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Ptychography
Ptychography (/t(a)ɪˈkɒgrəfi/ t(a)i-KO-graf-ee) is a computational microscopy method and a major advance of Coherent diffraction imaging, coherent diffractive imaging (CDI), which was first experimentally demonstrated in 1999 using synchrotron X-rays and iterative phase retrieval. It unifies principles from microscopy, microscopy and crystallography, crystallography to reconstruct high-resolution, quantitative images by analyzing a series of overlapping coherent diffraction patterns acquired as a focused beam is scanned across the sample. Its defining characteristic is translational Invariant (physics), invariance, which means that the interference patterns are generated by one constant function (e.g. a field of illumination or an aperture, aperture stop) moving Geometric terms of location, 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptychography Imaging Data Collection Single Aperture
Ptychography (/t(a)ɪˈkɒgrəfi/ t(a)i-KO-graf-ee) is a computational microscopy method and a major advance of coherent diffractive imaging (CDI), which was first experimentally demonstrated in 1999 using synchrotron X-rays and iterative phase retrieval. It unifies principles from microscopy and crystallography to reconstruct high-resolution, quantitative images by analyzing a series of overlapping coherent diffraction patterns acquired as a focused beam is scanned across the sample. 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" (, "ptychē" is 'fold') into one another as shown in the figure. ... [...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 ("ptych� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherent Diffraction Imaging
Coherent diffractive imaging (CDI) a computational microscopy method that reconstructs images from coherent diffraction patterns without the use of lenses. It was first experimentally demonstrated in 1999 by Miao and collaborators using synchrotron X-rays and iterative phase retrieval. CDI has been applied to image structures such as nanotubes, nanocrystals, porous nanocrystalline layers, defects, potentially proteins, and more. In CDI, a highly coherent beam of X-rays, electrons or other wavelike particle or photon is incident on an object. The beam scattered by the object produces a diffraction pattern downstream which is then collected by a detector. This recorded pattern is then used to reconstruct an image via an iterative feedback algorithm. Effectively, the objective lens in a typical microscope is replaced with software to convert from the reciprocal space diffraction pattern into a real space image. The advantage in using no lenses is that the final image is aberratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Rodenburg
John Marius Rodenburg is emeritus professor in the Department of Electronic and Electrical Engineering at the University of Sheffield. He was elected a Fellow of the Royal Society (FRS) in 2019 for "internationally recognised... work on revolutionising the imaging capability of light, X-ray and electron transmission microscopes". 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 worked until 1999 in the University of Cambridge as a University Research Fellow of the Royal Society. He is currently emeritus professor in the Department of Electronics and Electrical Engineering at the University of Sheffield. His research interests have mostly been in improving the resolution and other ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impulse Response
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system). In all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects. Since the impulse function contains all frequencies (see the Fourier transform of the Dirac delta function, showing infinite frequency bandwidth that the Dirac delta function has), the impulse response defines the response of a linear time-invariant system for all frequencies. Mathematical considerat ... [...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 f and g that produces a third function f*g, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term ''convolution'' refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). Graphically, it expresses how the 'shape' of one function is modified by the other. 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 f(x) or g(x) is reflected about the y-axis in convolution; thus i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image
An image or picture is a visual representation. An image can be Two-dimensional space, two-dimensional, such as a drawing, painting, or photograph, or Three-dimensional space, three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a Projector, projection on a surface, activation of electronic signals, or Display device, digital displays; they can also be reproduced through mechanical means, such as photography, printmaking, or Photocopier, photocopying. Images can also be Animation, animated through digital or physical processes. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term ''image'' (or ''optical image'') refers specifically to the reproduction of an object formed by light waves coming from the object. A ''volatile image'' exists or is perceived only for a short period. This may be a reflection of an object by a mirror, a projection of a camera obscura, or a scene d ... [...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 \ll 1 the diffracted wave is considered to be in the Fraunhofer 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction Pattern
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Diffraction is the same physical effect as interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed. 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 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. ... [...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, 21 is the product of 3 and 7 (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). When one factor is an integer, the product is called a '' multiple''. 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 di ... [...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 import ... [...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 eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
