Evaluation and suppression of systematic errors in optical subwavelength gratings

2000 ◽  
Author(s):  
Bernd Schnabel ◽  
Ernst-Bernhard Kley
Keyword(s):  
Systematic Errors ◽  
Subwavelength Gratings

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.

Dielectronic Recombination in the Average-Atom Model

1988 ◽  
Vol 102 ◽  
pp. 215
Author(s):  
R.M. More ◽  
G.B. Zimmerman ◽  
Z. Zinamon
Keyword(s):  
Detailed Balance ◽  
Systematic Errors ◽  
Dielectronic Recombination ◽  
Rate Equations ◽  
Strong Correlations ◽  
Dense Plasmas ◽  
Atom Model ◽  
New Feature ◽  
Average Atom Model ◽  
Attachment Process

Autoionization and dielectronic attachment are usually omitted from rate equations for the non–LTE average–atom model, causing systematic errors in predicted ionization states and electronic populations for atoms in hot dense plasmas produced by laser irradiation of solid targets. We formulate a method by which dielectronic recombination can be included in average–atom calculations without conflict with the principle of detailed balance. The essential new feature in this extended average atom model is a treatment of strong correlations of electron populations induced by the dielectronic attachment process.

Precise on-line Measurement of Lattice Vectors

1990 ◽  
Vol 48 (1) ◽  
pp. 530-531
Author(s):  
W.J. de Ruijter ◽  
Sharma Renu
Keyword(s):  
Electron Microscope ◽  
Measurement Errors ◽  
Dynamic Range ◽  
Structural Information ◽  
Statistical Parameter ◽  
Systematic Errors ◽  
Geometric Distortion ◽  
Crystal Silicon ◽  
Camera System ◽  
On Line

Established methods for measurement of lattice spacings and angles of crystalline materials include x-ray diffraction, microdiffraction and HREM imaging. Structural information from HREM images is normally obtained off-line with the traveling table microscope or by the optical diffractogram technique. We present a new method for precise measurement of lattice vectors from HREM images using an on-line computer connected to the electron microscope. It has already been established that an image of crystalline material can be represented by a finite number of sinusoids. The amplitude and the phase of these sinusoids are affected by the microscope transfer characteristics, which are strongly influenced by the settings of defocus, astigmatism and beam alignment. However, the frequency of each sinusoid is solely a function of overall magnification and periodicities present in the specimen. After proper calibration of the overall magnification, lattice vectors can be measured unambiguously from HREM images.Measurement of lattice vectors is a statistical parameter estimation problem which is similar to amplitude, phase and frequency estimation of sinusoids in 1-dimensional signals as encountered, for example, in radar, sonar and telecommunications. It is important to properly model the observations, the systematic errors and the non-systematic errors. The observations are modelled as a sum of (2-dimensional) sinusoids. In the present study the components of the frequency vector of the sinusoids are the only parameters of interest. Non-systematic errors in recorded electron images are described as white Gaussian noise. The most important systematic error is geometric distortion. Lattice vectors are measured using a two step procedure. First a coarse search is obtained using a Fast Fourier Transform on an image section of interest. Prior to Fourier transformation the image section is multiplied with a window, which gradually falls off to zero at the edges. The user indicates interactively the periodicities of interest by selecting spots in the digital diffractogram. A fine search for each selected frequency is implemented using a bilinear interpolation, which is dependent on the window function. It is possible to refine the estimation even further using a non-linear least squares estimation. The first two steps provide the proper starting values for the numerical minimization (e.g. Gauss-Newton). This third step increases the precision with 30% to the highest theoretically attainable (Cramer and Rao Lower Bound). In the present studies we use a Gatan 622 TV camera attached to the JEM 4000EX electron microscope. Image analysis is implemented on a Micro VAX II computer equipped with a powerful array processor and real time image processing hardware. The typical precision, as defined by the standard deviation of the distribution of measurement errors, is found to be <0.003Å measured on single crystal silicon and <0.02Å measured on small (10-30Å) specimen areas. These values are ×10 times larger than predicted by theory. Furthermore, the measured precision is observed to be independent on signal-to-noise ratio (determined by the number of averaged TV frames). Obviously, the precision is restricted by geometric distortion mainly caused by the TV camera. For this reason, we are replacing the Gatan 622 TV camera with a modern high-grade CCD-based camera system. Such a system not only has negligible geometric distortion, but also high dynamic range (>10,000) and high resolution (1024x1024 pixels). The geometric distortion of the projector lenses can be measured, and corrected through re-sampling of the digitized image.

