The most recent developments on the propagation of optical beams in a turbulent medium, such as the clear atmosphere, are reviewed. Among the phenomena considered are beam spreading, beam wander, loss of coherence, scintillations, angle-of-arrival variations, and short-pulse effects.

Electromagnetic beam propagation in turbulent media

1 .1 The Function of Astronomical Telescopes Astronomical telescopes are devices which collect as much radiation from astronomical (stellar) objects and put it in as sharp (small) an image as possible. Both collecting area and angular resolution play a role. The relative merit of these two functions has changed over the years in optical astronomy, with the angular resolution initially dominating and then, as the atmospheric seeing limit was reached, the collecting area becoming the most important factor. Therefore it is the habit these days to express the quality of a telescope by its (collecting) diameter rather than by its angular resolution. With the introduction of techniques that overcome the limits set by atmospheric seeing, the emphasis is changing back to angular res­ olution. This time, however, the constraint is set by the diffraction limit of the telescope so that both angular resolution and collecting power of a telescope will be determined by its diameter. Both telescope functions will therefore go hand-in-hand. Although speckle image reconstruction techniques have been successful in giving diffraction-limited images, the most powerful and promising technique for all astronomical applications is the one using adaptive optics. For an unresolved image, this technique puts most of the collected photons in as small an image as possible, thereby allowing better discrimination against the sky background, improving high spectral and spatial resolution spectroscopy, and enhancing inter-

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ADAPTIVE OPTICS FOR ASTRONOMY: Principles, Performance, and Applications

A partially coherent quasi-monochromatic Gaussian laser beam propagating in atmospheric turbulence is examined by using a derived analytic expression for the cross-spectral density function. Expressions for average intensity, beam size, phase front radius of curvature, and wave-front coherence length are obtained from the cross-spectral density function. These results provide a model for a free-space laser transmitter with a phase diffuser used to reduce pointing errors.

Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication.

This paper presents a new approach to scattering center extraction based on a scattering model derived from the geometrical theory of diffraction (GTD). For stepped frequency measurements at high frequencies, the model is better matched to the physical scattering process than the damped exponential model and conventional Fourier analysis. In addition to determining downrange distance, energy, and polarization, the GTD-based model extracts frequency dependent scattering information, allowing partial identification of scattering center geometry. We derive expressions for the Cramer-Rao bound of this model; using these expressions, we analyze the behavior of the new model as a function of scatterer separation, bandwidth, number of data points, and noise level. Additionally, a maximum likelihood algorithm is developed for estimation of the model parameters. We present estimation results using data measured on a compact range to validate the proposed modeling procedure. >

A GTD-based parametric model for radar scattering

The extended Huygens-Fresnel principle is used to formulate general expressions of the mutual intensity function for a finite optical source with partial spatial coherence propagating in the weakly turbulent atmosphere. Formulations are developed for both the focused and collimated Gaussian beam. Generalized criterion for the effective far-field range is defined in terms of the source aperture, optical wave number, source coherence, and characteristic length associated with the atmospheric turbulence. Beam spread and lateral coherence length in the near and far field are investigated for a combination of parameter variations and the physical implications discussed. Finally, analytic results are calculated and plotted to illustrate the functional behavior of relevant physical parameters.

Optical beam propagation for a partially coherent source in the turbulent atmosphere

Using a Gaussian weighting function for the receiver aperture, we obtain a closed-form representation for the receiver-aperture averaging effect for the intensity fluctuation of a beam wave in the turbulent atmosphere. It is shown that, unlike for the plane-wave case, the power scintillations do not always decrease when the receiver aperture is increased. The reasons are that (1) the intensity fluctuations on the axis for a coherent beam-wave source are smaller than these off the axis and (2) the averaging effect cannot show up when the total beam is within a coherent patch (i.e., the coherence length is larger than the beamwidth).

Receiver-aperture averaging effects for the intensity fluctuation of a beam wave in the turbulent atmosphere

The scintillation index for weak atmospheric turbulence is formulated for a partially coherent source (in space and time). We obtain results for two cases when the detector has a slow and a fast response time. Our solutions correctly reduce to the known scintillation index in the limit of coherent and incoherent sources. Transmitter aperture averaging and frequency averaging effects are shown as special cases of our results. The limitations of the source model used and the solution obtained for a fast detector are discussed.

The scintillations for weak atmospheric turbulence using a partially coherent source

Geometrical and physical optics techniques, supplemented by their respective extensions, i.e., geometrical and physical diffraction, are applied to the problem of finite cylindrically curved plates. Numerical calculations of the radar backscattering cross sections were made, and a graphical comparison of these methods with experimental results is made. Keller's and Ufimtsev's theories axe discussed and compared as they apply to this problem.

Radar cross section of curved plates using geometrical and physical diffraction techniques

All the existing Rytov method solutions in atmospheric turbulence deal with coherent sources. In this paper we introduce the spatial partial coherence of a beam wave source to Rytov’s method and evaluate the intensity covariance and the scintillation index due to a spatially partially coherent beam wave source. The advantage of this solution is that in the calculation of the scintillations, the need for the use of the quadratic approximation for the medium structure functions is eliminated. The disadvantage is that, since it is a weak-fluctuation solution, we cannot extend the results to the incoherent source limit when (weak) turbulence is present.

Martin A Plonus

Papers

Optical beam propagation for a partially coherent source in the turbulent atmosphere

Receiver-aperture averaging effects for the intensity fluctuation of a beam wave in the turbulent atmosphere

The scintillations for weak atmospheric turbulence using a partially coherent source

Radar cross section of curved plates using geometrical and physical diffraction techniques

Intensity fluctuations due to a spatially partially coherent source in atmospheric turbulence as predicted by Rytov’s method