Roarke Horstmeyer

Wide-field, high-resolution Fourier ptychographic microscopy

In this article, we report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope’s depth-of-focus beyond the physical limitations of its optics. As a demonstration, we built a microscope prototype with a resolution of 0.78 μm, a field-of-view of ~120 mm2, and a resolution-invariant depth-of-focus of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify FPM’s successful operation. The reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

Quantitative phase imaging via Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a systems performance beyond the limit defined by its optical components. The FPM technique applies a novel phase-retrieval procedure to achieve resolution enhancement and complex image recovery. In this Letter, we compare FPM data to theoretical prediction and phase-shifting digital holography measurement to show that its acquired phase maps are quantitative and artifact-free. We additionally explore the relationship between the achievable spatial and optical thickness resolution offered by a reconstructed FPM phase image. We conclude by demonstrating enhanced visualization and the collection of otherwise unobservable sample information using FPMs quantitative phase.

Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE)

Focusing of light in the diffusive regime inside scattering media has long been considered impossible. Recently, this limitation has been overcome with time reversal of ultrasound-encoded light (TRUE), but the resolution of this approach is fundamentally limited by the large number of optical modes within the ultrasound focus. Here, we introduce a new approach, time reversal of variance-encoded light (TROVE), which demixes these spatial modes by variance-encoding to break the resolution barrier imposed by the ultrasound. By encoding individual spatial modes inside the scattering sample with unique variances, we effectively uncouple the system resolution from the size of the ultrasound focus. This enables us to demonstrate optical focusing and imaging with diffuse light at unprecedented, speckle-scale lateral resolution of ~ 5 μm.

Flexible multimodal camera using a light field architecture

We present a modified conventional camera that is able to collect multimodal images in a single exposure. Utilizing a light field architecture in conjunction with multiple filters placed in the pupil plane of a main lens, we are able to digitally reconstruct synthetic images containing specific spectral, polarimetric, and other optically filtered data. The ease with which these filters can be exchanged and reconfigured provides a high degree of flexibility in the type of information that can be collected with each image. This paper explores the various tradeoffs involved in implementing a pinhole array in parallel with a pupil-plane filter array to measure multi-dimensional optical data from a scene. It also examines the design space of a pupil-plane filter array layout. Images are shown from different multimodal filter layouts, and techniques to maximize resolution and minimize error in the synthetic images are proposed.

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging

We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging. The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object. The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process. We demonstrate two applications of the reported scheme. In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects. The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object. We also demonstrate a reconstruction resolution better than the detector pixel limit (i.e., pixel super-resolution). In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging. By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field. This platforms maximum achievable resolution is ultimately determined by the cameras traveling range, not the aperture size of the lens. The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy.

High numerical aperture Fourier ptychography: principle, implementation and characterization

Fourier ptychography (FP) utilizes illumination control and computational post-processing to increase the resolution of bright-field microscopes. In effect, FP extends the fixed numerical aperture (NA) of an objective lens to form a larger synthetic system NA. Here, we build an FP microscope (FPM) using a 40X 0.75NA objective lens to synthesize a system NA of 1.45. This system achieved a two-slit resolution of 335 nm at a wavelength of 632 nm. This resolution closely adheres to theoretical prediction and is comparable to the measured resolution (315 nm) associated with a standard, commercially available 1.25 NA oil immersion microscope. Our work indicates that Fourier ptychography is an attractive method to improve the resolution-versus-NA performance, increase the working distance, and enlarge the field-of-view of high-resolution bright-field microscopes by employing lower NA objectives.

Translation correlations in anisotropically scattering media

Controlling light propagation across scattering media by wavefront shaping holds great promise for a wide range of communications and imaging applications. But, finding the right shape for the wavefront is a challenge when the mapping between input and output scattered wavefronts (that is, the transmission matrix) is not known. Correlations in transmission matrices, especially the so-called memory effect, have been exploited to address this limitation. However, the traditional memory effect applies to thin scattering layers at a distance from the target, which precludes its use within thick scattering media, such as fog and biological tissue. Here, we theoretically predict and experimentally verify new transmission matrix correlations within thick anisotropically scattering media, with important implications for biomedical imaging and adaptive optics.

Physical key-protected one-time pad

We describe an encrypted communication principle that forms a secure link between two parties without electronically saving either of their keys. Instead, random cryptographic bits are kept safe within the unique mesoscopic randomness of two volumetric scattering materials. We demonstrate how a shared set of patterned optical probes can generate 10 gigabits of statistically verified randomness between a pair of unique 2 mm3 scattering objects. This shared randomness is used to facilitate information-theoretically secure communication following a modified one-time pad protocol. Benefits of volumetric physical storage over electronic memory include the inability to probe, duplicate or selectively reset any bits without fundamentally altering the entire key space. Our ability to securely couple the randomness contained within two unique physical objects can extend to strengthen hardware required by a variety of cryptographic protocols, which is currently a critically weak link in the security pipeline of our increasingly mobile communication culture.

A phase space model of Fourier ptychographic microscopy

A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution complex sample estimate. Here, we propose a mathematical model of FPM that explicitly connects its operation to conventional ptychography, a common procedure applied to electron and X-ray diffractive imaging. Our mathematical framework demonstrates that under ideal illumination conditions, conventional ptychography and FPM both produce datasets that are mathematically linked by a linear transformation. We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures. In addition, the coherence state of the illumination source used by each imaging platform is critical to successful operation, yet currently not well understood. We apply our mathematical framework to demonstrate that partial coherence uniquely alters both conventional ptychographys and FPMs captured data, but up to a certain threshold can still lead to accurate resolution-enhanced imaging through appropriate computational post-processing. We verify this theoretical finding through simulation and experiment.

Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.