Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions

Detection strategies for an optical communication system using Gaussian vortex beams

In this paper, we describe the details of different detection strategies of a communication system using Gaussian vortex beams. These are listed as (a) simultaneous transmission of actual data symbol and reference signals (no multiplexing), (b) transmission of data symbol and reference signals in a wavelength division multiplexed manner, and (c) transmission of data symbol and reference signals in a time-division multiplexed manner. The performance of each one is evaluated for strong turbulence regimes with the help of an appropriately arranged random phase screen setup. It is found that the first two detection strategies work error-free within the source and propagation parameters chosen. In the last detection strategy, performance depends on the transverse wind velocity.

Numerical simulation of a large area scintillometer and laser differential image motion monitor

Measurements of atmospheric turbulence along a path can be quantified by scintillometers and differential image motion monitors (DIMMs). The two instruments often measure different levels of turbulence, sometimes varying by nearly an order of magnitude. A high-fidelity numerical simulation was leveraged to assess the measurement performance of both a scintillometer and a DIMM system. When a non-ideal detector is combined with range-dependent turbulence, significant differences between the scintillometer and DIMM are observed. The difference in measurements obtained with the numerically simulated scintillometer and DIMM was consistent with those observed in side-by-side measurements with the instruments.

Joint object classification and turbulence strength estimation using convolutional neural networks

In a recent paper, Kee et al. [Appl. Opt.59, 9434 (2020)APOPAI0003-693510.1364/AO.405663] use a multilayer perceptron neural network to classify objects in imagery after degradation through atmospheric turbulence. They also estimate turbulence strength when prior knowledge of the object is available. In this work, we significantly increase the realism of the turbulence simulation used to train and evaluate the Kee et al. neural network. Second, we develop a new convolutional neural network for joint character classification and turbulence strength estimation, thereby eliminating the prior knowledge constraint. This joint classifier-estimator expands applicability to a broad range of remote sensing problems, where the observer cannot access the object of interest directly.

Variational scaling law for atmospheric propagation

A new scaling law model for propagation of optical beams through atmospheric turbulence is presented and compared to a common scalar stochastic waveoptics technique. This methodology tracks the evolution of the important beam wavefront and phasefront parameters of a propagating Gaussian-shaped laser field as it moves through atmospheric turbulence, assuming a conservation of power. As with other scaling laws, this variational technique makes multiple simplifying assumptions about the optical beam to capture the essential features of interest, while significantly reducing the computational cost of calculation. This variational scaling law is shown to work reliably with moderately high turbulence strengths.

Scintillation analysis of truncated Bessel beams via numerical turbulence propagation simulation

Scintillation aspects of truncated Bessel beams propagated through atmospheric turbulence are investigated using a numerical wave optics random phase screen simulation method. On-axis, aperture averaged scintillation and scintillation relative to a classical Gaussian beam of equal source power and scintillation per unit received power are evaluated. It is found that in almost all circumstances studied, the zeroth-order Bessel beam will deliver the lowest scintillation. Low aperture averaged scintillation levels are also observed for the fourth-order Bessel beam truncated by a narrower source window. When assessed relative to the scintillation of a Gaussian beam of equal source power, Bessel beams generally have less scintillation, particularly at small receiver aperture sizes and small beam orders. Upon including in this relative performance measure the criteria of per unit received power, this advantageous position of Bessel beams mostly disappears, but zeroth- and first-order Bessel beams continue to offer some advantage for relatively smaller aperture sizes, larger source powers, larger source plane dimensions, and intermediate propagation lengths.

Sparse spectrum model for a turbulent phase

Monte Carlo (MC) simulation of phase front perturbations by atmospheric turbulence finds numerous applications for design and modeling of the adaptive optics systems, laser beam propagation simulations, and evaluating the performance of the various optical systems operating in the open air environment. Accurate generation of two-dimensional random fields of turbulent phase is complicated by the enormous diversity of scales that can reach five orders of magnitude in each coordinate. In addition there is a need for generation of the long "ribbons" of turbulent phase that are used to represent the time evolution of the wave front. This makes it unfeasible to use the standard discrete Fourier transform-based technique as a basis for the MC simulation algorithm. We propose a new model for turbulent phase: the sparse spectrum (SS) random field. The principal assumption of the SS model is that each realization of the random field has a discrete random spectral support. Statistics of the random amplitudes and wave vectors of the SS model are arranged to provide the required spectral and correlation properties of the random field. The SS-based MC model offers substantial reduction of computer costs for simulation of the wide-band random fields and processes, and is capable of generating long aperiodic phase "ribbons." We report the results of model trials that determine the number of sparse components, and the range of wavenumbers that is necessary to accurately reproduce the random field with a power-law spectrum.

Method of estimation of turbulence characteristic scales

We propose an optical method that uses phase data of a laser beam obtained from a Shack-Hartmann sensor to estimate both the inner and outer scales of turbulence. The method is based on the sequential analysis of normalized correlation functions of Zernike coefficients. It allows the exclusion C(n)(2) from the analysis and reduces the solution of a two-parameter problem to a sequential solution of two single-parameter problems. The method has been applied to estimate the outer and inner scales of turbulence induced in the water cell.

