Relationship between turbulent image variance and average image gradient.

Optical turbulence can cause substantial distortions in imaging over long horizontal paths. For Lambertian objects, these distortions are only seen where there is a gradient in the object's radiance. It is possible to establish a relationship between the intensity variance of a turbulent image and the average image's gradient squared. We test the validity of a linear relationship between these quantities using turbulent imaging data. We find that it performs reasonably well for weak and intermediate optical turbulence regimes, but that some discrepancies remain to be explained.

Comparative analysis of C n2 estimation methods for sonic anemometer data.

Wind speed and sonic temperature measured with ultrasonic anemometers are often utilized to estimate the refractive index structure parameter C n2, a vital parameter for optical propagation. In this work, we compare four methods to estimate C n2 from C T2, using the same temporal sonic temperature data streams for two separated sonic anemometers on a homogenous path. Values of C n2 obtained with these four methods using field trial data are compared to those from a commercial scintillometer and from the differential image motion method using a grid of light sources positioned at the end of a common path. In addition to the comparison between the methods, we also consider appropriate error bars for C n2 based on sonic temperature considering only the errors from having a finite number of turbulent samples. The Bayesian and power spectral methods were found to give adequate estimates for strong turbulence levels but consistently overestimated the C n2 for weak turbulence. The nearest neighbors and structure function methods performed well under all turbulence strengths tested.

General Rytov approximation.

We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

Hydrodynamics of the turbulent point-spread function.

We derive hydrodynamic equations for the point-spread function of an imaging system looking through atmospheric turbulence at an incoherent object. These are derived from the hydrodynamics of the index of refraction of the air. We use the path integral representation of the paraxial approximation for wave propagation through turbulence. We then study the case of a frozen turbulent refractive index field being advected past the imaging system with a constant wind and discuss the implications for optical flow estimation. We conclude by discussing possible directions for future work.

Some theoretical aspects of the turbulent point-spread function.

In a previous work [J. Opt. Soc. Am. A24, 753 (2007)], we developed a theory describing the space-time statistics of the scintillation and displacement fields of the turbulent point-spread function (PSF), which we validated using imaging data. We now expand on that work by deriving the theoretical expression for the spread fields of the PSF. We also show how the displacement and spread fields are derivable from a set of potentials, and we discuss some of the properties of those potentials.

Some space-time statistics of the turbulent point-spread function.

We consider the point-spread function (PSF) of an imaging system looking through weak optical turbulence along a horizontal path through the atmospheric surface layer. From this PSF we derive a scalar total irradiance field and a center-of-mass vector field. Theoretical values are found for the space-time autocorrelation and cross-correlation functions for these fields, which are then compared with the observed correlation functions obtained from data taken at the Validation Measurements on Propagation in the Infrared and Radar (VAMPIRA) measurement trial. We discuss the meaning of these results and possible directions for future work.

Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface.

A statistical sea surface specular BRDF (bidirectional reflectance distribution function) model is developed that includes mutual shadowing by waves, wave facet hiding, and projection weighting. The integral form of the model is reduced to an analytical form by making minor and justifiable approximations. The new form of the BRDF thus allows one to compute sea reflected radiance more than 100 times faster than the traditional numerical solutions. The repercussions of the approximations used in the model are discussed. Using the analytical form of the BRDF, an analytical approximation is also obtained for the reflected sun radiance that is always good to within 1% of the numerical solution for sun elevations of more than 10 degrees above the horizon. The model is validated against measured sea radiances found in the literature and is shown to be in very good agreement.