We propose new techniques for the reconstruction of complex fields through the development of new iterative algorithms based on propagation equations and the representation of complex objects on orthogonal bases. These techniques use the advantages of the latest phase retrieval techniques and single pixel (SP) detection to retrieve the complex field. These techniques as a whole form a suitable tool for the characterization of dynamically perturbed scalar beams with singular phase profiles.
This research is based in the analysis of the decomposition of Laguerre-Gaussian modes into Hermite-Gaussian modes when propagating through turbulence. This effect can be clearly observed by cancelling the original Laguerre-Gaussian beam with another of different topological charge. The results of the propagations of these beams through Kolmogorov phase masks were analyzed, identifying which turbulences achieved the decomposition. The turbulences were then decomposed into the first 15 Zernike polynomials and used as new "Zernike turbulences". We discovered that the turbulence internal process that allows the decomposition has a high correlation with a phase distortion based on a single Zernike polynomial or a combination of them.
Free-space optical communications are highly sensitive to distortions induced by atmospheric turbulence. This is particularly relevant when using orbital angular momentum (OAM) to send information. As current machine learning techniques for computer vision allow for accurate classification of general images, we have studied the use of a convolutional neural network for recognition of intensity patterns of OAM states after propagation experiments in a laboratory. The effect of changes in magnification and level of turbulence were explored. An error as low as 2.39% was obtained for a low level of turbulence when the training and testing data came from the same optical setup. Finally, in this article we suggest data augmentation procedures to face the problem of training before the final calibration of a communication system, with no access to data for the actual magnification and level of turbulence of real application conditions.
An Adaptive Optics (AO) system may offer an alternative to compensate and correct for beam degradation by reducing turbulence distortions that affect signal detection over horizontal propagation. Based on an experimental testbed placed in the laboratory, we simultaneously study the effects of the communication signal detection, beam wavefront and image quality using a continuous membrane-type deformable mirror and Shack- Hartmann wavefront sensor. By inducing distorting effects on the beam with a Spatial Light Modulator and turbulence masks that are Rytov variance-equivalent to that of actual atmospheric scenarios, and by employing a Zernike polynomials decomposition, beam correction was achieved and signal detection improved. Our results show that both beam-spreading and beam-wandering were reduced after correction, but more significantly, the beam's intensity percentage over detector surface increased in 164%. Future improvements are discussed as an experimental campaign is being prepared to evaluate a closed-loop AO setup for an FSO communication link over a 400-m range at the university campus to evaluate the effectiveness of such approach at different hours of the day and weather conditions.
Wavefront reconstruction of Laguerre-Gaussian (LG) beams presents a great challenge due to the singularities in their phase profiles. Interferometric methods are difficult to implement since they require a reference beam and they are very sensitive to mechanical perturbations. Deterministic methods such as those based on the phase-transport or intensity-transport equation are limited to the paraxial approximation. Furthermore, if such beams propagate in atmospheric turbulence, complex dynamic characteristics are added to the problem. We seek to find an implementation of a technique that is capable of dynamically recovering the singular phases of LG beams under such random conditions. In this work, we will demonstrate a phase-retrieval technique that allows the recovery of LG wavefronts in turbulence and will characterize its effectiveness under a range of atmospheric parameters and propagation length. This technique is based on binary amplitude modulation and is suitable for dynamic applications.
The Shack-Hartmann wavefront sensor has proven to be a valuable detector particularly in the context of turbulence and adaptive optics. In this work we take advantage of its capacity of characterizing orbital-angular-momentum (OAM) states under certain conditions, in the context of a free-space optical communication link. First, we propose a method to compute the locations of the light spots created by the lenslet array that is more robust than the simple centroid formula when atmospheric turbulence is present. Second, we propose a “local OAM” estimation that avoids the computation of a circulation integral in the discrete Shack-Hartmann array. Our proposal does not require prior knowledge of beam diameter or OAM state. We show simulations and laboratory experiments for OAM beams in turbulence conditions at which reliable detection is feasible. We analyze the quality of detection as a function of turbulence strength, Shack-Hartmann resolution and number of acquisitions. These ideas can be applied to coherent coaxial superpositions of two or more OAM states if the light rings are non-overlapping. Using the concept of “optical ferris-wheels” introduced by Franke-Arnold et al. (2007), the detection can be implemented for a limited set of pairs of vortices. We propose a generalization of the recipe for generation of ferris-wheels now for pairs of orthogonal vortices with arbitrary OAM states. The proposal is supported by simulations in turbulence conditions. An extension of our work considers the use of error-correcting codes that take advantage of the large set of available combinations of OAM states.
Atmospheric turbulence is usually simulated at the laboratory by generating convective free flows with hot
surfaces, or heaters. It is tacitly assumed that propagation experiments in this environment are comparable to
those usually found outdoors. Nevertheless, it is unclear under which conditions the analogy between convective
and isotropic turbulence is valid; that is, obeying Kolmogorov isotropic models. For instance, near-ground-level
turbulence often is driven by shear ratchets deviating from established inertial models. In this case, a value for
the structure constant can be obtained but it would be unable to distinguish between both classes of turbulence.
