arXiv subjects

Knut Sølna

Publications and source records attributed to Knut Sølna.

5 recordsLinked to original sources

arXiv2026

Imaging through rough interfaces: The shower curtain effect

The quality of an image observed through a scattering layer, such as a shower curtain, depends strongly on the relative position of the scattering layer between the object and the observer. This well-known phenomenon is commonly referred to as the shower curtain effect. When the scattering layer is placed close to the observer, the image is strongly degraded, whereas if it is located close to the object, the object may still be observed with relatively high resolution. Previous analyses of the shower curtain effect have primarily modeled the scattering layer as a section of a random medium. In this work, we present a new analysis in which the scattering layer is modeled instead as a rough interface, a description that arises naturally in many physical configurations. Within this framework, we derive explicit characterizations of both the image resolution and the signal-to-noise ratio, and determine how these quantities depend on the statistical properties of the rough interface and on its relative location between the object and the observer.

math-ph↗

arXiv2026

Generalized Snell's laws for rough interfaces

In this paper, we consider the reflection and transmission problem of waves by a rapidly oscillating rough interface that exhibits general mixing properties. Using an asymptotic analysis based on a separation of scales, corresponding to a paraxial (parabolic) scaling regime, we precisely characterize the specular and speckle (diffusive) components of the reflected and transmitted fields. A critically scaled interface is considered, in the sense that the amplitudes of the interface fluctuations and the central wavelength are of the same order. When the correlation length of the interface fluctuations is of the same order as the beam width, random specular components arise in both the reflected and transmitted waves, while no speckle component is observed. Equivalently, the reflected and transmitted fields are essentially confined to the cones formed by the specular components (specular cones) with directions given by the classical Snell's law of reflection and refraction. When the correlation length is smaller than the beam width, a specular homogenization regime emerges. In this case, the rough interface can be approximated by an effective flat interface, yielding deterministic specular reflected and transmitted cones. However, broader cones containing the specular cones appear, within which the wavefields form speckle patterns (speckle cones) whose total energy is of leading order. We provide the two-point correlation functions of these speckle patterns and establish a central-limit-theorem-type result, showing that they can be modeled as Gaussian random fields. These results enable the identification of generalized Snell's laws of reflection and transmission, which depend on an effective scattering operator at the interface.

math-ph↗

arXiv2022

Partially Coherent Electromagnetic Beam Propagation in Random Media

A theory for the characterization of the fourth moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian-Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth order equations are considered. The general fourth moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second wave moment. The fourth moment results for polarized waves is used in an application to imaging of partially coherent sources.

physics.optics↗

arXiv2010

A general framework for waves in random media with long-range correlations

We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in \citeMS and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian motion. Here we study the asymptotic transmitted pulse under very general assumptions on the long-range correlations. In the framework that we introduce in this paper, we prove in particular that the asymptotic time-shift can be described in terms of non-Gaussian and/or multifractal processes.

math.PR↗

arXiv2009

Coupled paraxial wave equations in random media in the white-noise regime

In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schrödinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation functions are determined by a closed system of transport equations. The Wigner distribution is then used to describe the enhanced backscattering phenomenon for the reflected field.

math.PR↗