Velocity and temperature fluctuations have been studied in the framework of wave propagation theory. The asymptote of the velocity spectrum for isotropic turbulence is derived in the analytical form and found to agree well with the experimental data. A similar result for the temperature spectrum aggrees qualitatively with experimental data.

Theoretical research on acoustic wave generation by the absorption of laser radiation is reviewed. Relations between acoustic fields generated by laser beams in the air and intensity and energy distributions in cross-sections of laser beams are described for the case of finite thermalization time. It is concluded that acoustic methods might be used for the energy and power restoration of spatial distributions in the laser beams, restoration of laser radiation absorption parameters, and testing of absorption kinetic models.

In this report we present a model for turbulent mixing that can be incorporated into the wave optics codes describing turbulence and thermal blooming. The model for the turbulent velocity is three-dimensional. Because the resulting integrals are computationally intensive we have simultaneously developed a unified analytical approach for determining the three-dimensional random velocity field. The approach is based upon an orthogonal expansion of the velocity fields. The coefficients of the expansion are statistically independent Gaussian random variables. One of the important advantages of the analytical approach is the reduced computer memory and disk I/O requirements when the correlation length is much greater than the beam diameter. Only a few terms in the series are required to treat this important limiting case.

Propagation calculations were performed to illustrate the effects of cirrus on high energy laser propagation far field calculations using the 4D wave optics code with adaptive optics (Schafer, 1990). Results show that, for linear effects, subvisible and thin cirrus clouds have small effect on GPL propagation at 1.06 and 3.8 micron. For nonlinear effects for the power/diameter choices, cirrus clouds contribute significant thermal blooming at 3.8 micron for a cirrus thickness above the thin level.

Rotating or variable cross wind directions that normally occur in the atmosphere along the propagation path of a high power laser beam are important since they can result in significant reductions in both the amount of whole beam thermal blooming phase distortion as well as the growth of the small-scale blooming instabilities which often limit the effectiveness of atmospheric compensation. In this paper we describe a time-dependent, atmospheric propagation and compensation simulation code, APAC, which includes the effects of variable wind directions on blooming compensation. Simulation results are presented for a particular measured vertical wind profile which show that small-scale blooming instability effects are significantly reduced when the effects of the actual wind direction variations are included. A simple model has also been developed to calculate the number of waves of blooming phase delta(phi), to use as an appropriate scaling parameter for blooming with rotating winds, rather than the standard distortion parameter N(D) defined for the constant wind direction case.

The objective of this investigation has been the determination of the sensitivity of instability growth in high energy laser propagation as seen in computer simulation to the variation of certain computational and physical parameters. The laser field has been sampled at high density in both the axial and transverse directions. Particular emphasis has been placed on the computational simulation of the instability damping effect of wind fluctuation. Because of the extreme computational demands of the full four dimensional propagation problem at high sampling density the simplifying assumption of neglect of a single transverse dimension has been made. This assumption restricts the range of phenomena which can be explored and somewhat modifies the interpretation of results, however, it reduces computational costs to the point where a hitherto unexplored region of parameter space becomes accessible. It is believed that these computational experiments are useful in validation of full four dimensional code results and determination of those physical effects which are likely to warrant further study.

Time dependent propagation code simulations are described for phase compensation of atmospheric turbulence and thermal blooming. Test results, using convected phase screens to represent the optical turbulence, are compared with steady-state simulation results and, also, for fixed and variable direction wind conditions. Realistic wind effects on propagation are investigated by performing 4D code simulations to compare the effects of actual wind observations with monthly mean wind profile models for the White Sands Missile Range (WSMR). Critical power levels are compared for the mean and observed wind conditions at WSMR within the same month. Estimates of the critical power are also compared with the simulation results using the wind shear damping model for blooming instabilities, developed by Morris, et al. (1990).

The problem of minimizing thermal distortions of laser beams in the atmosphere is considered using optical adaptive systems to eliminate the effects of jitter, twinkling, and spread of optical beams and images. Topics discussed include thermal self-action in a turbulent medium, phase correction of thermal distortions along vertical paths, and adaptive distortion compensation of focused laser beams using the phase conjugation method for reference waves.

A novel scheme for remote alignment of adaptive optical systems is presented. In comparison to conventional methods where near-field measurements (in the form of near-field phase across the adaptive component or gaps between neighboring segments) are used for feedback control, Far-Field Optimization utilizes only the far-field intensity. A figure of merit based solely on the point spread function is used to iteratively configure the adaptive elements to optical alignment. In this review paper, we first describe the far-field optimization method and then discuss its application to three different adaptive optical systems - a deformable mirror, a segmented mirror and a multiple mirror telescope. The convergence, efficiency and robustness of the iterative far-field optimization are illustrated with computer simulations. Experimental validation of the novel technique for adaptive optics alignment is demonstrated with results from a laboratory test with a segmented mirror. Potential utility of far-field optimization for dynamic wavefront control (e.g. atmospheric turbulence compensation) is briefly discussed.

