Ptychography

Abstract

Ptychography is a computational imaging technique. A detector records an extensive data set consisting of many inference patterns obtained as an object is displaced to various positions relative to an illumination field. A computer algorithm of some type is then used to invert this data into an image. It has three key advantages: it does not depend upon a good-quality lens, or indeed on using any lens at all; it can obtain the image wave in phase as well as in intensity; and it can self-calibrate in the sense that errors that arise in the experimental set-up can be accounted for and their effects removed. Its transfer function is in theory perfect, with resolution being wavelength-limited. Although the main concepts of ptychography were developed many years ago, it has only recently (over the last ten years) become widely adopted. This chapter surveys visible light, X-ray, electron, and EUV ptychography as applied to microscopic imaging. It describes the principal experimental arrangements used at these various wavelengths. It reviews the most common inversion algorithms that are nowadays employed, giving examples of meta code to implement these. It describes, for those new to the field, how to avoid the most common pitfalls in obtaining good quality reconstructions. It also discusses more advanced techniques such as modal decomposition and strategies to cope with 3D multiple scattering. 'STE/XM'. This is because, being optically equivalent to one another, ptychography treats them both identically.Ronchigram: This term is used in the electron literature but rarely in the X-ray imaging literature. It refers to the unscattered beam created by a convergent focused beam in the far-field. This is usually circular in electron microscopy (being the shadow image cast by the condenser aperture). For an X-ray Fresnel zone plate lens it is usually doughnut-shaped because of the central stop required to block undiffracted intensity. If Kirkpatrick-Baez (KB) mirrors are used, it is rectangular. When the probe is defocused from the object plane, it is equivalent to a Gabor in-line hologram.Circles: As a warning to the reader, we remark that the science of ptychography involves lots of diagrams of circles. The probe function (in real space) is often circular, or represented by a circle. Diffraction disks (in reciprocal space) from a crystalline object are circular when a focused lens with an aperture in its back focal plane is used to form the probe. The Fat-H and the trotters are made out of parts of circles. Fourier ptychography and SAP ptychography have their own circular apertures. The modulus constraint in the complex plane is circular. Know which circle is which: they are not all the same! 2) A Brief HistoryThis Chapter is not an historical review. However, for the benefit of those new to the subject, we now make one or two non-essential observations about its history.First -where did the name come from? Ptychography derives from the Greek 'ptycho', meaning to fold. Hoppe and Hegerl [1] introduced it to describe a method ...

Hot electrons in a nanowire hard X-ray detector

“…In particular, a spatial resolution of 0.51 µm was achieved for InP nanowires 23 , much higher than in conventional detectors with pixel sizes of tens of microns 26 . Yet, in order to reach such a resolution, sophisticated and computationally demanding ptychographic reconstruction techniques 27 were required.…”

Fourier ptychography: current applications and future promises

“…Since its first demonstration, a number of alternative reconstruction algorithms have been proposed to improve the reconstructed image quality and speed. A careful presentation of different ptychography algorithms and their advantages and benchmarks are outside of this review's scope, but may be found elsewhere in the literature [19,[71][72][73][74]. Readers interested in learning about the reconstruction process in more detail should refer to [75] which provides detailed steps along with some Matlab tutorials.…”

“…Properties of a ptychographic system that help differentiate it from other coherent diffractive imaging methods were previously defined [88]. These definitions are also applicable to FP due to the reciprocity between the two procedures [72]. We restate those properties in the context of FP as follows:…”

“…Apart from obvious experimental distinctions and their mathematical reciprocity, a key difference with FP is that its imaging FOV is typically divided into multiple small segments and processed independently [72]. The illumination is treated as coherent within each small image segment [27] and this division allows one to correct for spatially varying aberrations [24,31,89].…”

Reference-free quantitative microscopic imaging of coherent arbitrary vectorial light beams

“…In most previous versions of ptychography, both object and illumination were modeled as scalar quantities [21]. Their reconstructions could be performed simultaneously by phase retrieval algorithms, thanks to the diversity introduced by the ptychographic scan [22,23]. Here in comparison, the vectorial formalism of Eq.…”