Computational resources are constantly becoming faster, cheaper and more portable. Coupled with mass production and the use of sophisticated hardware components in the consumer electronics market, the abundance of computational power opens numerous opportunities in reducing the cost and extending the capabilities of traditional biomedical imaging and sensing devices. Toward this end, myriad computational imaging methods have been devised; among them is lensfree holographic imaging that provides a portable, cost- effective and yet powerful alternative to traditional bright field microscopy tools. Additionally, lensfree microscopy provides significantly larger fields-of-view (e.g., 30mm2) when compared to a typical bright-field transmission microscope with comparable resolution (e.g., 60-100� objective lens with a numerical aperture of 0.8-1.0).

This dissertation introduces the unique architecture of lensfree on-chip microscopy, its computational reconstruction methods, and several biomedical-imaging applications that utilize on-chip imaging. Lensfree microscopy has a distinct architecture when compared to other imaging systems. First, rather than recording a direct image of the specimen, an on-chip in-line hologram is acquired. In addition, the sample is positioned in close proximity to the image sensor (typically sub-mm); and finally, lenses are not used between the object and the image sensor. These unique attributes enable the simplification of the microscope's hardware to solely an image sensor and a partially coherent light source (both temporally and spatially), thus resulting in a cost-effective and portable microscope where hardware is replaced with computational reconstruction methods. These computational methods can push the resolution of the on-chip microscope to a deeply sub-micron range (e.g., 225 nm) by employing pixel-super-resolution, a method that synthesizes one high-resolution image from various lower resolution images of the same object. Additionally, to image dense and confluent samples, multi-height-based phase- recovery is introduced in partially coherent holography. This iterative method recovers the lost phase of an optical field from few intensity measurements, each captured with a different sample-to-sensor distance. Lastly, to provide accurate colorization, especially challenging for holographic methods, two different algorithms are utilized, one based on Dijkstra's shortest path algorithm, and the other based on the YUV color space. Based on these computational reconstruction blocks, the performance of lensfree on-chip microscopy can be demonstrated in various biomedical imaging applications that require both high-resolution and high-throughput, including Papanicolaou smears, human breast cancer slides and sickle cell anemia blood smears.