Frida Strömqvist Vetelino

Aperture averaging effects on the probability density of irradiance fluctuations in moderate-to-strong turbulence

The lognormal (LN) and gamma-gamma (GG) distributions are compared to simulated and experimental data of the irradiance fluctuations of a Gaussian beam wave propagating through the atmosphere along a horizontal path, near the ground, in the moderate-to-strong turbulence regime. Irradiance data were collected simultaneously at three receiving apertures of different sizes. Atmospheric parameters were inferred from the measurements and scintillation theory and were used to develop the parameters for the theoretical probability density functions. Numerical simulations were produced with the same C(n)(2) value as the experimental data. Aperture-averaging effects were investigated by comparing the irradiance distributions for the three apertures at two different values of the structure parameter C(n)(2), and, hence, different values of the coherence radius rho(0). For the moderate-to-strong fluctuation regime, the GG distribution provides a good fit to the irradiance fluctuations collected by finite-sized apertures that are significantly smaller than rho(0). For apertures larger than or equal to rho(0), the irradiance fluctuations appear to be LN distributed.

Fade statistics and aperture averaging for Gaussian beam waves in moderate-to-strong turbulence

The performance of lasercom systems operating in the atmosphere is reduced by optical turbulence, which causes irradiance fluctuations in the received signal. The result is a randomly fading signal. Fade statistics obtained from experimental data were compared to theoretical predictions based on the lognormal and gamma-gamma distributions. The probability of fade, the expected number of fades per second, and the mean fade time were calculated from the irradiance fluctuations of a Gaussian beam wave propagating through the atmosphere along a horizontal path, near ground, in the moderate-to-strong optical turbulence regime. Irradiance data were collected simultaneously at three receiving apertures, each with a different size. Atmospheric propagation parameters were inferred from the measurements and were used in calculations for the theoretical distributions. It was found that fade predictions made by the gamma-gamma and lognormal distributions provide an upper and lower bound, respectively, for the probability of fade and the number of fades per second for the irradiance data collected in the moderate-to-strong fluctuation regime. What is believed to be a new integral expression for the expected number of fades based on the gamma-gamma distribution was developed. This new expression tracked the gamma-gamma distributed data more closely than the existing approximation and resulted in a higher number of fades.

Characterizing the propagation path in moderate to strong optical turbulence

In February 2005 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation and the University of Central Florida. A Gaussian beam was propagated along a horizontal 1500 m path near the ground. Scintillation was measured simultaneously at three receivers of diameters 1, 5, and 13 mm. Scintillation theory combined with a numerical scheme was used to infer the structure constant C2n, the inner scale l0, and the outer scale L0 from the optical measurements. At the same time, C2n measurements were taken by a commercial scintillometer, set up parallel to the optical path. The C2n values from the inferred scheme and the commercial scintillometer predict the same behavior, but the inferred scheme consistently gives slightly smaller C2n values.

Inferring path average C 2 n values in the marine environment

Current mathematical scintillation theory describing laser propagation through the atmosphere has been developed for terrestrial environments. Scintillation expressions valid in all regimes of optical turbulence for propagation in the maritime environment, based on what we believe to be a newly developed marine atmospheric spectrum, have been developed for spherical waves. Path average values of the structure parameter, C(n)(2), were inferred from optical scintillation measurements of a diverged laser beam propagating in a marine environment, using scintillation expressions based on both terrestrial and marine refractive index spectra. In the moderate-to-strong fluctuation regime, the inferred marine C(n)(2) values were about 20% smaller than inferred terrestrial C(n)(2) values, but a minimal difference was observed in the weak fluctuation regime. Measurements of angle-of-arrival fluctuations were used to infer C(n)(2) values in the moderate-to-strong fluctuation regime, resulting in values of the structure parameter that were at least an order of magnitude larger than the two scintillation-inferred C(n)(2) values.

Scintillation : theory vs. experiment

In May 2004 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation, the Office of Naval Research and the University of Central Florida. A 45 mm divergent Gaussian beam was propagated along a horizontal 1500 meter path approximately 2 meters above the ground. At the receiver were 3 apertures of diameter 1mm, 5mm, and 13mm. The scintillation was measured at each aperture and compared to scintillation theory, recently developed for all regimes of optical turbulence. Three atmospheric parameters, Cn2, lo and Lo, were inferred from these optical measurements. Simultaneously, a commercial scintillometer, which recorded values for Cn2, was set up parallel to the optical path. In this paper, a numerical scheme is used to infer the three atmospheric parameters and comparisons are made with the Cn2 readings from the scintillometer.

