T. B. Edo

Separation of three-dimensional scattering effects in tilt-series Fourier ptychography

We investigate a strategy for separating the influence of three-dimensional scattering effects in tilt-series reconstruction, a method for computationally increasing the resolution of a transmission microscope with an objective lens of small numerical aperture, as occurs in the transmission electron microscope (TEM). Recent work with visible light refers to the method as Fourier ptychography. To date, reconstruction methods presume that the object is thin enough so that the beam tilt induces only a shift of the diffraction pattern in the back focal plane. In fact, it is well known that the diffraction pattern changes as a function of beam tilt when the object is thick. In this paper, we use a simple visible light model to demonstrate a proof-of-principle of a new reconstruction algorithm that can cope with this difficulty and compare it with the aperture-scanning method. Although the experiment uses a model specimen with just two distinct layers separated along the optic axis, it should in principle be extendable to continuous objects.

Multiple mode x-ray ptychography using a lens and a fixed diffuser optic

We employ a novel combination of a Fresnel lens and a diffuser for x-ray ptychography. The setup uses increased flux by enlarging the width of the coherence-defining slits upstream of the experimental station. In the reconstruction algorithm, modal decomposition is used to account for the resulting partial coherence in the beam. We show that if the object has sparse feactures and large areas of flat contrast, the diffuser facilitates a better reconstruction and the extra diversity in the data also allows cleaner separation of the constituent modes in the illumination. The setup also allows a quick, real-time measure of the beam coherence.

Probe position recovery for ptychographical imaging

Ptychographical iterative phase retrieval is a promising new transmission imaging technique which uses a set of measured intensities from the consecutive illumination of overlapping regions of the specimen to form an image of the transmission function in phase and amplitude. Although the technique has been shown to work very effectively in both the light-optical and X-ray domains, electron ptychography poses significant difficulties, not least of which is the uncertainty in probe position due to drift and other instabilities. We demonstrate three methods for deriving the relative positions of the illumination spot on the specimen a-posteriori.

Ptychography: a novel phase retrieval technique, advantages and its application

This paper is intended to introduce ptychography, a novel and very promising phase retrieval technique. It is based on the lens-less recording of a series of diffraction patterns caused by coherent object illumination. In the visible region of light, ptychography has successfully been implemented for visible light microscopy and optical metrology. Ptychography has also successfully been applied to X-ray microscopy where it is difficult to manufacture good quality lenses and where, at high X-ray energies, absorption contrast is low but where phase contrast is significant. In the course of this paper theoretical fundamentals of ptychography are explained, advantages in comparison to traditional optical techniques are represented and applications are shown.

Resolution Improvement in Coherent Diffractive Imaging (Ptychography)

In the field of diffraction microscopy, a coherent illuminating beam of finite extent impinges on a specimen and the resulting diffraction pattern is recorded. The complex transmission function of the specimen is recovered using iterative algorithms that exploit redundancies in the measured data. This is normally oversampling of the diffraction pattern when it is known the object or illumination is of the finite size. In the case of curved illumination, there is no direct relationship between the collection angle and the resolution of the recovered image. The result is a recovered image with varying resolution over the field of view as different parts of the object are illuminated by different wave-vectors. An extension of the Coherent Diffractive Imaging (CDI) technique (employing a single diffraction pattern) is to use multiple diffraction patterns collected from adjacent parts of the object and is called ptychography. In ptychography, translation of the illuminating wave across the specimen introduces translational diversity that leads to faster convergence of iterative phase retrieval as well as extending the field of view. In this paper we investigate the expression of resolution information in the diffraction pattern using curved illumination in order to facilitate specimen recovery with uniformly improved resolution over the entire field of view.

Noise limit on practical electron ptychography

Ptychography is a wavelength-limited phase retrieval method that promises to provide sub-0.5A resolution in the electron microscope, even if the lens employed (which is required only to form an illumination spot) can itself only achieve rather modest resolution. The fidelity of a practical specimen reconstruction using ptychography hinges on various experimental factors, the major one of which is the source brightness. Achieving a high degree of coherence of an electron beam requires source demagnification which reduces the electron counts reaching the detector for a given exposure time. Specimen drift, damage and contamination also limits the practical exposure time. In this paper we investigate the effect of the counting statistics required for a good quality ptychographic reconstruction