For various applications involving the propagation of light through the atmosphere, anisotropy of optical turbulence must be accounted for. At this point, however, there is no consensus about how to realistically model anisotropic turbulence. It is well established that at length scales small compared to a certain outer length scale, L-0, fully developed, optical turbulence is locally homogeneous and isotropic and is well described by the Obukhov-Corrsin similarity theory. At scales large compared to L-0, however, the turbulence is usually anisotropic, and the Obukhov-Corrsin similarity theory is no longer valid. In this paper, we discuss two questions: first, how to define and predict L-0; and second, how to model the 3D refractive-index spectrum, Phi(n)(k(x), k(y), k(z)), for wavenumbers comparable to and smaller than 1/L-0. We will address both questions on the basis of classical theoretical concepts and by means of field observations. The classical concepts include Tatarskii's original definition of L-0, the Richardson criterion, and the Monin-Obukhov similarity theory. Field observations include in-situ measurements by means of ultrasonic anemometer-thermometers and fine-wire turbulence sensors.

This joint feature issue in Applied Optics and JOSA A collects articles focused on the topic of propagation through and characterization of atmospheric oceanic phenomena. The papers cover a broad range of topics, many of which were addressed at the 2023 Propagation Through and Characterization of Atmospheric Oceanic Phenomena (pcAOP) Topical Meeting at the Optica Imaging Congress in Boston, Massachusetts, 14-17 August 2023. These papers are supplemented by numerous examples of the current state of research in the field. This is the first pcAOP feature issue, with the intention to produce an issue on this topic every two years.

An important characteristic of atmospheric turbulence is intermittency. Here we present and discuss fine-wire measurements of intermittency in optical turbulence near the ground.

First results of optical turbulence field measurements collected with a newly developed fine-wire temperature sensing system are presented and discussed. The centerpiece of the sensing system is an array of fine-wire platinum resistance thermometers. The active fine wire in each sensor element has a diameter of 0.64 μm and a length between 0.5 and 1 mm. The sampling rate is 44.1 kHz, and the noise level is 1 mK for a bandwidth of 10 kHz. Data were recorded while the car onto which the sensors were mounted was traveling at a speed of about 40 mph, or 18 m s . Estimates of the temperature structure function are compared against the classical Obukhov-Corrsin theory, which predicts power-law asymptotes with in the viscous-diffusive range and in the inertial-convective range. For the pair of separations  cm and  cm, we observed . The frequency spectrum follows the theoretically predicted power law in the inertial-convective subrange. The ‘Hill bump’ in the transition regime between the inertial-convective and viscous-diffusive subranges is visible.

The development and operation of a long-range optical propagation experiment for investigating scintillation and angle-of-arrival effects of atmospheric turbulence is described.

The fast-Fourier-transform-based filtering method for phase screen generation remains popular for numerical simulation of optical propagation through turbulence; however, these screens inherently underrepresent the spectral density at low wavenumbers. Here, the "Z-tilt" approach is explored to augment the spectral density at low wavenumbers by adding a random phase tilt, which is derived from the wavefront phase statistics of a Zernike polynomial basis. This approach is computationally efficient and can be applied to any statistically homogeneous and isotropic refractive index field. An analytic result is provided for the von Kármán spectrum with finite outer scale. In a quantitative comparison with phase screens compensated for using a common subharmonic approach, the Z-tilt method shows the best agreement with the analytical structure function when the outer scale is greater than about three times the screen dimension. For outer scales of the order of the screen dimension, the subharmonic and a modified Z-tilt method give the most accurate results. A propagation simulation demonstrates that the aperture-averaged angle-of-arrival variance is accurately predicted using the Z-tilt method.

We present and discuss measurements collected during a long-range optical propagation experiment conducted in October, 2022 at the White Sands Missile Range, NM. The propagation path was 84 km long, and most of the path was between 600 m and 1500 m above ground level.

Tatarskii’s first book on wave propagation through the turbulent atmosphere was published in English in 1961 and describes what we refer to as the classical theory of optical turbulence. It relies on a number of simplifying assumptions, such as the assumption of locally homogeneous and isotropic, fully developed turbulence; the Corrsin-Obukhov similarity theory; Taylor’s frozen-turbulence hypothesis; and the assumption of weak scattering. In this invited presentation, we review and discuss non-classical models of optical turbulence, which account for non-classical effects and phenomena, including anisotropy, intermittency, outer-scale effects, and non-Gaussianity of refractive-index increments.

The optical phase ϕ is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phase factor , ψ = exp ⁡ ( i ϕ ) , are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum F ψ ( κ ) of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function, D ϕ ( r ) = ( r / r c ) γ (where r c is the phase coherence length defined by D ϕ ( r c ) = 1 r a d 2 ), and a probability density function p α ( α ) of the phase increments for a given spatial lag. We analyze phase screens with turbulent ( γ = 5 / 3 ) and quadratic ( γ = 2 ) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phase-factor spectra F ψ ( κ ) . The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at κ ∼ 1 / r c . The bump is unrelated to the well-known “Hill bump” and is not caused by diffraction effects. It is solely a characteristic of the refractive-index statistics represented by the respective phase screen. We show that the second-order ψ statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order ϕ counterparts.

