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 propose the use of multifractal detrended fluctuation analysis (MF-DFA) to measure the influence of atmospheric turbulence on the chaotic dynamics of a HeNe laser. Fit ranges for MF-DFA are obtained with goodness of linear fit (GoLF) criterion. The chaotic behavior is generated by means of a simple interferometric setup with a feedback to the cavity of the gas laser. Such dynamics have been studied in the past and modeled as a function of the feedback level. Different intensities of isotropic turbulence have been generated with a turbulator device, allowing a structure constant for the index of refraction of air adjustable by means of a temperature difference parameter in the unit. Considering the recent interest in message encryption with this kind of setups, the study of atmospheric turbulence effects plays a key role in the field of secure laser communication through the atmosphere. In principle, different intensities of turbulence may be interpreted as different levels of white noise on the original chaotic series. These results can be of utility for performance optimization in chaotic free-space laser communication systems.
We have previously introduced the Differential Laser Tracking Motion Meter (DLTMM) [Proc. SPIE<strong> 7476</strong>, 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.
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
L<sup>2+2H </sup>, 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.
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 D<sup>2H-2</sup> dependence.