Gustavo Funes

Beam wandering statistics of twin thin laser beam propagation under generalized atmospheric conditions

Under the Geometrics Optics approximation is possible to estimate the covariance between the displacements of two thin beams after they have propagated through a turbulent medium. Previous works have concentrated in long propagation distances to provide models for the wandering statistics. These models are useful when the separation between beams is smaller than the propagation path-regardless of the characteristics scales of the turbulence. In this work we give a complete model for these covariances, behavior introducing absolute limits to the validity of former approximations. Moreover, these generalizations are established for non-Kolmogorov atmospheric models.

Characterizing inertial and convective optical turbulence by detrended fluctuation analysis.

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.

Turbulence characterization by studying laser beam wandering in a differential tracking motion setup

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.

Retrieving atmospheric turbulence features from differential laser tracking motion data

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.

A Quasi-Wavelet Model For The Turbulent Refractive Index

We apply the novel quasi-wavelet model to the turbulent refractive index, then the first-order phase fluctuations are calculated. We explore its potential by estimating the angle-of-arrival variance. We found a good correspondence with previous models.

Behavior of the laser beam wandering with the turbulent path length

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.

Angle-of-arrival variance behavior and scale filtering in indoor turbulence

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.