ARNOLD D. KIM
PROFESSOR OF APPLIED MATH


CURRENT RESEARCH PROJECTS

Radiative transfer theory for multiple scattering of light

Radiative transfer theory describes the transport of energy taking into account absorption and scattering of light due to inhomogeneities in the medium. This theory is useful for a broad array of applications such as optics in clouds, the ocean, and biological tissues, to name a few. We use asymptotic and numerical methods to study elementary boundary value problems and initial-boundary value problems for the radiative transfer equation to find canonical features that provide valuable insights required for applied problems.

 

Imaging and spectroscopy in multiple scattering media

We seek to develop methods to recover optical properties of a multiple scattering medium from measurements of scattered light. The key challenge here is developing a comprehensive understanding of how optical properties such as absorption, scattering, particle size distribution, etc are manifest in scattered light measurements. Through analysis of the inverse problem for the radiative transfer equation, we seek to develop novel computational methods that balance the need for high resolution with the inherent ill-posedness of these problems.

 

Numerical evaluation of nearly singular integrals

Nearly singular integrals arise in potential theory, plasmonics, and highly anisotropic scattering media. We seek to develop highly accurate methods to numerically evaluate nearly singular integrals that can be applied generally through a combination of asymptotic and numerical analyses. In particular, we seek to study electromagnetic scattering by metal obstacles that accurately capture the coupling of near and far fields for applications to photonics and sensing.

 

Intensity-only synthetic aperture radar

Intensity-only imaging methods are useful for high frequency active radar imaging where issues of synchronous signal processing at the receiver become restrictively challenging, for example. To compensate for the phase information lost in intensity-only measurements, one must consider an increase in spatial, time, and frequency diversity at either the source or receiver antennas. We seek to develop analytical and computational methods to introduce, analyze, and simulate new methods for intensity-only synthetic aperture array imaging.