The resolution of short-exposure imaging through turbulence is studied with simulation for two phase tilt definitions, Z-tilt and G-tilt, which are applied to remove the instantaneous aperture averaged tilt in a short exposure. Applying the Z-tilt definition provides results that are consistent with Fried’s short-exposure theory. Applying the G-tilt definition produces narrower point spread functions that can deviate significantly from far-field theory.

We characterize the impact of turbulence on optical pulse timing jitter over a uniform, near-ground path and compare the results with theory. Use of frequency combs enabled phase-continuous measurements down to 200-fs over multiple hours.

During propagation through atmospheric turbulence, variations in the refractive index of air cause fluctuations in the time-of-flight of laser light. These timing jitter fluctuations are a major noise source for precision laser ranging, optical time transfer, and long-baseline interferometry. While there exist models that estimate the turbulence-induced timing jitter power spectra using parameters obtainable from conventional micrometeorological instruments, a direct and independent comparison of these models to measured timing jitter data has not been done. Here we perform this comparison, measuring turbulence-induced optical pulse timing jitter over a horizontal, near-ground path using frequency comb lasers while independently characterizing the turbulence along the path using a suite of micrometeorological sensors. We compare the power spectra of measured optical pulse timing jitter to predictions based on the measured micrometeorological data and standard turbulence theory. To further quantitatively compare the frequency comb data to the micrometeorological measurements, we extract and compare the refractive index structure parameter, Cn2, from both systems and find agreement to within a factor of 5 for wind speed >1 m/s, and further improvement is possible as wind speed increases. These results validate the use of conventional micrometeorological instruments in predicting optical timing jitter statistics over co-located laser beam paths.

We measure optical timing jitter due to atmospheric turbulence using frequency comb lasers. Retrieving the refractive index structure parameter, Cn2, from this data, we find windspeed- dependent agreement to Cn2 values derived from in situ instruments.

Wave optics simulation results of scintillation index and log amplitude variance differ from analytic models in the saturation regime. A spherical wave and point receiver are assumed in turbulence without inner and outer scales.

We present and discuss probability densities of optical scintillation observed with large apertures in the atmosphere. We interpret the observations on the basis of theoretical models and compare them with scintillation statistics obtained from computer simulations.

Split-step Fourier-Fresnel algorithms based on phase screens are powerful tools to computationally simulate optical propagation through atmospheric and oceanic turbulence. Usually, phase screens are generated by means of idealized turbulence models. Here we present and discuss phase screens resulting from direct numerical simulation of the Navier-Stokes equations and the scalar transport equation.

It is known that certain geometrical-optics predictions often agree well with optical turbulence field observations even though theoretical constraints for ignoring diffraction may be violated. Geometrical optics assumptions can simplify analyses, and ray optics can significantly reduce simulation computation time. Here, an investigation into angle-of-arrival fluctuations is presented involving wave optics and geometrical (ray) optics computer simulations of a plane wave of visible light propagating through a turbulent refractiveindex field. The simulation and Rytov-based theory results for the variances of aperture-filtered angle-of-arrival fluctuations generally agree well for weak scattering (Rytov variance, sigma(2)(R) less than or similar to 0.2), but for increasing Rytov variance, the simulation results demonstrate a positive slope that can be significantly shallower than that predicted by the theory. For weak-to-moderate scattering regimes (sigma(2)(R) less than or similar to 2.67), a comparison of the ray and wave results show they match for aperture diameters greater than about two Fresnel lengths. This result is consistent with a previous theoretical analysis by Cheon and Muschinski. For the strongest scattering case studied (sigma(2)(R) = 26.7), the wave and ray simulations match for aperture diameters greater than about 10 Fresnel lengths. For smaller apertures, we attribute the disparity between the wave and ray simulation results to a Fresnel filtering effect. (C) The Authors. Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License.

Occasionally, non-Kolmogorov turbulence plays an important role for optical propagation in the turbulent atmosphere. Here, we discuss two major causes of non-Kolmogorov turbulence: Batchelor scaling in the viscous-convective range, and anisotropy.

The analysis of optical propagation through both deterministic and stochastic refractive-index fields may be substantially simplified if diffraction effects can be neglected. With regard to simplification, it is known that certain geometrical-optics predictions often agree well with field observations but it is not always clear why this is so. Here, a new investigation of this issue is presented involving wave optics and geometrical (ray) optics computer simulations of a beam of visible light propagating through fully turbulent, homogeneous and isotropic refractive-index fields. We compare the computationally simulated, aperture-averaged angle-of-arrival variances (for aperture diameters ranging from 0.5 to 13 Fresnel lengths) with theoretical predictions based on the Rytov theory.