We present some results obtained by numerical modeling of the propagation of vortex beams ${\mathrm{LG}}_{0l}$ through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre–Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (${\mathrm{LG}}_{0l}$) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge $l$ is, the smaller the beam broadening is.

We propose an optical correlation algorithm illustrating a new general method for reconstructing the phase skeleton of complex optical fields from the measured two-dimensional intensity distribution. The core of the algorithm consists in locating the saddle points of the intensity distribution and connecting such points into nets by the lines of intensity gradient that are closely associated with the equi-phase lines of the field. This algorithm provides a new partial solution to the inverse problem in optics commonly referred to as the phase problem.

Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.

In the present work, we briefly describe a model for atmospheric turbulence energy on the basis of experimental data obtained in Siberia. A series of new studies is considered and the results of our long-term experimental observations are summarized. The results of these studies form the basis for an explanation of some effects in interactions between optical waves and atmospheric turbulence. Our numerous experimental results point to the possible generation of so-called coherent turbulence in the atmosphere. When analyzing the problem, we proceeded based on our own experimental data and comprehension that the coherent turbulence is a result of the action of self-organizing nonlinear processes, which run in continuous media, including atmospheric air. The experimental data confirmed the effect of attenuation of light fluctuations in coherent turbulence.

In ultrasonic equipment (anemometers and thermometers), for the measurement of parameters of atmospheric turbulence, a standard algorithm that calculates parameters from temporary structural functions constructed on the registered data is usually used. The algorithm is based on the Kolmogorov–Obukhov law. The experience of using ultrasonic meters shows that such an approach can lead to significant errors. Therefore, an improved algorithm for calculating the parameters is developed, which allows more accurate estimation of the structural characteristics of turbulent fluctuations, with an error that is not more than 10%. The algorithm was used in the development of a new ultrasonic hardware-software complex, autonomous meteorological complex AMK-03-4, which differs from similar measuring instruments of turbulent atmosphere parameters by the presence of four identical ultrasonic anemometers. The design of the complex allows not only registration of the characteristics of turbulence, but also measurement of the statistical characteristics of the spatial derivatives of turbulent temperature fluctuations and orthogonal components of wind speed along each of the axes of the Cartesian coordinate system. This makes it possible to investigate the space–time structure of turbulent meteorological fields of the surface layer of the atmosphere for subsequent applications in the Monin–Obukhov similarity theory and to study turbulent coherent structures. The new measurement data of the spatial derivatives of temperature at stable stratification (at positive Monin–Obukhov parameters) were obtained, at which the behavior of the derivatives was been investigated earlier. In the most part of the interval of positive Monin–Obukhov parameters, the vertical derivative of the temperature is close to a constant value. This fact can be considered as a new significant result in similarity theory.

Modern methods for altitude profiling of atmospheric turbulence are discussed. A method for estimating the altitudes of atmospheric layers characterized by strong turbulence, which is an alternative to the Slodar method, is suggested. The method is based on estimation of the spatiotemporal cross-covariances between local wavefront slopes on subapertures spaced in the telescope field of view and a known angular shift of an object observed due to the Sun motion. Turbulence characteristics are estimated for the Big Solar Vacuum Telescope site.