, the TACCNN model compensates turbulence aberration for VVB quickly and accurately. For the first time, experimental results show that through correction, the mode purity of the distorted VVB improves from 19% to 70% under the turbulence strength of D/r0 = 5.28 with correction time 100 ms. Furthermore, both spatial modes and the light intensity distribution can be well compensated in different atmospheric turbulence.

Turbulence aberration correction for vector vortex beams using deep neural networks on experimental data.

An algorithm is described which simulates atmospherically distorted wavefronts using a Zernike expansion
of randomly weighted Karhunen-Loeve functions. Its performance are presented and analyzed thereafter. The
program is then used to forecast resulting structure function and Strehl resolution for adaptive optics systems.

Nicolas A. Roddier

Papers

Atmospheric wavefront simulation and Zernike polynomials