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 mm^2 and a resolution-invariant depth of focus
of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM 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.

Wide-field, high-resolution Fourier ptychographic microscopy

Coherent diffractive imaging (CDI) and scanning transmission x-ray microscopy (STXM) are two popular microscopy techniques that have evolved quite independently. CDI promises to reach resolutions below 10 nanometers, but the reconstruction procedures put stringent requirements on data quality and sample preparation. In contrast, STXM features straightforward data analysis, but its resolution is limited by the spot size on the specimen. We demonstrate a ptychographic imaging method that bridges the gap between CDI and STXM by measuring complete diffraction patterns at each point of a STXM scan. The high penetration power of x-rays in combination with the high spatial resolution will allow investigation of a wide range of complex mesoscopic life and material science specimens, such as embedded semiconductor devices or cellular networks.

https://science.sciencemag.org/content/sci/321/5887/379.full.pdf

High-Resolution Scanning X-ray Diffraction Microscopy

http://xrm.phys.northwestern.edu/research/pdf_papers/2009/maiden_ultramic_2009.pdf

An improved ptychographical phase retrieval algorithm for diffractive imaging.

X-ray tomography is an invaluable tool in biomedical imaging. It can deliver the three-dimensional internal structure of entire organisms as well as that of single cells, and even gives access to quantitative information, crucially important both for medical applications and for basic research. Most frequently such information is based on X-ray attenuation. Phase contrast is sometimes used for improved visibility but remains significantly harder to quantify. Here we describe an X-ray computed tomography technique that generates quantitative high-contrast three-dimensional electron density maps from phase contrast information without reverting to assumptions of a weak phase object or negligible absorption. This method uses a ptychographic coherent imaging approach to record tomographic data sets, exploiting both the high penetration power of hard X-rays and the high sensitivity of lensless imaging. As an example, we present images of a bone sample in which structures on the 100 nm length scale such as the osteocyte lacunae and the interconnective canalicular network are clearly resolved. The recovered electron density map provides a contrast high enough to estimate nanoscale bone density variations of less than one per cent. We expect this high-resolution tomography technique to provide invaluable information for both the life and materials sciences.

/pdf/ptychographic-x-ray-computed-tomography-at-the-nanoscale-15wem0r262.pdf

Ptychographic X-ray computed tomography at the nanoscale

We demonstrate a hard-x-ray microscope that does not use a lens and is not limited to a small field of view or an object of finite size. The method does not suffer any of the physical constraints, convergence problems, or defocus ambiguities that often arise in conventional phase-retrieval diffractive imaging techniques. Calculation times are about a thousand times shorter than in current iterative algorithms. We need no a priori knowledge about the object, which can be a transmission function with both modulus and phase components. The technique has revolutionary implications for x-ray imaging of all classes of specimen.

/pdf/hard-x-ray-lensless-imaging-of-extended-objects-2fg1czgkvw.pdf

Hard-X-Ray Lensless Imaging of Extended Objects

We propose a method of iterative phase retrieval that uses measured intensities in the diffraction plane to solve the phase problem in a way that bypasses the problem of lens aberration, leading to greatly improved spatial resolution. This method is stable, easy to implement experimentally, and can be used to view a large area of the specimen when that is desired.

/pdf/a-phase-retrieval-algorithm-for-shifting-illumination-3s6ep81l6j.pdf

A phase retrieval algorithm for shifting illumination

We propose an iterative phase retrieval method that uses a series of diffraction patterns, measured only in intensity, to solve for both amplitude and phase of the image wave function over a wide field of view and at wavelength-limited resolution. The new technique requires an aperture that is scanned to two or more positions over the object wave function. A simple implementation of the method is modeled and demonstrated, showing how the algorithm uses overlapping data in real space to resolve ambiguities in the solution. The technique opens up the possibility of practical transmission lensless microscopy at subatomic resolution using electrons, x rays, or nuclear particles.

Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm.

http://xrm.phys.northwestern.edu/research/pdf_papers/2005/faulkner_ultramic_2005.pdf

Helen Mary Louise Faulkner

Papers

A phase retrieval algorithm for shifting illumination

Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm.

Error tolerance of an iterative phase retrieval algorithm for moveable illumination microscopy