Phase Retrieval From Two Defocused Images By The Transport Of Intensity Equation Formalism With Fast Fourier Transform
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| Total Pages | : |
| Release | : 2001 |
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The problem of phase retrieval from intensity measurements plays an important role in many fields of physical research, e.g. optics, electron and x-ray microscopy, crystallography, diffraction tomography and others. In practice the recorded images contain information only on the intensity distribution I(x, y)=[Psi]*[Psi]=[vert-bar]A[vert-bar][sup 2] of the imaging wave function[Psi]= A*exp( -i[var-phi]) and the phase information[var-phi](x, y) is usually lost. In general, the phase problem can be solved either by special holographic/interferometric methods, or by non-interferometric approaches based on intensity measurements in far Fraunhofer zone or in the Fresnel zone at two adjacent planes orthogonal to the optical axis. The latter approach uses the transport-of-intensity equation (TIE) formalism, introduced originally by Teague[1] and developed later in[2]. Applications of TIE to nonmagnetic materials and magnetic inductance mapping were successfully made in[3,4]. However, this approach still needs further improvement both in mathematics and in practical solutions, since the result is very sensitive to many experimental parameters.
| Author | : Graham N. Craik |
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| Release | : 2010 |
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This thesis considers the calculation of phase from sets of phase contrast and defocused images. An improvement to phase contrast imaging is developed that combines three phase contrast images. This method results in a reduction in the phase error by a factor of up to 20 in comparison to using a single image. Additionally the method offers the potential for optimisation and the extension to an arbitrary number of images. Phase diversity using defocused images is considered in more depth where the intensity transport equation is used to calculate the phase. First a Green's function approach to solving this equation was considered. One of the Green's functions stated in the literature is shown to be incorrect, the other two are shown to be correct both giving equivalent phase estimates. A further improvement is made to this method by removing the singularities in the phase calculation process. As an alternative to the Green's function solution a Fourier transform approach is also considered. A complete solution to the intensity transport equation is derived with inclusion of the boundary conditions. This completes the method incompletely described in the literature. Through simulation, generic key factors are identified for the potential optimisation of experimental and numerical process to improve the estimated phase. Determining 3D structural information of an object from the phase calculated in a single plane is considered using an iterative process. It is shown that this process is limited but can be used, in some cases, to generate an approximate representation of the object.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 307 |
| Release | : 2001-09-25 |
| Genre | : Technology & Engineering |
| ISBN | : 0080525466 |
Advances in Imaging and Electron Physics merges two long-running serials—Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.
| Author | : Mahmudunnabi Basunia |
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| Total Pages | : 78 |
| Release | : 2016 |
| Genre | : Optical measurements |
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Transport of intensity is a noninterferometric method to find the phase of an object by recording optical intensities at different distances of propagation. The transport of intensity equation results from the imaginary part of the complex paraxial wave equation and is equivalent to the principle of conservation of energy. The real part of the paraxial wave equation gives the eikonal equation in the presence of diffraction, which can be also termed the transport of phase equation. The amplitude and phase of the optical field must simultaneously satisfy both the real and imaginary parts of the paraxial wave equation during propagation. In this dissertation, it is demonstrated, using illustrative examples, how to exploit this to retrieve the phase through recursive calculations of the phase and intensity. This is achieved using the transport of intensity equation which is solved using standard Fourier transform techniques and the transport of phase equation, which is solved using a Gauss-Seidel iterative method. Examples include calculation of the imaged phase induced through self-phase modulation of a focused laser beam in a liquid, and the imaged phase of light reflected from a surface which yields its 3d surface profile.
| Author | : N.E. Hurt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 328 |
| Release | : 2001-11-30 |
| Genre | : Mathematics |
| ISBN | : 9781402003370 |
'Et moi, ... , si j'avait su comment en :revenir, One scrvice mathematics has rendered the je n'y scrais point alle.' human race. lt has put common sense back Jules Veme where it bdongs, on the topmost shelf next to the dusty canister labclled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Erle T. Bc1l 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'.All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
| Author | : Marc De Graef |
| Publisher | : Cambridge University Press |
| Total Pages | : 718 |
| Release | : 2003-03-27 |
| Genre | : Science |
| ISBN | : 9780521629959 |
A graduate level textbook covering the fundamentals of conventional transmission electron microscopy, first published in 2003.
| Author | : Alexander H. Barnett |
| Publisher | : Cambridge University Press |
| Total Pages | : 321 |
| Release | : 2022-05-05 |
| Genre | : Mathematics |
| ISBN | : 1009007785 |
Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and place it in the context of practical applications.
| Author | : Juan Martinez-Carranza |
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| Release | : 2017 |
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Dotyczy: ilościowe obrazowanie fazowe, równanie transportu intensywności, rekonstrukcja fazy, jednowiązkowa mikroskopia fazowa, algorytmy uciąglania fazy, quantitative phase imaging, transport of intensity equation, phase reconstruction, single beam phase microscopy, algorithms for phase unwrapping.
| Author | : Danielle Honigstein |
| Publisher | : |
| Total Pages | : 105 |
| Release | : 2011 |
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| Author | : K.R. Rao |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2011-02-21 |
| Genre | : Mathematics |
| ISBN | : 1402066295 |
This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