We have performed a conceptually simple experiment of laser beam propagation through two types of artificial
turbulence: isotropic turbulence generated by a turbulator [Proc. SPIE 8535, 853508 (2012)], and convective
turbulence by controlling the temperature of electric heaters. In both cases, a thin laser beam propagates across
the turbulent path, and its wandering is registered by a position sensor detector. The strength of the optical
turbulence, in terms of the structure constant, is obtained from the wandering variance. It is expressed as a
function of the temperature difference between cold and hot sources in each setup. We compare the time series
behaviour for each turbulence with increasing turbulence strength by estimating the Hurst exponent, H, through
detrended fluctuation analysis (DFA). Refractive index fluctuations are inherently fractal; this characteristic is
reflected in their spectra power-law dependence—in the inertial range. This fractal behaviour is inherited by time
series of optical quantities, such as the wandering, by the occurrence of long-range correlations. By analyzing
the wandering time series with this technique, we are able to correlate the turbulence strength to the value of
the Hurt exponent. Ultimately, we characterize both types of turbulence.
We have previously introduced the Differential Laser Tracking Motion Meter (DLTMM) [Proc. SPIE 7476, 74760D (2009)] as a robust device to determine many optical parameters related to atmospheric turbulence. It consisted of two thin laser beams—whose separations can be modified—that propagate through convective air, then each random wandering was registered with position detectors, sampled at 800 Hz. The hypothesis that the analysis of differential coordinates is less affected by noise induced by mechanical vibration was tested. Although we detected a trend to the Kolmogorov’s power exponent with the turbulence increasing strength, we were unable to relate it to the Rytov variance. Also, analyzing the behaviour of the multi-fractal degree estimator (calculated by means of multi-fractal detrended fluctuation analysis, MFDFA) at different laser-beam separations for these differential series resulted in the appreciation of characteristic spatial scales; nevertheless, errors induced by the technique forbid an accurate comparison with scales estimated under more standard methods. In the present work we introduce both an improved experimental setup and refined analyses techniques that eliminate many of the uncertainties found in our previous study. A new version of the DLTMM employs cross-polarized laser beams that allows us to inspect more carefully distances in the range of the inner-scale, thus even superimposed beams can be discriminated. Moreover, in this experimental setup the convective turbulence produced by electrical heaters previously used was superseded by a chamber that replicates isotropic atmospheric turbulence—anisotropic turbulence is also reproducible. Therefore, we are able to replicate the same state of the turbulent flow, specified by Rytov variance, for every separation between beams through the course of the experience. In this way, we are able to study the change in our MFDFA quantifiers with different strengths of the turbulence, and their relation with better known optical quantities. The movements of the two laser beams are recorded at 6 kHz; this apparent oversampling is crucial for detecting the turbulence’s characteristics scales under improved MFDFA techniques. The estimated characteristic scales and multi-fractal nature detected by this experiment provides insight into the non-Gaussian nature of propagated light.
The Differential Image Motion Monitor (DIMM) is a standard and widely used instrument for astronomical
seeing measurements. The seeing values are estimated from the variance of the differential image motion over
two equal small pupils some distance apart. The twin pupils are usually cut in a mask on the entrance pupil
of the telescope. As a differential method, it has the advantage of being immune to tracking errors, eliminating
erratic motion of the telescope. The Differential Laser Tracking Motion (DLTM) is introduced here inspired
by the same idea. Two identical laser beams are propagated through a path of air in turbulent motion, at the
end of it their wander is registered by two position sensitive detectors-at a count of 800 samples per second.
Time series generated from the difference of the pair of centroid laser beam coordinates is then analyzed using
the multifractal detrended fluctuation analysis. Measurements were performed at the laboratory with synthetic
turbulence: changing the relative separation of the beams for different turbulent regimes. The dependence, with
respect to these parameters, and the robustness of our estimators is compared with the non-differential method.
This method is an improvement with respect to previous approaches that study the beam wandering.
KEYWORDS: Turbulence, Collimation, Motion models, Lanthanum, Sensors, Stochastic processes, Fractal analysis, Data modeling, System on a chip, Americium
We analyze the angle-of-arrival variance of an expanded and collimated laser beam after it has traveled through indoor
convective turbulence. A continuous position detector is set at the focus of a lens collecting the light coming from this
collimated laser beam. The effect of the different turbulent scales, above the inner scale, is studied changing the
diameter of a circular pupil before the lens. The experimental setup follows the design introduced by Masciadri and
Vernin (Appl. Opt., Vol. 36, N° 6, pp. 1320-1327, February 2004). Tilt data measurements are studied within the
fractional Brownian motion model for the turbulent wave-front phase. In a previous paper the turbulent wave-front
phase was modeled by using this stochastic process (J. Opt. Soc. Am. A, Vol. 21, N° 10, pp. 1962-1969, October 2004).
The Hurst exponents associated to the different degree of turbulence are obtained from the new D2H-2 dependence.
We experimentally study the variance of the transverse displacement (wandering) of a laser beam after it has traveled
through indoor artificially convective turbulence. In a previous paper (Opt. Comm., Vol. 242, N° 1-3, pp. 76-63,
November 2004) we have modeled the atmospheric turbulent refractive index as a fractional Brownian motion. As a
consequence, a different behavior is expected for the wandering variance. It behaves as
L2+2H , where L is the
propagation length and
H the Hurst exponent associated to the fractional Brownian motion. The traditional cubic
dependence is recovered when
H=1/2--the ordinary Brownian motion. That is the case of strong turbulence or long
propagation path length. Otherwise, for weak turbulence and short propagation path length some deviations from the
usual expression should be found. In this presentation we experimentally confirm the previous assertion.
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