Image Enhancement in Optics and Ultrasound using Nonlinearity

Abstract

Conventional imaging systems based on linear wave propagation suffer many limitations, including diffraction-limited resolution, a trade-of between contrast and resolution, and limited sensitivity to phase. In this dissertation, we overcome these limits by developing new imaging schemes using nonlinear effects and computational imaging techniques. The methods are demonstrated in optical imaging and medical ultrasound imaging.

The first part of the thesis focuses on enhancing phase reconstruction using nonlinear propagation. The feedback between amplitude and phase upon nonlinear propagation makes the system very sensitive to phase, which we demonstrate experimentally with a photorefractive crystal. Phase matching (conservation of energy and momentum) leads to a zero-crossing convergence profile, where the known amplitude error and the unknown phase error reach their minimum at the same iteration. This zero crossing, not present in linear systems, provides a previously unavailable criterion for stopping the iterative algorithm. The nonlinear algorithm performs twice as well as conventional algorithms using linear propagation.

In the second part of the dissertation, we use an electro-optic spatial light modulator to produce nonlinear effects without a physical medium. Specifically, we use feedback between the diffraction pattern of an object and the illumination pattern on the modulator. This "digital" nonlinearity greatly facilitates nonlinear optics, because it works for any light intensity, has a fast response time, operates over a broad bandwidth, is dynamically adjustable, and is compatible with nearly any arbitrarily mathematical form. We demonstrate the method in phase imaging using both coherent and incoherent light.

In the final part of the thesis, we apply these ideas to ultrasound imaging. We consider both traditional nonlinear imaging (tissue harmonic imaging) and tissue-specific imaging (object-dependent adjustments to the speed of sound). We then numerically compare these images with the fundamental image. By leveraging the mutual information between the signals, we create a composite image with better contrast, higher resolution, lower noise, fewer artifacts, and more tissue-specific response than is possible with each image individually.