Michael Chen

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.

Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC)

We present a new technique for quantitative phase and amplitude microscopy from a single color image with coded illumination. Our system consists of a commercial brightfield microscope with one hardware modification—an inexpensive 3D printed condenser insert. The method, color-multiplexed Differential Phase Contrast (cDPC), is a single-shot variant of Differential Phase Contrast (DPC), which recovers the phase of a sample from images with asymmetric illumination. We employ partially coherent illumination to achieve resolution corresponding to 2× the objective NA. Quantitative phase can then be used to synthesize DIC and phase contrast images or extract shape and density. We demonstrate amplitude and phase recovery at camera-limited frame rates (50 fps) for various in vitro cell samples and c. elegans in a micro-fluidic channel.

3D Phase Microscopy with Coded Illumination

We demonstrate 3D phase reconstruction from through-focus intensity images taken in an LED array microscope. Using the first Born and weak object approximations, 3D refractive index can be linearly related to measured intensity.

Modeling light propagation in 3D phase objects

Accurate and fast simulation of light propagating through 3D biological cells is important to the development of new computational imaging systems. We compare the finite-difference time-domain (FDTD), multislice, first Born approximation, and series-expanded Born (SEAGLE) simulation methods.

3D differential phase contrast microscopy

We demonstrate three-dimensional (3D) optical phase and amplitude reconstruction based on coded source illumination using a programmable LED array. Multiple stacks of images along the optical axis are computed from recorded intensities captured by multiple images under off-axis illumination. Based on the first Born approximation, a linear differential phase contrast (DPC) model is built between 3D complex index of refraction and the intensity stacks. Therefore, 3D volume reconstruction can be achieved via a fast inversion method, without the intermediate 2D phase retrieval step. Our system employs spatially partially coherent illumination, so the transverse resolution achieves twice the NA of coherent systems, while axial resolution is also improved 2× as compared to holographic imaging.

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.