Propagation Phasor Approach in Holographic Image Reconstruction

High-resolution and wide-field imaging is of great value for various scientific disciplines; such tasks demand the imaging modalities to possess large space-bandwidth products. The rapid evolutions of modern image sensor technologies and computing power have provided tremendous opportunities for development of new imaging systems with significantly larger space-bandwidth products than conventional lens-based systems. This dissertation introduces the latest advance in lensfree holographic microscopy, a computational imaging technique that serves as a potent solution for high-resolution, wide-field microscopy. By placing the specimen at a close proximity to the image sensor (e.g., ~100 μm - 1 mm), lensfree microscopy runs at unit magnification and possesses significantly larger field-of-view (FOV) than conventional lens-based systems. There are two major challenges in lensfree holographic microscopy: (1) undersampling by the image sensor; and (2) phase retrieval of the light field. This work first shows that, by using the two-dimensional pixel function of an image sensor-array as an input to lensfree holographic image reconstruction, pixel super-resolution can improve the numerical aperture (NA) of the reconstructed image by a factor of ~3 compared to a raw lensfree image. This pixel super-resolution-based lensfree microscope, when combined with an ultra-violet (UV) light emitting diode (LED), is capable of resolving 225 nm line-width gratings and is useful for wide-field on-chip imaging of nano-scale objects such as helical multi-walled carbon nanotubes. To further increase the bandwidth of this imaging modality, I developed lensfree imaging using synthetic aperture (LISA), which delivers an effective numerical aperture of ~1.4 across a wide FOV of ~20 mm2. LISA utilizes multiple angles of illumination to holographically synthesize the largest numerical aperture for an on-chip microscope and enables color imaging of tissue samples, including pathology slides, using complex wave retrieval. In the pursuit of more efficient pixel super-resolution techniques, I developed a fundamentally new resolution enhancement technique, namely wavelength scanning pixel super-resolution. It relies on an iterative algorithm to generate high-resolution reconstructions of the specimen using undersampled diffraction patterns recorded at a few wavelengths, covering a narrow spectrum (~10-30 nm). When combined with synthetic aperture technique, this wavelength scanning super-resolution approach can achieve a resolution of ~250 nm, corresponding to a numerical aperture of ~1.0 across a wide field-of-view (>20 mm2). Compared to lateral displacement-based super-resolution, wavelength scanning brings uniform resolution improvement in all directions across the sensor array and requires significantly less number of measurements. The development of wavelength scanning pixel super-resolution eventually led to a new computational framework, termed as propagation phasor approach, which for the first-time combines pixel super-resolution and phase retrieval techniques into a unified mathematical framework. In contrast to previous holographic reconstruction algorithms, my new algorithm reduces the number of raw measurements by five to seven folds, while at the same time achieving a competitive resolution across a large field-of-view. These technological advances could greatly benefit the development of high-resolution, wide-field computational imaging modalities with compactness, cost-effectiveness and superior data efficiency