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Optics & Infrared Sensing

Atmospheric Turbulence Modeling

Understanding the effects of atmospheric turbulence on laser propagation through the atmosphere is critical for light detection and ranging (LIDAR) systems as well as free space optical communication applications. Temperature fluctuations in the atmosphere generate index of refraction fluctuations that can cause a laser beam to steer off of a target and to break up. As a result, when a constant intensity laser beam is directed to a target, atmospheric turbulence generates intensity fluctuations or scintillation. This is illustrated by the following figure.

Figure 1 Return laser intensity from a constant power laser beam directed through a turbulent atmosphere. The inset figure shows a one second interval and illustrates the time scales of intensity fluctuations.

The severity of the scintillation depends on the wavelength of light, the pathlength, L, through the atmosphere and C_n², the index of refraction structure constant that quantifies the severity of the atmospheric turbulence. These three quantities can be combined together into the Rytov parameter. C_n² is greatest during the midday and has minimums associated with sunrise and sunset. The figure below shows how C_n² can vary throughout the day and at different geographical locations.

Figure 2 Severity of atmospheric turbulence over a 24 hour period from three different locations: Hanford Townsite, Nevada Test Site and Sequim Marine Site. The impact of atmospheric turbulence varies according to the time of day and geographic locations. Minimums are associated with the atmospheric stability transition near sunrise and sunset. The terrain and vegetation makes typical mid-day turbulence at Hanford roughly 10 times worse than the dry lakebeds of the Nevada Test Site and 100 times worse than the marine environment of Sequim Bay.

The effects of atmospheric turbulence can be quantified by determining the scintillation index, which is related to the mean and standard deviation of the intensity distribution. The figure below shows how the scintillation index varies as a function of the Rytov parameter.

Figure 3 Scintillation index collected over three different paths during the course of three days at the Hanford Townsite. The scintillation index increases as a function of both distance and Cn2 until reaching a shoulder and rolling off. The two different branches are due to the optical receiver that was used to make the measurements.

To better understand the effects of atmospheric turbulence PNNL has developed a numerical simulation based on Fourier optics techniques and random phase screens that agrees well with experimental measurements. Once the modeling has been validated, a virtual system can be built within the simulation and used to inform the design of LIDAR systems; for example, determining the optimum receiver area, laser divergence and detector size for a particular pathlength and atmospheric turbulence conditions.

The figure below shows simulated returns of the FM DIAL system for different input conditions related to the Rytov parameter. For small Rytov parameters, atmospheric turbulence doesn't have a large effect and the return signal still maintains some of its "beam" qualities. As the Rytov parameter increases, the effects of turbulence increase and the return signal is more and more broken up until the return is essentially a random distribution. At this point the scintillation index rolls off and approaches one.

Figure 4 Simulations for different values of the Rytov parameter. The four graphics illustrate how the return laser beam breaks up and varies with time. At short distances or under weak turbulence conditions, the Gaussian structure of the beam is still apparent. As turbulence and/or path length increase, the beam breaks up until it is entirely broken up. Once this occurs, further increases in pathlength or turbulence have no effect, causing the scintillation index to approach a constant value of 1.