|
Electron Ptychography
Ptychography (/t(ʌ)ɪˈkogræfi/ t(a)i-KO-graf-ee) is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function (e.g. a field of illumination or an aperture stop) moving laterally by a known amount with respect to another constant function (the specimen itself or a wave field). The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" ( grc, πτύξ is 'fold') into one another as shown in the figure. Ptychography can be used with visible light, X-rays, extreme ultraviolet (EUV) or electrons. Unlike conventional lens imaging, ptychography is unaffected by lens-induced aberrations or diffraction effects caused by limited numerical aperture. This is partic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptychography Imaging Data Collection Single Aperture
Ptychography (/t(ʌ)ɪˈkogræfi/ t(a)i-KO-graf-ee) is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function (e.g. a field of illumination or an aperture stop) moving laterally by a known amount with respect to another constant function (the specimen itself or a wave field). The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" ( grc, πτύξ is 'fold') into one another as shown in the figure. Ptychography can be used with visible light, X-rays, extreme ultraviolet (EUV) or electrons. Unlike conventional lens imaging, ptychography is unaffected by lens-induced aberrations or diffraction effects caused by limited numerical aperture. This is particul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects. Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They have wide application in system identification, optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, slope stability analysis and man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Ptychography
Fourier ptychography is a computational imaging technique based on optical microscopy that consists in the synthesis of a wider numerical aperture from a set of full-field images acquired at various coherent illumination angles, resulting in increased resolution compared to a conventional microscope. Each image is acquired under the illumination of a coherent light source at various angles of incidence (typically from an array of LEDs); the acquired image set is then combined using an iterative phase retrieval algorithm into a final high-resolution image that can contain up to a billion pixels (a gigapixel) with diffraction-limited resolution, resulting in a high space-bandwidth product. Fourier ptychography reconstructs the complex image of the object (with quantitative phase information), but contrary to holography, it is a non-interferometric imaging technique and thus often easier to implement. The name "ptychography" comes from the ancient Greek word πτυχή ("to fold ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fresnel Diffraction Pattern
In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, , of the optical arrangement. When F \gg 1 the diffracted wave is considered to be in the near field. However, the validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must be negligible, a condition that may be written as \frac \ll 1, where \theta is the maximal angle described by \theta \approx a/L, and the same as in the definition of the Fresnel number. The m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction Pattern
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength, as shown in the inserted image. This is due to the addition, or interference, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product (mathematics)
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 30 is the product of 6 and 5 (the result of multiplication), and x\cdot (2+x) is the product of x and (2+x) (indicating that the two factors should be multiplied together). The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the ''commutative law'' of multiplication. When matrices or members of various other associative algebras are multiplied, the product usually depends on the order of the factors. Matrix multiplication, for example, is non-commutative, and so is multiplication in other algebras in general as well. There are many different kinds of products in mathematics: besides being able to multiply just numbers, polynomials or matrices, one can also define products on many different algebraic structures. Product of two numbers Product of a seque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invariant (mathematics)
In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class. Invariants are used in diverse areas of mathematics such as geometry, topology, algebra and discrete mathematics. Some important classes of transformations are defined by an invariant they leave unchanged. For example, conformal maps are defined as transformations of the plane that preserve angles. The discovery of invariants is an important ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Rodenburg
John Marius Rodenburg One or more of the preceding sentences incorporates text from the royalsociety.org website where: is Professor in the Department of Electronic and Electrical Engineering at the University of Sheffield. Education Rodenburg was educated at University of Exeter where he was awarded a Bachelor of Science degree in Physics with Electronics. He moved to the Cavendish Laboratory to complete his PhD on the detection and interpretation of electron diffraction patterns which was awarded by the University of Cambridge in 1986. Career and research Rodenburg's research interests are in microscopy, materials analysis and the use of ptychography and algorithms for phase retrieval. He co-founded Phase Focus Limited and served as its director and Chief Scientific Officer from 2006 to 2015. Awards and honours Rodenburg was elected a Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wigner Distribution Function
The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis. The WDF was first proposed in physics to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, and it is of importance in quantum mechanics in phase space (see, by way of comparison: ''Wigner quasi-probability distribution'', also called the ''Wigner function'' or the ''Wigner–Ville distribution''). Given the shared algebraic structure between position-momentum and time-frequency conjugate pairs, it also usefully serves in signal processing, as a transform in time-frequency analysis, the subject of this article. Compared to a short-time Fourier transform, such as the Gabor transform, the Wigner distribution function provides the highest possible temporal vs frequency resolution which is mathematically possible within the limitations of the uncertainty principle. The downside is the introduction of large cross terms between every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Retrieval
Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal F(k), of amplitude , F (k), , and phase \psi(k): ::F(k) = , F(k), e^ =\int_^ f(x)\ e^\,dx where ''x'' is an ''M''-dimensional spatial coordinate and ''k'' is an ''M''-dimensional spatial frequency coordinate. Phase retrieval consists of finding the phase that satisfies a set of constraints for a measured amplitude. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which M = 2. Uniqueness theorems for both 1-D and 2-D cases of the phase retrieval problem, including the phaseless 1-D inverse scattering problem, were proven by Klibanov and his collaborators (see References). Problem formulation Here we consider 1-D discrete Fourier transform (DFT) phase retrieval problem. The DFT of a complex signal f /math> is given by F \sum_^ f e^=, F \cdot e^ \quad k=0,1, \ldots, N-1, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
