scholarly journals The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

2018 ◽  
Vol 25 (3) ◽  
pp. 717-728 ◽  
Author(s):  
Anders Filsøe Pedersen ◽  
Hugh Simons ◽  
Carsten Detlefs ◽  
Henning Friis Poulsen
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Imaging System ◽  
Single Step ◽  
Fourier Optics ◽  
Simulation Tool ◽  
Optical Components ◽  
X Ray ◽  
Chromatic Aberrations ◽  
On Line

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non-monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.

Early results for the STIX image reconstruction problem: imaging from visibility amplitudes

2021 ◽  
Author(s):  
michele piana ◽  
paolo massa ◽  
emma perracchione ◽  
andrea francesco battaglia ◽  
federico benvenuto ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Image Reconstruction ◽  
Imaging System ◽  
X Rays ◽  
Pixel Detector ◽  
Reconstruction Problem ◽  
Solar Dynamics Observatory ◽  
X Ray ◽  
Early Results ◽  
The Fourier Transform

<p>The Spectrometer/Telescope for Imaging X-rays (STIX) is the instrument of the Solar Orbiter mission conceived for the observation of the hard X-ray flaring emission, with the objective of providing insights on the diagnosis of thermal and non-thermal accelerated electrons at the Sun. The STIX imaging system is composed of 30 pairs of tungsten grids, each one placed in front of a four-pixel detector, and produces as many Fourier components of the angular distribution of the flaring source, via Moiré pattern modulation. Therefore, the data recorded by STIX, named visibilities, can be interpreted as a sparse sampling of the Fourier transform of the X-ray signal and the corresponding image reconstruction problem requires the inversion of the Fourier transform from limited data, usually addressed with regularization techniques. Since the current calibration status of STIX measurements still prevents the use of visibility phases for imaging purposes, here we propose a parameter identification process based on forward fitting  just the amplitude of the experimental visibilities. Specifically, we have parameterized the flaring source by means of pre-assigned source shapes (e.g., circular and elliptical bi-variate Gaussian functions), and we relied on several approaches to non-linear optimization in order to estimating the shape parameters. In particular, we have implemented a forward-fit method based on deterministic chi-squared minimization, a stochastic optimization algorithm and a deep neural approach based on ensemble learning, also equipping them with an ad hoc statistical technique for uncertainty quantification. The performances of the three approaches are compared in the case of both microflares and M class events recorded by STIX during its commissioning phase and the validation of results is realized also exploiting the EUV information provided by the Atmospheric Imaging Assembly within the Solar Dynamics Observatory.</p>

scholarly journals X-ray coherent diffraction interpreted through the fractional Fourier transform

2012 ◽  
Vol 407 (11) ◽  
pp. 1855-1858 ◽  
Author(s):  
D. Le Bolloc'h ◽  
E. Pinsolle ◽  
J.F. Sadoc
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
X Ray

USE OF A SOFT X-RAY IMAGING SYSTEM FOR ON-LINE DETECTION OF SPONGY TISSUE IN 'ALPHONSO' MANGO FRUIT

2013 ◽  
pp. 575-578 ◽  
Author(s):  
V.B. Mehta ◽  
P.M. Haldankar ◽  
M.M. Burondkar ◽  
B.B. Jadhav ◽  
V.V. Shinde ◽  
...  
Keyword(s):  
Imaging System ◽  
Line Detection ◽  
Spongy Tissue ◽  
Mango Fruit ◽  
X Ray ◽  
X Ray Imaging ◽  
On Line ◽  
Alphonso Mango

New Aspects in the Design of Electron Optical Magnification Systems

1972 ◽  
Vol 30 ◽  
pp. 606-607
Author(s):  
Willem H.J. Andersen
Keyword(s):  
Electron Microscope ◽  
Imaging System ◽  
Chromatic Aberration ◽  
Research Tool ◽  
Energy Losses ◽  
Objective Lens ◽  
Theoretical Limit ◽  
Optical Magnification ◽  
Chromatic Aberrations ◽  
High Degree

Electron microscope design, and particularly the design of the imaging system, has reached a high degree of perfection. Present objective lenses perform up to their theoretical limit, while the whole imaging system, consisting of three or four lenses, provides very wide ranges of magnification and diffraction camera length with virtually no distortion of the image. Evolution of the electron microscope in to a routine research tool in which objects of steadily increasing thickness are investigated, has made it necessary for the designer to pay special attention to the chromatic aberrations of the magnification system (as distinct from the chromatic aberration of the objective lens). These chromatic aberrations cause edge un-sharpness of the image due to electrons which have suffered energy losses in the object.There exist two kinds of chromatic aberration of the magnification system; the chromatic change of magnification, characterized by the coefficient Cm, and the chromatic change of rotation given by Cp.

A Retrieval System for a Library of Pathology Reports, Slides and Kodachromes

1972 ◽  
Vol 11 (03) ◽  
pp. 152-162 ◽  
Author(s):  
P. GAYNON ◽  
R. L. WONG
Keyword(s):  
Medical Records ◽  
Operative Procedure ◽  
Clinical Findings ◽  
Free Text ◽  
X Ray ◽  
Inverted File ◽  
Natural Language Parsing ◽  
On Line ◽  
Pathology Reports ◽  
Frequency Counts

With the objective of providing easier access to pathology specimens, slides and kodachromes with linkage to x-ray and the remainder of the patient’s medical records, an automated natural language parsing routine, based on dictionary look-up, was written for Surgical Pathology document-pairs, each consisting of a Request for Examination (authored by clinicians) and its corresponding report (authored by pathologists). These documents were input to the system in free-text English without manual editing or coding.Two types of indices were prepared. The first was an »inverted« file, available for on-line retrieval, for display of the content of the document-pairs, frequency counts of cases or listing of cases in table format. Retrievable items are patient’s and specimen’s identification data, date of operation, name of clinician and pathologist, etc. The English content of the operative procedure, clinical findings and pathologic diagnoses can be retrieved through logical combination of key words. The second type of index was a catalog. Three catalog files — »operation«, »clinical«, and »pathology« — were prepared by alphabetization of lines formed by the rotation of phrases, headed by keywords. These keywords were automatically selected and standardized by the parsing routine and the phrases were extracted from each sentence of each input document. Over 2,500 document-pairs have been entered and are currently being utilized for purpose of medical education.

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