Adaptive phase-distortion correction based on parallel gradient-descent optimization.

We describe an adaptive wave-front control technique based on a parallel stochastic perturbation method that can be applied to a general class of adaptive-optical system. The efficiency of this approach is analyzed numerically and experimentally by use of a white-light adaptive-imaging system with an extended source. To create and compensate for static phase distortions, we use 127-element liquid-crystal phase modulators. Results demonstrate that adaptive wave-front correction by a parallel-perturbation technique can significantly improve image quality.

Adaptive imaging system for phase-distorted extended source and multiple-distance objects.

We introduce an incoherent adaptive imaging system based on optimization of an image quality metric measured using a coherent optical system. Experimental results and numerical simulations are presented that demonstrate adaptive correction of phase-distorted extended source images containing objects located at multiple distances.

Spatiotemporal dynamics of self-pumped phase conjugation in a photorefractive crystal: multipattern storage using incremental recording.

We investigate the spatiotemporal dynamics of self-pumped phase conjugation for superimposed incrementally recorded images. Experimental evidence of time delay in the appearance of phase-conjugation patterns was observed during both the recording and the readout phases.

Effective beam parameters and the turbulent beam waist for convergent Gaussian beams.

Expressions are developed for the location and the size of the beam waist for a convergent Gaussian beam in statistically homogeneous and isotropic atmospheric turbulence. Subsidiary expressions are presented that lead to the maximum distance from the transmitter at which the beam waist can be located under given optical turbulence conditions and the optimal initial radius of curvature required for placing the beam waist at a desired location. The free-space beam radius W of a Gaussian beam satisfies the relationship ∂W/∂z = - W/R, where z represents the path length and R is the phase-front radius of curvature at z. By enforcing this relation on the effective beam spot size in turbulence W(e), we can define an effective radius of curvature R(e). In addition to specifying the beam waist, R(e) leads to a pair of effective beam parameters θ(e) and Λ(e) that provide a natural extension to the complex amplitude plane. Within this context, general propagation characteristics may be described, including the coherence properties of a Gaussian beam in both weak and strong optical turbulence.

Scintillation of initially convergent Gaussian beams in the vicinity of the geometric focus.

As an initially convergent Gaussian beam enters the vicinity of the geometric focus, weak fluctuation theory predicts a drop in the longitudinal component of the log-irradiance variance and an increase in the radial component off the beam center. The phenomenon intensifies as the beam nears the geometric focus, also with decreasing magnitude of the focusing parameter. Precisely at the geometric focus, first-order weak fluctuation theory further predicts that as the initial beam size continues to increase, the longitudinal component of the log-irradiance variance decreases toward zero, while the radial component increases without bound. This eventually entails a rapid change in scintillation across the beam surface that has yet to be verified experimentally, to our knowledge. We demonstrate that when diffractionlike effects produced by optical turbulence are introduced, predicted log-irradiance variance exhibits such extremes in behavior only in the case of weak turbulence. Also, at the exact geometric focus, scintillation does not vanish with increasing initial beam size but achieves a value determined by and growing with turbulence strength and nearly independent of initial beam size. The radial component of log-irradiance quickly loses significance as turbulence strength increases. In fact, general extremal behavior of the log-irradiance variance in the vicinity of the geometric focus is drastically curtailed. Differences across the diffractive beam surface become small and exhibit only a modest dependence on the initial beam size.

Geometrical representation of Gaussian beams propagating through complex paraxial optical systems.

Geometric relations are used to study the propagation environment of a Gaussian beam wave propagating through a complex paraxial optical system characterized by an ABCD ray matrix in two naturally linked complex planes. In the plane defined by beam transmitter parameters Ω(o) and Ω, the propagation path is described by a ray line similar to the ray line in the y? diagram method, whereas the path in the plane of beam receiver parameters θ and Λ is described by a circular arc. In either plane the amplitude, phase, spot size, and radius of curvature of the Gaussian beam are directly related to the modulus and argument of the complex number designating a particular transverse plane along the propagation path. These beam parameters also lead to simple geometric relations for locating the beam waist, Rayleigh range, focal plane, and sister planes, which share the same radius of curvature but have opposite signs. Combined with the paraxial wave propagation technique based on a Huygens-Fresnel integral and complex ABCD ay matrices, this geometric approach provides a new and powerful method for the analysis and design of laser systems.