Accurate Determination of Object Position from Imprecise Data

1998 ◽  
Vol 120 (4) ◽  
pp. 559-564 ◽  
Author(s):  
K. C. Gupta ◽  
P. Chutakanonta
Keyword(s):  
Accurate Determination ◽  
Measurement Data ◽  
Decomposition Methods ◽  
Basic Method ◽  
Random Errors ◽  
Object Position ◽  
Cad Cam ◽  
Simulator Design ◽  
Vehicle Simulator

The problem of accurate determination of object position from imprecise and excess measurement data arises in kinematics, biomechanics, robotics, CAD/CAM and flight/vehicle simulator design. Several methods described in the literature are reviewed. Two new methods which take advantage of the modern matrix oriented software (e.g., MATLAB, IMSL, EISPACK) are presented and compared with a “basic” method. It is found that both of the proposed decomposition methods (I: SVD/QR and II: SVD/QS) give better absolute results than a “basic” method available from the text books. On a relative basis, the second method (SVD/QS Decomposition) gives slightly better results than the first method (SVD/QR Decomposition). Examples are presented for the cases when the points chosen are nearly dependent and when the independent points have small random errors in their coordinates.

Accurate Determination of Object Position From Imprecise Data

1998 ◽  
Author(s):  
Krishna C. Gupta ◽  
Puckpol Chutakanonta
Keyword(s):  
Accurate Determination ◽  
Measurement Data ◽  
Decomposition Methods ◽  
Random Errors ◽  
Object Position ◽  
New Methods ◽  
Cad Cam ◽  
Simulator Design ◽  
Vehicle Simulator

Abstract The problem of accurate determination of object position from imprecise and excess measurement data arises in kinematics, biomechanics, robotics, CAD/CAM and flight/vehicle simulator design. Several methods described in the literature are reviewed. Two new methods which take advantage of the modern matrix oriented software (e.g. MATLAB, IMSL, EISPACK) are presented and compared with a “basics” method. It is found that both of the proposed decomposition methods (I: SVD/QR and II: SVD/QS) give better absolute results than a “basic” method available from the text books. On a relative basis, the second method (SVD/QS Decomposition) gives slightly better results than the first method (SVD/QR Decomposition). Examples are presented for the cases when the points chosen are nearly dependent and when the independent points have small random errors in their coordinates.

Utilization of Multi-Axis Positioning Repeatability Performance in Kinematic Modelling

2019 ◽  
Vol 13 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Károly Szipka ◽  
◽  
Andreas Archenti
Keyword(s):  
Laser Interferometer ◽  
Measurement Data ◽  
Repeated Measurements ◽  
Random Errors ◽  
Statistical Population ◽  
Measurement Results ◽  
Kinematic Modelling ◽  
Kinematic Models

Detailed description of the multi-axis repeatability performance and the modelling of non-systematic variations in the positioning performance of machine tools can support the understanding of root-causes of capability variations in manufacturing processes. Kinematic characterization is implemented through repeated measurements, which include variations related to the performance of the machine tool. This paper addresses the integration of the positional repeatability in kinematic modelling through the employment of direct measurement results. The findings of this research can be used to develop standardized approaches. The statistical population of random errors along the multi-axis travel first requires the proper management of experimental data. In this paper a methodology and its application are presented for the determination of repeatability under static and unloaded conditions as an inhomogeneous parameter in the work space. The proposed approach is demonstrated in a case study, where the component errors of a linear axis are investigated with repeated laser interferometer measurements to quantify the estimated repeatability and express it in the composed repeatability budget. The conclusions of the proposed methodology outline the sensitivity of kinematic models relying on measurement data, as the repeatability of the system can be in the same magnitude as the systematic errors.

Statistics and parallaxes

1978 ◽  
Vol 48 ◽  
pp. 7-29
Author(s):  
T. E. Lutz
Keyword(s):  
Experimental Design ◽  
Statistical Methods ◽  
Review Paper ◽  
Systematic Errors ◽  
Past Experience ◽  
Random Errors ◽  
Trigonometric Parallaxes ◽  
Systematic And Random Errors

This review paper deals with the use of statistical methods to evaluate systematic and random errors associated with trigonometric parallaxes. First, systematic errors which arise when using trigonometric parallaxes to calibrate luminosity systems are discussed. Next, determination of the external errors of parallax measurement are reviewed. Observatory corrections are discussed. Schilt’s point, that as the causes of these systematic differences between observatories are not known the computed corrections can not be applied appropriately, is emphasized. However, modern parallax work is sufficiently accurate that it is necessary to determine observatory corrections if full use is to be made of the potential precision of the data. To this end, it is suggested that a prior experimental design is required. Past experience has shown that accidental overlap of observing programs will not suffice to determine observatory corrections which are meaningful.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Fast calibration of CBED patterns for quantitative analysis

1993 ◽  
Vol 51 ◽  
pp. 674-675
Author(s):  
M.A. Gribelyuk ◽  
M. Rühle
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Incident Beam ◽  
Crystal Thickness ◽  
Structure Model ◽  
Beam Direction ◽  
Transmitted Beam ◽  
Reciprocal Vector ◽  
On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

Computer-Assisted High-Re Solution TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 162-163
Author(s):  
F.A. Ponce ◽  
H. Hikashi
Keyword(s):  
Signal To Noise Ratio ◽  
Accurate Determination ◽  
Computer Software ◽  
Video Camera ◽  
Image Contrast ◽  
Objective Lens ◽  
Computer Assisted ◽  
Optical Parameters ◽  
Astigmatism Correction

The determination of the atomic positions from HRTEM micrographs is only possible if the optical parameters are known to a certain accuracy, and reliable through-focus series are available to match the experimental images with calculated images of possible atomic models. The main limitation in interpreting images at the atomic level is the knowledge of the optical parameters such as beam alignment, astigmatism correction and defocus value. Under ordinary conditions, the uncertainty in these values is sufficiently large to prevent the accurate determination of the atomic positions. Therefore, in order to achieve the resolution power of the microscope (under 0.2nm) it is necessary to take extraordinary measures. The use of on line computers has been proposed [e.g.: 2-5] and used with certain amount of success.We have built a system that can perform operations in the range of one frame stored and analyzed per second. A schematic diagram of the system is shown in figure 1. A JEOL 4000EX microscope equipped with an external computer interface is directly linked to a SUN-3 computer. All electrical parameters in the microscope can be changed via this interface by the use of a set of commands. The image is received from a video camera. A commercial image processor improves the signal-to-noise ratio by recursively averaging with a time constant, usually set at 0.25 sec. The computer software is based on a multi-window system and is entirely mouse-driven. All operations can be performed by clicking the mouse on the appropiate windows and buttons. This capability leads to extreme friendliness, ease of operation, and high operator speeds. Image analysis can be done in various ways. Here, we have measured the image contrast and used it to optimize certain parameters. The system is designed to have instant access to: (a) x- and y- alignment coils, (b) x- and y- astigmatism correction coils, and (c) objective lens current. The algorithm is shown in figure 2. Figure 3 shows an example taken from a thin CdTe crystal. The image contrast is displayed for changing objective lens current (defocus value). The display is calibrated in angstroms. Images are stored on the disk and are accessible by clicking the data points in the graph. Some of the frame-store images are displayed in Fig. 4.

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