Broadband ptychography using curved wavefront illumination

We examine the interplay between spectral bandwidth and illumination curvature in ptychography. By tailoring the divergence of the illumination, broader spectral bandwidths can be tolerated without requiring algorithmic modifications to the forward model. In particular, a strong wavefront curvature transitions a far-field diffreaction geometry to an effectively near-field one, which is lees affected by temporal coherence effects. The relaxed temporal coherence requirements allow for leveraging wider spectral bandwidths and larger illumination spots. Our findings open up new avenues towards utilizing pink and broadband beams for increased flux and throughput at both synchrotron facilities and lab-scale beamlines

Computational Depth-resolved Imaging and Metrology

In this thesis, the main research challenge boils down to extracting 3D spatial information of an object from 2D measurements using light. Our goal is to achieve depth-resolved tomographic imaging of transparent or semi-transparent 3D objects, and to perform topography characterization of rough surfaces. The essential tool we used is computational imaging, where depending on the experimental scheme, often indirect measurements are taken, and tailored algorithms are employed to perform image reconstructions. The computational imaging approach enables us to relax the hardware requirement of an imaging system, which is essential when using light in the EUV and x-ray regimes, where high-quality optics are not readily available. In this thesis, visible and infrared light sources are used, where computational imaging also offers several advantages. First of all, it often leads to a simple, flexible imaging system with low cost. In the case of a lensless configuration, where no lenses are involved in the final image-forming stage between the object and the detector, aberration-free image reconstructions can be obtained. More importantly, computational imaging provides quantitative reconstructions of scalar electric fields, enabling phase imaging, numerical refocus, as well as 3D imaging

Image Recovery for Blind Polychromatic Ptychography

Ptychography is a lensless imaging technique, which considers reconstruction from a set of far-field diffraction patterns obtained by illuminating small overlapping regions of the specimen. In many cases, a distribution of light inside the illuminated region is unknown and has to be estimated along with the object of interest. This problem is referred to as blind ptychography. While in ptychography the illumination is commonly assumed to have a point spectrum, in this paper we consider an alternative scenario with non-trivial light spectrum known as blind polychromatic ptychography. Firstly, we show that non-blind polychromatic ptychography can be seen as a recovery from quadratic measurements. Then, a reconstruction from such measurements can be performed by a variant of Amplitude Flow algorithm, which has guaranteed sublinear convergence to a critical point. Secondly, we address recovery from blind polychromatic ptychographic measurements by devising an alternating minimization version of Amplitude Flow and showing that it converges to a critical point at a sublinear rate. Keywords: ptychography, phase retrieval, blind, alternating minimization, gradient descent.Comment: 33 pages, 11 figure

Spectroscopic imaging with single acquisition ptychography and a hyperspectral detector

We present a new method of single acquisition spectroscopic imaging with high spatial resolution. The technique is based on the combination of polychromatic synchrotron radiation and ptychographic imaging with a recently developed energy discriminating detector. We demonstrate the feasibility with a Ni-Cu test sample recorded at I13-1 of the Diamond Light Source, UK. The two elements can be clearly distinguished and the Ni absorption edge is identified. The results prove the feasibility of obtaining high-resolution structural and chemical images within a single acquisition using a polychromatic X-ray beam. The capability of resolving the absorption edge applies to a wide range of research areas, such as magnetic domains imaging and element specific investigations in biological, materials, and earth sciences. The method utilises the full available radiation spectrum and is therefore well suited for broadband radiation sources

New approaches for coherent and incoherent implementation of x-ray phase contrast imaging

Two new x-ray imaging modalities exploiting the phase delay electromagnetic waves experience when travelling through matter are introduced in this work. The first, called beam tracking, allows the measurement of three different physical properties of an object: absorption, refraction and ultra-small-angle scattering. This is achieved by tracking the variations induced to a reference beam by a sample through a multi-Gaussian interpolation. Beam tracking can be implemented with both monochromatic, coherent radiation (available at e.g. synchrotron facilities) and polychromatic, incoherent radiation produced by standard laboratory sources. The nature of the three extracted signals allows the implementation of beam tracking in computed tomography, resulting in the three-dimensional reconstruction of the real and imaginary part of the sample refractive index, alongside its local scattering power. The second proposed method, called one dimensional ptychography, exploits the coherent properties of synchrotron radiation to retrieve the sample complex refractive index. The peculiar feature of this method is the strongly asymmetric beam used to illuminate the sample. Unlike standard ptychographic techniques, this enables scanning the sample in one direction only, which can lead to a possible reduction in exposure time when large field of views are covered. At the same time, ptychographic, sub-pixel resolution can be obtained only in the scan direction, while pixel-limited resolution is obtained in the orthogonal one. Prior to the introduction of these methods, the theoretical foundations are laid down, and the development of a fast and effective simulation software allowing their implementation is described

Diffraction tomography with Fourier ptychography

This paper presents a technique to image the complex index of refraction of a sample across three dimensions. The only required hardware is a standard microscope and an array of LEDs. The method, termed Fourier ptychographic tomography (FPT), first captures a sequence of intensity-only images of a sample under angularly varying illumination. Then, using principles from ptychography and diffraction tomography, it computationally solves for the sample structure in three dimensions. The experimental microscope demonstrates a lateral spatial resolution of 0.39 μm and an axial resolution of 3.7 μm at the Nyquist–Shannon sampling limit (0.54 and 5.0 μm at the Sparrow limit, respectively) across a total imaging depth of 110 μm. Unlike competing methods, this technique quantitatively measures the volumetric refractive index of primarily transparent and contiguous sample features without the need for interferometry or any moving parts. Wide field-of-view reconstructions of thick biological specimens suggest potential applications in pathology and developmental biology

Numerical and experimental aspect of coherent lensless imaging

This thesis is devoted to the understanding, application, and extension of coherent lensless imaging methods for microscopy purposes. Particular attention is given to the Fourier transform holography and coherent diffractive imaging methods.These two methods share several properties such as the ability for singleshot imaging and their experimental geometries, but differ greatly in their reconstruction approach. Holographic approaches use reference waves to encode phase information into the measurements which means the reconstruction quality is controlled, to a large extent, by the characteristics of the reference wave. In contrast, coherent diffractive imaging utilizes prior knowledge to iteratively recover the phase information; this has the effect that the reconstruction quality is independent of any optics or references, but relies heavily on the performance of iterative numerical algorithms. The complex nature of the phase retrieval problem raises questions regarding the existence and uniqueness of a solution which makes understanding the numerical and mathematical aspects of the problem of central importance. The main topics in this thesis include: the extension of coherent diffractive imaging to multi-wavelength diffraction data, effects related to optically thick references in Fourier transform holography and an alternative numerical approach to phase retrieval which is based on non-rigid image registration. Along the way, various topics are covered which form the foundations of these techniques, or could be useful to a practioner in the field