We consider general theoretical aspects of level crossings of multidimensional fluctuating functions. Examples of such functions are turbulent fields such as refractive-index functions or turbulence-aberrated fields such as laser intensity functions in free-space laser communications. From a practical point of view, it is important to consider level crossings because they correspond to the temporal instances or spatial occurrences of when or where a signal of interest reaches, exceeds, or falls below a particular threshold. For example, the statistics of level crossings for a laser communication signal at a threshold corresponding to the minimum detection signal are important in order to study the probability density of the extent of intervals of down-time for communication links. For 1-D signals, the concept of the level crossing scale is clear and well established as it is the extent of the interval between successive level crossings. However, for multidimensional fields, this concept cannot be utilized directly because it is not clear how to define or identify successive level crossings, and therefore level crossing scales, in multiple dimensions. We describe a theoretical formulation which enables a consistent definition of level crossing scales for multidimensional fields, i.e. consistent with the traditional 1-D definition. We use the recently-developed concept of the shortest-distance scale because the latter applies naturally to multiple dimensions. We define the probability density function of level crossing scales, in any number of dimensions, in terms of a derivative of the probability density function of shortest-distance scales. Analytically, we illustrate this approach using exact theoretical examples with 2-D objects and we also provide results for exponential, lognormal, and power-law level crossing statistics which are basic models for applications involving turbulence and free-space laser communications.
This work is part of an effort to investigate methodologies for active turbulence control of laser beam
propagation through separated flows relevant to airborne laser applications as well as to detect the turbulenceinduced
laser aberrations with Shack-Hartmann sensing. Large scale turbulence suppression control in
separated compressible flows is investigated as a means to directly reduce aero-optical aberrations in laser
propagation for airborne directed energy capabilities. Experiments are conducted on forced and unforced
large-Reynolds-number compressible separated shear layers. Flow forcing is realized using a custom-built
dielectric barrier discharge pulsed plasma actuator that can operate at elevated pressures. Results from flow
control experiments show significant reductions in the root-mean-square optical path difference depending on
the pulsed plasma actuator forcing frequency. Shack-Hartmann wavefront sensor laser profiling is conducted
to measure directly the aero-optical aberrations. The flow conditions used in this research are Reynolds
number of 6 million, based on the visual thickness of the turbulent separated shear layer, a freestream Mach
number of 0.9, and an elevated test section pressure of 3 atm. The Shack-Hartmann sensor provides pathintegrated
information regarding the turbulent refractive field and interfaces that the laser wavefront
propagated through. Experimental comparison of control on vs. off cases indicates evidence showing the
effectiveness of pulsed plasma forcing for the direct reduction of the laser aberrations. Since the dominant
contributions to the aberrations, in unforced flows, are caused by large-scale organized structures, our
findings indicate that the mechanism by which the significant reduction is observed in the present forced
experiments is due to large-scale organized structure suppression effected by pulsed plasma forcing.
Laboratory experiments, computations, and physical modeling of laser wavefronts propagating through variable-refractive-index separated shear layers at large Reynolds numbers are conducted in order to examine the relation between the flow behavior and the laser wavefront behavior for airborne laser communications. The new
element of this work is the focus on the dependence on scale of the optical behavior as well as of the flow behavior, using multiresolution analysis of the measured and computed data. The experiments are conducted using the UC Irvine variable-pressure
turbulent flow facility. Direct non-intrusive imaging of the refractive index field is accomplished with laser-induced fluorescence and a high-resolution digital camera that resolves
three decades of scales. Simultaneously, direct imaging of the
propagated laser wavefront phase profile is conducted using a
Shack-Hartmann array sensor that also has a resolution of three decades of scales. The computational component consists of near-field wavefront propagation through the measured refractive index field, validated by the direct wavefront measurements. We
have conducted multiresolution analysis of the flow data and optical
data, by a posteriori reducing the resolution of the refractive-index field and phase field. We present evidence of strong scale dependence at large scales, i.e. in the
energy-containing range of scales. Physical modeling of this behavior is developed based on the structure of the coarse-grained refractive turbulent interfaces. This approach is useful in order to relate the root-mean-squared optical path difference and Strehl ratio, at variable resolutions, to the refractive-index variations along the laser wavefront propagation path. This facilitates the
identification of the dominant refractive interfaces and serves as a
guide to developing aero-optical optimization methods for airborne
laser communication applications.
A combined experimental/computational approach is conducted using a specially-designed laboratory facility and a physical framework based on refractive fluid interfaces in order to enable the direct examination of the turbulent refractive-index field along laser beam propagation paths, as well as of the corresponding optical-wavefront distortions of the propagated beam. The experimental facility utilized is the variable-pressure flow facility at UC Irvine which enables direct imaging of the turbulent refractive-index field at large Reynolds numbers in controlled laboratory flows. Laser-induced fluorescence of acetone vapor seeded in air is utilized to directly image the turbulent refractive-index spatial fluctuations along the beam propagation paths. A custom-built high-resolution Shack-Hartmann wavefront sensor is utilized that is useful to measure the optical-wavefront distortions of the propagated optical beam. The flow-imaging measurements, combined with the beam-wavefront data, enable a direct study of the correspondence between the turbulent refractive interfacial-fluid thickness variations and the beam-propagation parameters of interest in free-space laser communications such as the Strehl ratio. Combined with the experiments, computations are also conducted on the flow-imaging data in order to study the structure of the optical beam as it propagates through the measured refractive-index variations. This enables a one-to-one correspondence to be established between the refractive interfacial-fluid thickness variations encountered by the beam and their effect on the distortions of the optical wavefronts, quantified in terms of a cumulative Strehl ratio, along the entire propagation path examined through the flow.
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