Li-Hao Yeh

Experimental robustness of Fourier ptychography phase retrieval algorithms

Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, an inverse algorithm can be used to computationally reconstruct the high-resolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i.e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensity-based ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities. Both noise (e.g. Poisson noise) and model mis-match errors are shown to scale with intensity. Hence, algorithms that use an appropriate cost function will be more tolerant to both noise and model mis-match. Given these insights, we propose a global Newtons method algorithm which is robust and accurate. Finally, we discuss the impact of procedures for algorithmic correction of aberrations and mis-calibration.

Computational illumination for high-speed in vitro Fourier ptychographic microscopy

We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or high resolution, not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixel-scale image having both wide FOV and high resolution, i.e. large space-bandwidth product (SBP). FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (on the order of minutes), limiting throughput. Faster capture times would not only improve imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g. pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4x FOV with sub-second capture times. We propose an improved algorithm and new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time.

Structured illumination microscopy with unknown patterns and a statistical prior

Structured illumination microscopy (SIM) improves resolution by down-modulating high-frequency information of an object to fit within the passband of the optical system. Generally, the reconstruction process requires prior knowledge of the illumination patterns, which implies a well-calibrated and aberration-free system. Here, we propose a new algorithmic self-calibration strategy for SIM that does not need to know the exact patterns a priori, but only their covariance. The algorithm, termed PE-SIMS, includes a pattern-estimation (PE) step requiring the uniformity of the sum of the illumination patterns and a SIM reconstruction procedure using a statistical prior (SIMS). Additionally, we perform a pixel reassignment process (SIMS-PR) to enhance the reconstruction quality. We achieve 2× better resolution than a conventional widefield microscope, while remaining insensitive to aberration-induced pattern distortion and robust against parameter tuning.

Computational microscopy: illumination coding and nonlinear optimization enables Gigapixel 3D phase imaging

Microscope lenses can have either large field of view (FOV) or high resolution, not both. Computational microscopy based on illumination coding circumvents this limit by fusing images from different illumination angles using nonlinear optimization algorithms. The result is a Gigapixel-scale image having both wide FOV and high resolution. We demonstrate an experimentally robust reconstruction algorithm based on a 2nd order quasi-Newtons method, combined with a novel phase initialization scheme. To further extend the Gigapixel imaging capability to 3D, we develop a reconstruction method to process the 4D light field measurements from sequential illumination scanning. The algorithm is based on a ‘multi-slice’ forward model that incorporates both 3D phase and diffraction effects, as well as multiple forward scatterings. To solve the inverse problem, an iterative update procedure that combines both phase retrieval and ‘error back-propagation’ is developed. To avoid local minimum solutions, we further develop a novel physical model-based initialization technique that accounts for both the geometric-optic and 1st order phase effects. The result is robust reconstructions of Gigapixel 3D phase images having both wide FOV and super resolution in all three dimensions. Experimental results from an LED array microscope were demonstrated.

3D super-resolution optical fluctuation imaging (3D-SOFI) with speckle illumination

We demonstrate a 3D super-resolution optical fluctuation imaging (SOFI) method using speckle illumination. Resolution enhancement of 1.6× is demonstrated in all three dimensions, as compared to traditional wide-field fluorescence images.

Experimental robustness of Fourier Ptychographic phase retrieval algorithms

We compare the results from several previously proposed phase retrieval algorithms using experimental Fourier Ptychography datasets and show importance of background subtraction and regularization for robustness with noisy imperfect data.

X-ray Phase Imaging and Computed Tomography with Sandpaper Analyzer

We experimentally demonstrate X-ray phase imaging and tomography with a sandpaper analyzer. Digital image correlation and filtered back projection algorithms are adopted for phase gradient calculation and three-dimensional reconstruction, respectively.