Physics (Internal)

Imaging and Scattering in Porous Media

This event is part of the Preliminary Oral Exam.

Examining Committee: Bennett Goldberg, Thomas Bifano, Jerome Mertz, Steve Ahlen, Pankaj Mehta

Abstract: Porous media occur throughout nature. In biology, one can measure brain activity through the skull by imaging molecules tagged with fluorescent markers. In ceramics, one can map the pore structure of a ceramic material by imaging the local reflectance. In the oil industry, one can characterize oil flow in rock by mixing in fluorescent beads and tracking them. Because they are porous, these materials are all strongly scattering media: imaging more than a few pore lengths into the material is frequently difficult, if not impossible. The primary means of constructing an image is by scanning a focus across the imaging area and capturing the reflected or re-emitted light. For each of these applications, the goal is to produce a high-contrast, aberration-free image; frequently the interesting features are at a depth far greater than the characteristic pore size. In any porous medium, the pores frequently have a different index of refraction than the surrounding solid material. The index mismatch between the solid medium and the pores scatters and reflects the incident light, destroying the focus used for imaging. The thicker the material and the stronger the scattering, the more the focus spreads, blurring the image. For every material there is a certain thickness (L) where the focus disappears entirely, and the phase beyond is randomized. This distance L, called the transport mean free path, is considered the maximum imaging depth for traditional (ballistic) optics. The main challenge of our research is imaging beyond L*. In my presentation, I will discuss the theoretical tools used to describe scattering effects; specifically, the use of both particle and wave models of light propagation. By considering the particle aspect of light, one arrives at a diffusive model of photons undergoing multiple scattering from distinct, separated pores. The statistics of the pore distribution provide predictive power, where one can calculate low order moments of the intensity distribution at an imaging plane. By considering the wave nature of light, one considers a transmission matrix with random coefficients. The transmission matrix relates the incident and transmitted electric fields, decomposed into 2D spatial modes. This provides a framework for understanding various techniques for imaging through highly scattering media. I will also discuss one specific technique to imaging beyond the transport mean free path. This method is an iterative procedure called coherent optimization. By using a spatial light modulator, one can adjust the input field to direct most of the power into a single output mode. This creates an effective focal spot, allowing for imaging deep into the scattering medium. Lastly, I will discuss the different ways we characterize the optical properties of the porous media: the maximum imaging depth and the maximum intensity enhancement of a particular spatial mode.