Performance Characteristics of Methods for the Bacteriological Examination of Water

1993 ◽  
Vol 27 (3-4) ◽  
pp. 1-13 ◽  
Author(s):  
Arie H. Havelaar ◽  
Siem H. Heisterkamp ◽  
Janneke A. Hoekstra ◽  
Kirsten A. Mooijman
Keyword(s):  
Sensitivity And Specificity ◽  
Measurement Errors ◽  
Systematic Errors ◽  
General Concept ◽  
Growth Characteristics ◽  
Performance Characteristics ◽  
Logarithmic Scale ◽  
Bacteriological Examination ◽  
Membrane Filters

The general concept of measurement errors is applied to quantitative bacteriological counts on membrane filters or agar plates. The systematic errors of these methods are related to the growth characteristics of the medium (recovery of target organisms and inhibition of non-target organisms) and to its differential characteristics (sensitivity and specificity). Factors that influence the precision of microbiological counts are the variation between replicates, within samples, between operators and between laboratories. It is also affected by the linearity of the method, the verification rate and, where applicable, the number of colonies subcultured for verification. Repeatability (r) and reproducibility (R) values can be calculated on the logarithmic scale.

NEW RESULTS IN REDUCED ESTIMATION WITH SYSTEMATIC ERRORS IN MEASUREMENTS AND THEIR APPLICATION FOR THE FORMATION OF A GROUP TIME SCALE

2018 ◽  
pp. 30-37
Author(s):  
A. P. Aleshkin ◽  
A. A. Makarov ◽  
Yu. F. Matasov
Keyword(s):  
Time Scale ◽  
Statistical Estimation ◽  
Systematic Errors ◽  
Random Component ◽  
Customer Support ◽  
Group Time ◽  
Reduction Coefficient ◽  
Systematic Component ◽  
Compression Parameter ◽  
Positive Effect

The article deals with the behavior of reduced scalar estimates in the presence of systematic errors in the observational data. The proposed procedure with a different method of forming the reduction coefficient. A quasi-optimal variant of the compression parameter formation is considered. Simulation results for different conditions of application of the proposed algorithms are presented. Currently, one of the ways to improve the accuracy of the formation of the time scale in solving the problems of frequency-time customer support is the averaging of the readings of several generators. At the same time, this approach, as shown in the theory of statistical estimation, is effective for parrying the random component of the error of the estimated process. However, for frequency generators random error can be effectively compensated for a long range of observations, but the systematic component - frequency drift - is a serious problem, which can be eliminated by averaging only under certain conditions. Therefore, the article proposes a version of the reduced estimate, effective, as shown, to parry the departure of the time scale by introducing a shift in the implementation of compression, defined by the reduction procedure. The conditions in which the degree of the achieved positive effect has a practical sense are considered.

Systematic errors in equilibrium composition of ternary liquid-liquid systems and their effect on the calculated number of theoretical stages of countercurrent extraction

1988 ◽  
Vol 53 (6) ◽  
pp. 1172-1180
Author(s):  
Ján Dojčanský ◽  
Soňa Bafrncová ◽  
Július Surový
Keyword(s):  
Equilibrium Composition ◽  
Systematic Errors ◽  
Liquid Equilibrium ◽  
Countercurrent Extraction ◽  
Liquid Systems ◽  
Equilibrium Concentrations ◽  
Line Slope ◽  
Tie Line ◽  
Calculated Number

The influence of magnitude of systematic errors in the determination of ternary liquid-liquid equilibrium concentrations on the accuracy of the calculated number of theoretical stages of countercurrent extraction is evaluated on using five hypothetical systems differing in the extent of mutual solubility of components, tie-line slope, and type of binodal curve.

The effect of systematic errors of the equilibrium distribution concentrations on the number of stages of countercurrent extraction with various consumption of extractant

1989 ◽  
Vol 54 (4) ◽  
pp. 981-989
Author(s):  
Ján Dojčanský ◽  
Soňa Bafrncová ◽  
Július Surový
Keyword(s):  
Equilibrium Distribution ◽  
Systematic Errors ◽  
Mutual Solubility ◽  
Operating Conditions ◽  
Liquid Equilibrium ◽  
Countercurrent Extraction ◽  
Absolute Deviation ◽  
Line Slope ◽  
Tie Line ◽  
Calculated Number

On using five hypothetical systems differing in the extent of mutual solubility of components, tie-line slope, and type of binodal curve, the effect is evaluated of systematic errors in the form of absolute deviation in the liquid-liquid equilibrium distribution concentrations on the accuracy of calculated number of theoretical stages of isothermal countercurrent extraction under various operating conditions.

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