The ground to space laser encounters the entire atmosphere and the laser power transmittable with good beam quality is ultimately limited by this propagation. For CW lasers, the ultimate limit is thermal blooming and this problem is addressed. The concept of a critical laser power is used which is the optimum laser power which leads to the highest far-field intensity. A perfect beacon is assumed and a perfect wave front sensor is also assumed to determine the maximum intensity achievable with adaptive optics phase conjugation of the thermal blooming. An analytic model is derived and its predicted results are compared with a wave optics computer code results. The agreement is quite good and shows the parametric dependence of the critical power on laser beam size, wavelength and atmospheric absorption and path length.

A prediction is made that, for small values of turbulence (L sub 0) in the range of 20-40 cm, ground-based laser beams at near infrared can be focused to diffraction limited accuracy on targets in space without using adaptive optics or other wavefront correction procedures. It is found that, at infrared wavelengths, resolution is more likely to be limited by the telescope size and aberrations than by atmospheric turbulence. By building large enough telescopes to diffraction limited standards rather than currently accepted standards which fall well short of this limit, there is almost no limit to achievable resolution.

A new technique for remote alignment of an adaptive optics system with far-field optimization is proposed. The Simplex function optimization algorithm is considered to be the most robust and efficient of several hill-climbing algorithms tried in aligning an experimental brassboard with multiple adaptive optics elements. The algorithm achieves the function minimum or near minimum. The robustness of the algorithm is verified by experimental results and corresponding simulations.

The phenomena of phase compensation instability (PCI) and mini-shear, i.e., the nonuniformity of the turbulent wind velocity along the propagation path, are discussed. A model is developed that describes the sections of the atmosphere in a way that allowed for the mini-shear induced fading-away of old heating patterns, previously deposited in a section. It is found that, for rather high laser power-density and high spatial frequency perturbations, there was a very pronounced and quite early onset of exponential growth of the Green's function solution, i.e., an early and clear manifestation of PCI. For lower spatial frequency perturbations and/or lower laser power densities, the long term behavior was virtually constant, i.e., there was no PCI. It is concluded that PCI could occur only if the laser-power density were high enough and if the adaptive optics could correct for high enough spatial frequencies.

This analysis provides modeling results for beam propagation of a low power HF chemical laser operating on the first overtone through summer conditions at a coastal site. The first set of cases consists of three low rotational quantum number (J) lines. The second set of cases consists of the single J = 6 line. While there is significant Strehl intensity degradation in only one case, many of the propagations exhibit the same small-scale structure expected in higher power systems.

We present the path integral representation of the Green's function for the linearized equations of isobaric thermal blooming for uniform wind and atmosphere. We first describe the path integrals for the Fresnel and Helmholtz propagators as an introduction to the path integral, and then use these results to define a perturbative expansion of the thermal blooming path integral. Each term in the perturbation series may be computed in closed form. Finally, a Feynman diagrammatic representation of the series is given.

We give an overview of functional reconstruction theory for predicting whole beam Strehl ratios as applied to thermal blooming. We begin by writing down the reconstruction formula that relates a finite sized beam Strehl ratio to a sum involving the Strehl ratio of an infinite beam or periodic patch. We then define what a dynamically equivalent patch is and follow by describing the functional approach to scaling patch Strehl curves using a metric on the space of absorption profiles. We end by comparing results from our systems model based on functional reconstruction, SWATM2, which takes only seconds on any machine, with results from large nonlinear 4D wave optics simulations.

Linear perturbation theory predicts unlimited exponential growth of small scale structure in high energy laser propagation in a nonshearing absorbing fluid. A nonlinear treatment of the paraxial wave equation shows, however, that sidebands of the perturbation spatial frequency are generated which do not grow without limit, but release their energy back to the fundamental perturbed mode to produce a so-called 'recurrence' of the initial state. Based on previous work with the nonlinear Schrodinger equation, this paper reviews both the linear and the nonlinear perturbative analysis which suggests there exists in this phenomenon a possible mechanism to limit small scale instability even without the presence of absorber velocity shear.

Measurements of the atmospheric tilt power spectral density performed in November 1989 using the 30 inch tower telescope of the National Solar Observatory at Sunspot, New Mexico are reported. The measurements were based on a solar pore on the sun as a near-point source and tracking the apparent angular tilt of that source with a fast tilt mirror and closed loop controler. Reliable spectral measurements were obtained past 400 Hz for effective telescope apertures of 22 and 76 cm.