scholarly journals On the Reconstruction of the Center of a Projection by Distances and Incidence Relations

2020 ◽  
Author(s):  
András Pongrácz ◽  
Csaba Vincze
Keyword(s):  
Algebraic Surface ◽  
Basic Problem ◽  
Rotational Symmetry ◽  
Image Plane ◽  
Equivalent Condition ◽  
Central Projection ◽  
Profile Curve ◽  
Reconstruction Process ◽  
Restricted Area ◽  
Photographic Images

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.

Measurements in 3D images

1991 ◽  
Vol 49 ◽  
pp. 408-409
Author(s):  
John C. Russ
Keyword(s):  
Three Dimensional ◽  
Image Plane ◽  
X Rays ◽  
Traditional Use ◽  
3D Images ◽  
Confocal Scanning Laser Microscope ◽  
Hard Materials ◽  
Depth Direction ◽  
Confocal Scanning ◽  
Confocal Scanning Laser

Three-dimensional (3D) images consisting of arrays of voxels can now be routinely obtained from several different types of microscopes. These include both the transmission and emission modes of the confocal scanning laser microscope (but not its most common reflection mode), the secondary ion mass spectrometer, and computed tomography using electrons, X-rays or other signals. Compared to the traditional use of serial sectioning (which includes sequential polishing of hard materials), these newer techniques eliminate difficulties of alignment of slices, and maintain uniform resolution in the depth direction. However, the resolution in the z-direction may be different from that within each image plane, which makes the voxels non-cubic and creates some difficulties for subsequent analysis.

Comparison of Conventional and Electron Spectroscopic Imaging in the Fixed Beam Electron Microscope of Ordered Protein Arrays

1985 ◽  
Vol 43 ◽  
pp. 74-75
Author(s):  
E. L. Buhle ◽  
U. Aebi
Keyword(s):  
Image Processing ◽  
Electron Microscope ◽  
High Resolution ◽  
Image Plane ◽  
Electron Spectroscopic Imaging ◽  
Protein Arrays ◽  
Beam Electron ◽  
Average Unit ◽  
Fixed Beam ◽  
Energy Components

CTEM brightfield images are formed by a combination of relatively high resolution elastically scattered electrons and unscattered and inelastically scattered electrons. In the case of electron spectroscopic images (ESI), the inelastically scattered electrons cause a loss of both contrast and spatial resolution in the image. In the case of ESI imaging on the Zeiss EM902, the transmited electrons are dispersed into their various energy components by passing them through a magnetic prism spectrometer; a slit is then placed in the image plane of the prism to select the electrons of a given energy loss for image formation. The purpose of this study was to compare CTEM with ESI images recorded on a Zeiss EM902 of ordered protein arrays. Digital image processing was employed to analyze the average unit cell morphologies of the two types of images.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

The restoration of blurred electron micrographs

1986 ◽  
Vol 44 ◽  
pp. 180-181
Author(s):  
Bridget Carragher ◽  
David A. Bluemke ◽  
Michael J. Potel ◽  
Robert Josephs
Keyword(s):  
Cross Section ◽  
Electron Micrographs ◽  
Relative Motion ◽  
Finite Thickness ◽  
Image Plane ◽  
Helical Axis ◽  
Thin Sections ◽  
Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

Electron holography of p-n junctions

1996 ◽  
Vol 54 ◽  
pp. 974-975
Author(s):  
B.G. Frost ◽  
D.C. Joy ◽  
L.F. Allard ◽  
E. Voelkl
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Field Emission ◽  
Ccd Camera ◽  
Image Plane ◽  
Reference Wave ◽  
Field Of View ◽  
Control Mode ◽  
Objective Lens ◽  
Electron Holography

A wide holographic field of view (up to 15 μm in the Hitachi-HF2000) is achieved in a TEM by switching off the objective lens and imaging the sample by the first intermediate lens. Fig.1 shows the corresponding ray diagram for low magnification image plane off-axis holography. A coherent electron beam modulated by the sample in its amplitude and its phase is superimposed on a plane reference wave by a negatively biased Möllenstedt-type biprism.Our holograms are acquired utilizing a Hitachi HF-2000 field emission electron microscope at 200 kV. Essential for holography are a field emission gun and an electron biprism. At low magnification, the excitation of each lens must be appropriately adjusted by the free lens control mode of the microscope. The holograms are acquired by a 1024 by 1024 slow-scan CCD-camera and processed by the “Holoworks” software. The hologram fringes indicate positively and negatively charged areas in a sample by the direction of the fringe bending (Fig.2).

Five-Dimensional Microscopy using Widefield-Deconvolution: Practical Considerations and Biological Applications

1996 ◽  
Vol 54 ◽  
pp. 268-269
Author(s):  
W.F. Marshall ◽  
K. Oegema ◽  
J. Nunnari ◽  
A.F. Straight ◽  
D.A. Agard ◽  
...  
Keyword(s):  
Confocal Microscopy ◽  
High Speed ◽  
Laser Scanning ◽  
Ccd Camera ◽  
Image Plane ◽  
Time Lapse ◽  
Laser Scanning Confocal Microscopy ◽  
Three Dimensions ◽  
Excitation Light ◽  
Cooled Ccd

The ability to image cells in three dimensions has brought about a revolution in biological microscopy, enabling many questions to be asked which would be inaccessible without this capability. There are currently two major methods of three dimensional microscopy: laser-scanning confocal microscopy and widefield-deconvolution microscopy. The method of widefield-deconvolution uses a cooled CCD to acquire images from a standard widefield microscope, and then computationally removes out of focus blur. Using such a scheme, it is easy to acquire time-lapse 3D images of living cells without killing them, and to do so for multiple wavelengths (using computer-controlled filter wheels). Thus, it is now not only feasible, but routine, to perform five dimensional microscopy (three spatial dimensions, plus time, plus wavelength).Widefield-deconvolution has several advantages over confocal microscopy. The two main advantages are high speed of acquisition (because there is no scanning, a single optical section is acquired at a time by using a cooled CCD camera) and the use of low excitation light levels Excitation intensity can be much lower than in a confocal microscope for three reasons: 1) longer exposures can be taken since the entire 512x512 image plane is acquired in parallel, so that dwell time is not an issue, 2) the higher quantum efficiently of a CCD detect over those typically used in confocal microscopy (although this is expected to change due to advances in confocal detector technology), and 3) because no pinhole is used to reject light, a much larger fraction of the emitted light is collected. Thus we can typically acquire images with thousands of photons per pixel using a mercury lamp, instead of a laser, for illumination. The use of low excitation light is critical for living samples, and also reduces bleaching. The high speed of widefield microscopy is also essential for time-lapse 3D microscopy, since one must acquire images quickly enough to resolve interesting events.

Quantitative analysis by reconstruction of HREM focal series

1994 ◽  
Vol 52 ◽  
pp. 740-741
Author(s):  
W. Coene ◽  
A. Thust ◽  
M. Op de Beeck ◽  
D. Van Dyck
Keyword(s):  
Phase Retrieval ◽  
Image Plane ◽  
Initial Guess ◽  
Recursive Least Squares ◽  
Objective Lens ◽  
Electron Wave ◽  
Electron Sources ◽  
Original Algorithm ◽  
Coherent Field ◽  
Direct Interpretation

Compared to conventional electron sources, the use of a highly coherent field-emission gun (FEG) in TEM improves the information resolution considerably. A direct interpretation of this extra information, however, is hampered since amplitude and phase of the electron wave are scrambled in a complicated way upon transfer from the specimen exit plane through the objective lens towards the image plane. In order to make the additional high-resolution information interpretable, a phase retrieval procedure is applied, which yields the aberration-corrected electron wave from a focal series of HRTEM images (Coene et al, 1992).Kirkland (1984) tackled non-linear image reconstruction using a recursive least-squares formalism in which the electron wave is modified stepwise towards the solution which optimally matches the contrast features in the experimental through-focus series. The original algorithm suffers from two major drawbacks : first, the result depends strongly on the quality of the initial guess of the first step, second, the processing time is impractically high.

Tandem scanning confocal light microscopy as compared with x-ray diffraction for characterizing the behavior of clays in fluid-saturated petroleum reservoir rock

1989 ◽  
Vol 47 ◽  
pp. 148-149
Author(s):  
C.J. Stuart ◽  
B.E. Viani ◽  
J. Walker ◽  
T.H. Levesque
Keyword(s):  
Light Microscopy ◽  
Image Plane ◽  
Reservoir Rock ◽  
Depth Of Field ◽  
Objective Lens ◽  
Scanning System ◽  
Light Sources ◽  
Petroleum Reservoir ◽  
Image Recording ◽  
Scan Speed

Many techniques of imaging used to characterize petroleum reservoir rocks are applied to dehydrated specimens. In order to directly study behavior of fines in reservoir rock at conditions similar to those found in-situ these materials need to be characterized in a fluid saturated state.Standard light microscopy can be used on wet specimens but depth of field and focus cannot be obtained; by using the Tandem Scanning Confocal Microscope (TSM) images can be produced from thin focused layers with high contrast and resolution. Optical sectioning and extended focus images are then produced with the microscope. The TSM uses reflected light, bulk specimens, and wet samples as opposed to thin section analysis used in standard light microscopy. The TSM also has additional advantages: the high scan speed, the ability to use a variety of light sources to produce real color images, and the simple, small size scanning system. The TSM has frame rates in excess of normal TV rates with many more lines of resolution. This is accomplished by incorporating a method of parallel image scanning and detection. The parallel scanning in the TSM is accomplished by means of multiple apertures in a disk which is positioned in the intermediate image plane of the objective lens. Thousands of apertures are distributed in an annulus, so that as the disk is spun, the specimen is illuminated simultaneously by a large number of scanning beams with uniform illumination. The high frame speeds greatly simplify the task of image recording since any of the normally used devices such as photographic cameras, normal or low light TV cameras, VCR or optical disks can be used without modification. Any frame store device compatible with a standard TV camera may be used to digitize TSM images.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

Detection, Averaging, and 3D Reconstruction of Biological Specimens on Hypercubes (Transputer-based) Computers

1990 ◽  
Vol 48 (1) ◽  
pp. 454-455
Author(s):  
Jose-Maria Carazo ◽  
I. Benavides ◽  
S. Marco ◽  
J.L. Carrascosa ◽  
E.L. Zapata
Keyword(s):  
3D Reconstruction ◽  
3D Structure ◽  
Three Dimensional ◽  
Software Tools ◽  
Mapping Method ◽  
Computer Architectures ◽  
Parallel Computer ◽  
Reconstruction Process ◽  
Computing Power ◽  
Order Of Magnitude

Obtaining the three-dimensional (3D) structure of negatively stained biological specimens at a resolution of, typically, 2 - 4 nm is becoming a relatively common practice in an increasing number of laboratories. A combination of new conceptual approaches, new software tools, and faster computers have made this situation possible. However, all these 3D reconstruction processes are quite computer intensive, and the middle term future is full of suggestions entailing an even greater need of computing power. Up to now all published 3D reconstructions in this field have been performed on conventional (sequential) computers, but it is a fact that new parallel computer architectures represent the potential of order-of-magnitude increases in computing power and should, therefore, be considered for their possible application in the most computing intensive tasks.We have studied both shared-memory-based computer architectures, like the BBN Butterfly, and local-memory-based architectures, mainly hypercubes implemented on transputers, where we have used the algorithmic mapping method proposed by Zapata el at. In this work we have developed the basic software tools needed to obtain a 3D reconstruction from non-crystalline specimens (“single particles”) using the so-called Random Conical Tilt Series Method. We start from a pair of images presenting the same field, first tilted (by ≃55°) and then untilted. It is then assumed that we can supply the system with the image of the particle we are looking for (ideally, a 2D average from a previous study) and with a matrix describing the geometrical relationships between the tilted and untilted fields (this step is now accomplished by interactively marking a few pairs of corresponding features in the two fields). From here on the 3D reconstruction process may be run automatically.

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