For long-distance imaging, spatial resolution is mainly limited by the small aperture size of the lens. To improve the performance, huge and high-precision lens systems are normally built, which are always bulky and expensive. In this thesis, I propose two methods to achieve high spatial resolution with light and low-cost lenses by phase retrieval algorithms.

In the first work, I present a reflective Fourier Ptychography system using a small-size lens. Multiple low-resolution images are captured from different locations, and then fused together to create a big synthetic aperture computationally. I demonstrate the first working prototype that can achieve six-times spatial-resolution improvements over any single captured image for various diffuse objects.

In the second work, I propose to correct arbitrary optical aberrations in a large but low-cost and low-quality lens by wavefront coding. A spatial light modulator (SLM) is placed in front of the sensor to randomly modulate phase distribution of the incident light field. Based on multiple SLM patterns and corresponding images on the sensor, the object field can be retrieved successfully. I build an experimental system to show a 2-inch Fresnel lens can reconstruct diffraction-limited images.