Ian Langmore

A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

Abstract A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.

Optical Tomography for Variable Refractive Index with Angularly Averaged Measurements

In optical tomography one seeks to use near-infrared light to determine the optical absorption and scattering properties of a medium X ⊂ ℝ n . If the refractive index is constant throughout the medium, the steady-state case is modeled by the stationary linear transport equation in terms of the Euclidean metric. In this work we consider the case of variable refractive index where the dynamics are modeled by writing the transport equation in terms of a Riemannian metric; in the absence of interaction, photons follow the geodesics of this metric. In particular we study the problem where our measurements allow the application of an in-going flux depending on both position and direction, but we allow only a weighted average measurement of the out-going flux. We show that making measurements on all of ∂ X determines the extinction coefficient and that once this is known, under additional assumptions, measurements at a single point on ∂ X determine the scattering kernel.

Multipixel Retrieval of Structural and Optical Parameters in a 2-D Scene With a Path-Recycling Monte Carlo Forward Model and a New Bayesian Inference Engine

Physics-based retrievals of atmosphere and/or surface properties are generally multi- or hyperspectral in nature; some use multi-angle information as well. Recently, polarization has been added to the available input from sensors and accordingly modeled with vector radiative transfer (RT). At any rate, a single pixel is processed at a time using a forward RT model predicated on 1-D transport theory. Neighboring pixels are sometimes considered but, generally, just to formulate statistical constraints on the inversion based on spatial context. Herein, we demonstrate the power to be harnessed by adding bona fide multipixel techniques to the mix. We use a forward RT model in 2-D, sufficient for this demonstration and easily extended to 3-D, for the response of a single-wavelength imaging sensor. The data, an image, is used to infer position, size, and opacity of an absorbing atmospheric plume somewhere in a deep valley in the presence of partially known/partially unknown aerosol. We first describe the necessary innovation to speed-up forward multidimensional RT. In spite of its reputation for inefficiency, we use a Monte Carlo (MC) technique. However, the adopted scheme is highly accelerated without loss of accuracy by using “recycled” MC paths. This forward model is then put to work in a novel Bayesian inversion adapted to this kind of RT model where it is straightforward to trade precision and efficiency. Retrievals target the plume properties and the specific amount of aerosol. In spite of the limited number of pixels and low signal-to-noise ratio, there is added value for certain nuclear treaty verification applications.

Single scattering estimates for the scintillation function of waves in random media

The energy density of high frequency waves propagating in highly oscillatory random media is well approximated by solutions of deterministic kinetic models. The scintillation function determines the statistical instability of the kinetic solution. This paper analyzes the single scattering term in the scintillation function. This is the term of the scintillation function that is linear in the power spectrum of the random fluctuations. We show that the structure of the scintillation function is already quite complicated in this simplified setting. It strongly depends on the singularity of the initial conditions for the wave field and on the correlation properties of the random medium. We obtain limiting expressions for the scintillation function as the correlation length of the random medium tends to zero.

Angular Average of Time-Harmonic Transport Solutions

We consider the angular averaging of solutions to time-harmonic transport equations. Such quantities model measurements obtained for instance in optical tomography, a medical imaging technique, with frequency-modulated sources. Frequency modulated sources are useful to separate ballistic photons from photons that undergo scattering with the underlying medium. This paper presents a precise asymptotic description of the angularly averaged transport solutions as the modulation frequency ω tends to ∞. Provided that scattering vanishes in the vicinity of measurements, we show that the ballistic contribution is asymptotically larger than the contribution corresponding to single scattering. Similarly, we show that singly scattered photons also have a much larger contribution to the measurements than multiply scattered photons. This decomposition is a necessary step toward the reconstruction of the optical coefficients from available measurements.

Parametric 3D Atmospheric Reconstruction in Highly Variable Terrain with Recycled Monte Carlo Paths and an Adapted Bayesian Inference Engine

We describe a method for accelerating a 3D Monte Carlo forward radiative transfer model to the point where it can be used in a new kind of Bayesian retrieval framework. The remote sensing challenge is to detect and quantify a chemical effluent of a known absorbing gas produced by an industrial facility in a deep valley. The available data is a single low-resolution noisy image of the scene in the near IR at an absorbing wavelength for the gas of interest. The detected sunlight has been multiply reflected by the variable terrain and/or scattered by an aerosol that is assumed partially known and partially unknown. We thus introduce a new class of remote sensing algorithms best described as “multi-pixel” techniques that call necessarily for a 3D radiative transfer model (but demonstrated here in 2D); they can be added to conventional ones that exploit typically multi-or hyper-spectral data, sometimes with multi-angle capability, with or without information about polarization. The novel Bayesian inference met...