In 1975, we reviewed the recent developments on wave propagation in turbulent media. In this paper, we update that paper to include recent results on adaptive optics, intensity scintillations, pulse propagation, atmospheric measurements at visible, IR, and millimeter wave frequencies, speckle interferometry, and other related topics.

Electromagnetic beam propagation in turbulent media: An update

In this Letter, we use laser beam intensity fluctuation measurements to model and describe the statistical properties of weak temperature-induced turbulence in underwater wireless optical communication (UWOC) channels. UWOC channels with temperature gradients are modeled by the generalized gamma distribution (GGD) with an excellent goodness of fit to the measured data under all channel conditions. Meanwhile, thermally uniform channels are perfectly described by the simple gamma distribution which is a special case of GGD. To the best of our knowledge, this is the first model that comprehensively describes both thermally uniform and gradient-based UWOC channels.

Simple statistical channel model for weak temperature-induced turbulence in underwater wireless optical communication systems.

Over the past decade adaptive optics (AO) has proved its worth as AO systems have been used successfully on several telescopes to improve image resolution. As scientists and engineers push the technological state of the art in an effort to make bigger, faster, and better systems, it has become more and more important to test and verify the operation of these systems in a controlled laboratory setting. To perform full-system tests in the presence of atmospheric turbulence, some sort of turbulence generator is needed. We describe a simple, low-cost approach to making static phase plates that generate atmosphericlike wave-front aberrations. These plates have several advantages over traditional heated-air turbulence generators and, as such, are better suited for well-controlled, detailed testing of an AO system.

Low-cost, broadband static phase plate for generating atmosphericlike turbulence.

The results of an experiment designed to test the feasibility of optical testing using subaperture test flats are presented in this paper. This testing technique involves the replacement of the monolithic optical flat used in conventional double-pass optical system testing by an array of small flats, or subapertures. Subaperture testing was conceived previously by other authors as a low-cost means of testing future telescope systems with large apertures (ca. 10 meters). Previous work by these authors involved the development of analytical techniques for combining subaperture testing data such that the wavefront over the full aperture may be obtained; the present work provides experimental verification of these analytical techniques. A brief description of the algorithms used to analyze the data is given along with a description of the experimental procedure. An array of seven subapertures was used. The subapertures contained random tilts and phase shifts relative to each other; thus the possibility of performing subaperture testing with such an unphased array was specifically tested. Control data were obtained with a monolithic flat. Experimental results are presented. Agreement among the subaperture data and the control data is good; thus it is found that subaperture testing is feasible. Knowledge of subaperture phases and tilts results in significantly increased accuracy. However, a lack of such knowledge may be compensated by increasing the amount of data collected. It is found that the dia-meters of the subapertures affect the accuracy more strongly than the knowledge of subaperture tilts. Data obtained with atmospheric turbulence deliberately introduced show that, in the presence of turbulence, subaperture testing is significantly less accurate than conventional testing.

Subaperture Optical Testing: Experimental Verification

Consideration is given to an atmospheric turbulence chamber designed for optical wave propagation experiments. The chamber consists of ten small electric heater/blowers with an aluminum foil screen and three screens of 2-mm aluminum wire meshes. Calculations are made of the temperature structure constant squared on the basis of temperature structure function measurements derived from a differential microthermocouple system. Values are presented for the refractive-index structure constant squared. The average wind velocity and temperature are found to be, respectively, 0.41 m/sec and 53 C. The inner and outer scales of turbulence are 5.0 mm and 6.5 cm. It is shown that the measured temperature structure function and the power spectrum of temperature fluctuations satisfy, respectively, the 2/3 and -5/3 power similarity laws in the inertial subrange. Possible chamber improvements are discussed.

Atmospheric turbulence chamber for optical transmission experiment: characterization by thermal method.

Accurate simulation, on a laboratory scale, of atmospherically induced scintillation phenomena is achieved by creating an unstable vertical temperature gradient in a 1.5-m long, 40-cm wide, and 60-cm deep water tank. The turbulent index of refraction has a statistical structure similar to that of the atmosphere, in particular, Kolmogorov’s inertial subrange model is verified. The measured saturation and supersaturation of the irradiance variance agree very well with theory and atmospheric data. The simulation results are properly scaled by the first-order expression for the log-amplitude variance, and the saturation distance is typically reduced by a factor of 300–400.

Bissonnette Lr

Papers

Atmospheric scintillation of optical and infrared waves: a laboratory simulation