Simulation of atmospheric turbulence for optical systems with extended sources

In this paper, the method of random wave vectors for simulation of atmospheric turbulence is extended to 2D×2D space to provide spatial degrees of freedom at both input and output planes. The modified technique can thus simultaneously simulate the turbulence-induced log-amplitude and phase distortions for optical systems with extended sources either implemented as a single large aperture or multiple apertures. The reliability of our simulation technique is validated in different conditions and its application is briefly investigated in a multibeam free-space optical communication scenario.

Statistical interpolation method of turbulent phase screen

A relative displacement between the grid points of optical fields and those of phase screens may occur in the simulation of light propagation through the turbulent atmosphere. A statistical interpolator is proposed to solve this problem in this paper. It is evaluated by the phase structure function and numerical experiments of light propagation through atmospheric turbulence with/without adaptive optics (AO) and it is also compared with the well-known linear interpolator under the same condition. Results of the phase structure function show that the statistical interpolator is more accurate in comparison with the linear one, especially in the high frequency region. More importantly, the long-exposure results of light propagation through the turbulent atmosphere with/without AO also show that the statistical interpolator is more accurate and reliable than the linear one.

Broadband, static wave-front generation: Na-Ag ion-exchange phase screens and telescope emulation

We test the statistical properties of static, atmospherelike wave fronts in glass that allow repeatable testing of astronomical adaptive optics instrumentation. The technology is mask-structured ion exchange (MSI) in glass and has significant advantages over other transmissive technologies. The screens are easy to clean, are insensitive to ambient temperature changes, and have high optical-to-near-infrared transmission. However, the effective coherence length (r0) on each of the fabricated screens is systematically too large or, equivalently, the fabricated aberrations are too weak. Despite this strong caveat, the screens appear to be quite useful: Long-exposure point-spread functions have realistic shapes, and power spectrum indices closely match those of the computer-generated wave fronts. Most significant, stacking screens with similar r0 values reduced r0 by the amount predicted by turbulence theory. The refractivity of MSI screens remains unmeasured. Finally, we present our design of an optical system that emulates the key characteristics of the Very Large Telescope, made to contain glass phase screens and to mimic an array of stars for multiconjugate adaptive optics system testing.

Measurement and data-processing approach for estimating the spatial statistics of turbulence-induced index of refraction fluctuations in the upper atmosphere

We present a method of data reduction and analysis that has been developed for a novel experiment to measure the spatial statistics of atmospheric turbulence in the tropopause. We took measurements of temperature at 15 points on a hexagonal grid for altitudes from 12,000 to 18,000 m while suspended from a balloon performing a controlled descent. From the temperature data we estimate the index of refraction and study the spatial statistics of the turbulence-induced index of refraction fluctuations. We present and evaluate the performance of a processing approach to estimate the parameters of isotropic models for the spatial power spectrum of the turbulence. In addition to examining the parameters of the von Kármán spectrum, we have allowed the so-called power law to be a parameter in the estimation algorithm. A maximum-likelihood-based approach is used to estimate the turbulence parameters from the measurements. Simulation results presented here show that, in the presence of the anticipated levels of measurement noise, this approach allows turbulence parameters to be estimated with good accuracy, with the exception of the inner scale.

Method of random wave vectors in simulation of anisoplanatic effects

A generalization of the method of random wave vectors [Appl. Opt. 36, 464 (1997)] that is suitable for a simulation of turbulence-induced anisoplanatic effects is proposed. A simulation of the cross-correlated phase fluctuations produced by two initially plane waves propagating through weak turbulence is considered. The variation of C(n)(2) along a propagation path and an effect of the finite outer scale of the turbulence are included in the simulation. The validity of the simulation method is verified by comparison of theoretical and simulated results. The simulation approach developed can be used in the problems related to adaptive optics, speckle inteferometry, guide stars, and imaging through turbulence.

Design of an adaptive secondary mirror: a global approach

We present the mechanical and actuator design of an adaptive secondary mirror that matches the optical requirements of the active and adaptive corrections. Conceived for the particular implementation for the 6.5-m conversion of the multiple-mirror telescope, with small variations of the input parameters this study is suitable for applications for telescopes of the same class. We found that a three-layer structure, i.e., a thin deformable shell, a thick reference plate, and a third plate that acts as actuator support and heat sink, is able to provide the required mechanical stability and actuator density. We also found that a simple electromagnetic actuator can be used. This actuator, when optimized, will dissipate a typical power of a few tenths of watts.

Performance analysis of and compensation for aspect-ratio effects of fast-fourier-transform-based simulations of large atmospheric wave fronts

Fast-Fourier-transform-based simulators of atmospheric wave fronts with a von Kármán turbulence spectrum were tested with reference to the phase-structure function and phase variance over a pupil on large square and rectangular formats. The symmetry and the accuracy of the phase-structure function were found to be limited by the aspect ratio and the size of the phase screen. The phase variance over a pupil is less sensitive to the aspect ratio than the phase-structure function and is dependent mainly on the size of the phase screen. Several tests are reported and discussed together with a method of compensation for the negative effects of rectangular formats.

Simulations of turbulence-induced phase and log-amplitude distortions

A new method, to our knowledge, allowing one to simulate correlated random processes is suggested. Structure (or correlation) functions of the processes under simulation are assumed to be given. The method is based on the generation of random wave vectors that allows one to simulate processes for a wide class of structure functions. The validity of the method proposed is illustrated by simulations of the turbulence-induced log-amplitude and phase distortions.