Computational Imaging with Self-Interference

 Interferometry records the relative phase between incident light and a reference beam. Since phase encodes the path information of the scene, it can be applied to tasks including 3D imaging or undoing effects of scattering. However, a reference beam requires a controllable external light source, which is not always available in many applications. The self-interference technique is one variant of interferometry that does not require a reference beam. In this thesis, we show that combining self-interference and computational imaging methods can improve phase-related tasks, including wavefront sensing, imaging fluorescent targets behind tissue, and passive textureless 3D reconstruction. 

For wavefront sensing, one of the classical results is phase-shifting point diffraction interferometry, where the phase of a wavefront is measured by interfering it with a planar reference created from the incident wave itself. The limiting drawback of this approach is that the planar reference, often created by passing light through a narrow pinhole, is dim and noise-sensitive. We address this limitation with a novel approach called ReWave that uses a non?planar reference that is designed to be brighter. The reference wave is designed in a specific way that would still allow for analytic phase recovery, exploiting ideas of sparse phase retrieval algorithms. ReWave requires only four image intensity measurements and is significantly more robust to noise compared to phase-shifting point diffraction interferometry. We validate the robustness and applicability of our approach using a suite of simulated and real results. 

For imaging fluorescent sources behind scattering tissue, we exploit memory effect correlations in speckles. These correlations are often weak when imaging thick scattering tissues and complex illumination patterns, both of which greatly limit the practicality of associated techniques. In our work, we introduce a spatial light modulator between the tissue sample and the imaging sensor and capture multiple modulations of the speckle pattern. We show that, by correctly designing the modulation patterns and the associated reconstruction algorithm, the statistical correlations in the measurements can be greatly enhanced. We exploit this to demonstrate the reconstruction of 300-micrometer-wide fluorescent patterns behind the scattering tissue around 150 micrometers thick in megapixel resolution. 

For passive textureless 3D reconstruction, note that passive depth estimation based on stereo or defocus relies on the presence of the texture on an object. Thus, recovering the depth of a textureless object, such as a large white wall, is not just hard but perhaps even impossible – until our work. We show that spatial coherence, a property of natural light sources, can be used to resolve the depth of a textureless scene. Our approach relies on the idea that natural light scattered off a scene point is locally coherent with itself, while incoherent with the light scattered from other surface points; we use this insight to design an optical setup that uses self-interference as a texture feature for estimating depth. Our lab prototype is capable of resolving the depths of textureless objects in sunlight as well as indoor lights. 

Together, we have further developed self-interferometry in various interesting applications. We hope the techniques we propose in this thesis can advance the next generation of computational imaging systems related to phase