Model validation of turbulence effects on orbital angular momentum of single photons for optical communication

The orbital angular momentum of photons in paraxial beams offers the possibility of arbitrary base-N digits for freespace laser communications. Atmospheric turbulence can cause the orbital angular momentum of photons in a propagating beam to scatter from its original azimuthal mode. The probability of obtaining correct or incorrect measurement of the transmitted orbital angular momentum state after propagation through atmospheric turbulence is calculated from the rotational field correlation (second order field moment). A previously published model of the rotational field correlation for Laguerre-Gaussian beams is limited to the weak turbulence regime and assumes that the turbulence effects can be considered a pure phase perturbation. This model is validated by calculating the same quantity with the extended Huygens-Fresnel integral, valid in all regimes of turbulence. To obtain closed form expressions, a quadratic structure function approximation was applied. The probability of receiving the transmitted orbital angular momentum state was calculated and compared to the existing model. The results indicate that the quadratic structure function approximation leads to a slight overprediction of the probability in the weak turbulence regime. For finite transmitter apertures, the previously published model, with a spherical wave structure function, rather than the plane wave structure function used in the original work, is believed to be the most accurate model in the weak turbulence regime.

A new marine atmospheric spectrum for laser propagation

Current mathematical models describing laser propagation through the atmosphere were developed for terrestrial environments. An atmospheric index of refraction power spectrum specifically tailored to the marine environment has been created and applied to scintillation theory. Optical measurements of a diverge laser beam propagating in a marine environment, in combination with scintillation theory and a numerical scheme, were used to infer the refractive index structure parameter, Cn2, along the propagation paths. The analysis was repeated for both marine and terrestrial theoretical scintillation expressions, each resulting in one set of inferred Cn2-values. In the moderate-to-strong fluctuation regime, the inferred Cn2-values based on marine theory were about 20% smaller than those based on terrestrial theory, but a minimal difference was observed in the weak fluctuation regime.

Orbital angular momentum receiver bandwidth for laser communications systems operating in atmospheric turbulence

The Orbital Angular Momentum (OAM) states of photons in paraxial beams allow, in theory, an unlimited number of bits per photon to be used for information encoding in lasercom systems. Atmospheric turbulence scatters the transmitted OAM mode to neighboring modes. The probability of receiving the transmitted mode number decreases with increasing turbulence strength. The degradation is more severe for larger transmitted mode numbers due to their bigger spot size, limiting the range of an OAM encoded lasercom system. To compensate for the lower probability of receiving higher order modes, the concept of receiver OAM bandwidth is defined as a range of received neighboring OAM states allocated to the transmitted OAM mode. By increasing the receiver OAM bandwidth for higher order transmitted modes, the probability to determine the transmitted mode number is similar for all transmitted mode numbers. The optimal system design for OAM encoding using higher order Laguerre-Gauss beams, with the suggested transmitted mode numbers and their corresponding receiver OAM bandwidth, is presented. A closed form analytical expression of the probability to determine the transmitted mode number of the system design is developed. It can be used to easily determine the maximum propagation distance for an OAM encoded lasercom system with a probability to determine the transmitted OAM mode number close to unity.

Initial Measurements of Atmospheric Parameters in a Marine Environment

April 2005, a laser propagation experiment was conducted over a 470m horizontal maritime path. Scintillation measurements of a divergent Gaussian beam wave were taken simultaneously for different receiver aperture sizes. Terrestrial scintillation theory combined with a numerical algorithm was used to infer the atmospheric parameters Cn2 and lo from the optical maritime scintillation measurements. This paper presents the initial results.

Characterization of the Shuttle Landing Facility as a laser range for testing and evaluation of EO systems

The Shuttle Landing Facility runway at the Kennedy Space Center in Cape Canaveral, Florida is almost 5 km long and 100 m wide. Its homogeneous environment makes it a unique and ideal place for testing and evaluating EO systems. An experiment, with the goal of characterizing atmospheric parameters on the runway, was conducted in June 2005. Weather data was collected and the refractive index structure parameter was measured with a commercial scintillometer. The inner scale of turbulence was inferred from wind speed measurements and surface roughness. Values of the crosswind speed obtained from the scintillometer were compared with wind measurements taken by a weather station.