Our research covers optics, signal processing, computer algorithms and system design. Optical waves can be treated in a signal processing framework, where optical beams are represented as complex fields split up into spatial frequencies and temporal frequencies (color). Coherence is the 2nd order correlation function of a statistical optical beam. We aim to measure and control all of these parameters for better imaging systems.
Phase ImagingLight is a wave, having both an amplitude and phase. Our eyes and cameras, however, only see real values (i.e. intensity), so cannot measure phase directly. Phase is important, especially in biological imaging, where cells are typically transparent (i.e. invisible) but yet impose phase delays. When we can measure the phase delays, we get back important shape and density maps. We develop methods for phase imaging from simple experimental setups and efficient algorithms which can be implemented in optics, Xray, neutron imaging, etc. Phase from chromatic aberrations: L. Waller, S. Kou, C. Sheppard, G. Barbastathis, Optics Express 18(22), 2281722825 (2010). Phase from throughfocus: L. Waller, M. Tsang, S. Ponda, G. Barbastathis, Opt. Express 19 (2011). Z. Jingshan, J Dauwels, M. A. Vasquez, L. Waller, Optics Express 21(15), 1812518137 (2013). Z. Jingshan, L. Tian, J. Dauwels, L. Waller, Biomedical Optics Express 6(1), 257265 (2014) Applications in lithography: A. Shanker, M. Sczyrba, B. Connolly, F. Kalk, A. Neureuther, L. Waller, in SPIE Photomask Technology (2013). A. Shanker, M. Sczyrba, B. Connolly, F. Kalk, A. Neureuther, L. Waller, in SPIE Advanced Lithography paper 905249, February 2014, San Jose, CA. R. Claus, A. Neureuther, P. Naulleau, L. Waller, Optics Express 23(20), 2667226682 (2015). 

LED array microscopeWe work on a new type of microscope hack, where the lamp of a regular microscope is replaced with an LED array, allowing many new capabilities. We do brightfield, darkfield, phase contrast, superresolution or 3D phase imaging, all by computational illumination tricks. Click the photo to the right to see high resolution phase images across a huge field of view. L. Tian, Z. Liu, L. Yeh, M. Chen, Z. Jingshan, L. Waller, Optica 2(10), 904911 (2015). 

Fourier ptychography algorithmsThe algorithms behind achieving large fieldof–view and high resolution are rooted in phase retrieval. We use largescale nonlinear nonconvex optimization, much like neural networks in machine learning, but we have new challenges for imaging applications. 
Computational CellScopeIn collaboration with the CellScope group at Berkeley (Fletcher Lab), we work on computational illumination and algorithms for cellphone based microscopes – in particular, the CellScope. 
10x, NA~0.25, 10 Hz, Elegans (Dillin lab) 
Realtime multimode microscope systemWe show here a singlecamera imaging system that can simultaneously acquire brightfield, darkfield and phase contrast (DPC) images in realtime. Our method uses a programmable LED array as the illumination source, which provides flexible patterning of illumination angles. We achieve a frame rate of 50 Hz with 2560X2160 pixels and 100Hz with 1920X1080 pixels, with speed only limited by the camera. 
Coherence engineering – phase space/statistical optics – light fieldsPartially coherent beams do not have a welldefined phase. Light at any point in space doesn’t travel in a single direction (with a single spatial frequency), but rather, has a statistical distribution of frequencies (phase values). This means that a spatially partially coherent 2D beam can only be described by a 4D coherence function, akin to a covariance matrix. We aim to measure these 4D correlations with high resolution in all 4D, which creates engineering challenges for data management and compression. Basically, it’s big data for imaging. L. Waller, G. Situ, J. W. Fleischer, Nature Photonics 6, 474479 (2012). 
Funding: