Projection Axis Research Articles

A Fast k Nearest Neighbor Finding Algorithm Based on the Ordered Partition

We propose a fast nearest neighbor finding algorithm, named tentatively an ordered partition, based on the ordered lists of the training samples of each projection axis. The ordered partition contains two properties, one is ordering¿to bound the search region, and the other is partitioning¿to reject the unwanted samples without actual distance computations. It is proved that the proposed algorithm can find k nearest neighbors in a constant expected time. Simulations show that the algorithm is rather distribution free, and only 4.6 distance calculations, on the average, were required to find a nearest neighbor among 10 000 samples drawn from a bivariate normal distribution.

Electron crystallography of epitaxially grown paraffin

AbstractThree‐dimensional electron diffraction data from the epitaxially crystallized paraffin n‐C36H74 are investigated in a structure analysis and are found to give a reasonable image of the structure, in agreement with the earlier x‐ray determination. An inconsistency in the refined isotropic temperature factors from different zonal projections, however, indicates the necessity for a more accurate physical model for epitaxially grown crystals which will account for a large spread of diffraction peaks along reciprocal lattice lines parallel to the projection axis.

Emergence of small defect contrast within HREM images of nonstoichiometric rutile

Calculations of HREM images have been used to define the conditions for which interpretable information may be obtained concerning the nature of small defects (traditionally called “point defects”) and their aggregation to form extended defects in nonstoichiometric rutile. At specific crystal thickness and lens defocus conditions as few as three small defects (aligned along the projection axis) become visible in lattice images. The emergence of stronger contrast, as extended defects develop, should allow the interstitial or vacancy nature of the defects to be distinguished. Experimental HREM images are also presented which show a variety of “small defect contrasts” for [001], [010] and [111] projections of nonstoichiometric rutiles (TiO 2- x ; 0.006 ≦ x ≦ 0.02). None of these allow interstitial versus vacancy defects to be distinguished directly, although some show evidence for aggregates of less than 10 small defects.

Molecular detail in electron micrographs of quaterrylene C40H20

The electron microscopy of organic compounds is beset by the problem of radiation damage due to the electron beam1. This radiation sensitivity is somewhat reduced in aromatic systems2 and organometallic complexes3–5 but it, nevertheless, limits the fineness of detail which can be resolved in images from these types of materials. Previous studies of the more stable compounds have concentrated on those where molecular superimposition normally occurred on a major crystallographic axis. The compound quaterrylene, C40H20, does not have such a projection axis and is therefore more typical of most organic crystals. We report here results from the examination of quaterrylene6 in the Cambridge University 600-kV high resolution electron microscope (HREM)7,8. These results provide direct information about intermolecular stacking and, after lattice averaging, show detail at the level of the six-membered aromatic rings within molecules of this material.

DIRECT OBSERVATION OF DISORDER WITHIN CRYSTALLOGRAPHIC SHEAR DEFECTS IN DEFORMED AND NON-STOICHIOMETRIC RUTILES

High resolution electron microscope images have been obtained at ~2.3 A point resolution showing mechanical twin lamellae with associated twin dislocations in stoichiometric TiO2.0000 and also a variety of novel crystallographic shear (CS) behaviours in a deformed non-stoichiometric rutile TiO1.9966. In many cases these images proved to be directly interpretable in terms of the positions of Ti atom rows viewed along the [100]r and [1[MATH]1]r projection axis. Thus structural models for a variety of defects could be deduced from the images. In situ observations of the annealing of mechanical twins, obtained at lower resolution using an environmental cell in a 1 MeV electron microscope are also described. New types of CS behaviour include : identification of (143)r CS planes (CSP) lying between the well-known (132)r and (011)r orientations ; disorder within CSP with respect to orientation, both uniform and non-uniform mixing of (121)r - and (011)r - type steps occur along individual boundaries ; the observation of closely-spaced pairs of CS boundaries containing varying degrees of disorder with regard to both orientation and the structure within the pairs ; evidence that defects other than CSP occur in slightly reduced rutile, which give rise to modulations of lattice fringes along both k (011)r and k (110)r, and other as yet uninterpreted contrast, but suggestive of poinf defect clustering.

Gaging By Remote Image Tracking

A method is described for performing noncontact optical gaging of complex parts in a production environment. The operational concept of the system, known as Gaging by Remote Image Tracking, relies upon an optical triangulation technique. A spot of light is projected from a gage head onto the surface of the part being gaged; an image of this spot is focused on the center of a tracking photodetector, mounted within the gage head. If the part is translated in a direction perpendicular to the projection axis, the focus spot on the surface of the photodetector will move as the surface curvature of the part changes. As a result of this movement, voltage signals are generated which provide: (1) a measure of the spot displacement on the photodetector, and (2) a signal for driving the optical head in a direction which recenters the image spot on the photodetector. The first signal, with appropriate scaling, provides virtually an instantaneous measure of the dimensional change of the part. The second signal is used to drive the system to a known distance from the part (system null). By monitoring the motion of the entire system with a linear encoder and adding this measurement to the instantaneous measure of surface curvature, the result is a fast, noncontact optical gaging system with large dynamic range.

Reconstruction of Objects from their Projections Using Orthogonal Functions

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.