Measurement of Straightness for Two-Dimensional Translatory Stage

2010 ◽  
Vol 437 ◽  
pp. 194-197
Author(s):  
Ryoshu Furutani ◽  
Masakazu Watanabe
Keyword(s):  
Laser Interferometer ◽  
Probe Method ◽  
Two Dimensional ◽  
Profile Error ◽  
Reference Mirror ◽  
One Dimensional ◽  
Dimensional Measurement ◽  
Adjustment Error ◽  
Profile Errors ◽  
The Relationship

The large scaled and high accurate 2D-stage is necessary for nanomanufacturing. In order to measure the position of stage, two direction sensors are used. These sensors measure the displacement from the metrological frame. However in nanometer application, as the profile error of metrological frame is comparable with the accuracy of 2D-stage, it is not negligible. Therefore the measuring result includes the displacement of stages and the profile error of metrological frame. So the multi-probe method is applied in one-dimensional measurement to separate the displacement error from the profile error of the metrological frame. In the multi-probe method, the zero adjustment error cannot be removed. So this article proposes a new method which separates the displacement of 2D-stage from the profile errors of the metrological frames in two directions. In this article, as the laser interferometer is used as the sensor, the measuring data is assumed as the shape of the axis of stages mixed with the profile error of the reference mirror in laser interferometer. The relationship during the measuring data, the shape of the axis and the profile error is described. The shape of axis of stage and the profile error of mirror are derived from the measuring result in experiment.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

Measurement of Temperature and Heat Flux Changes During the Fixing Process in Electrophotographic Machines

1996 ◽  
Vol 118 (1) ◽  
pp. 150-154 ◽  
Author(s):  
T. Mitsuya ◽  
K. Masuda ◽  
Y. Hori
Keyword(s):  
Heat Flux ◽  
Print Quality ◽  
Two Dimensional ◽  
Temperature Changes ◽  
One Dimensional ◽  
Temperature Heat ◽  
Rapid Temperature ◽  
Pressure Changes ◽  
The Relationship ◽  
Electrophotographic Printing

Increasingly higher speeds of modern electrophotographic printing force examination of the problem of retaining sufficient fixing strength without deterioration of print quality. In the nip region between the two rollers where fixing occurs, the significant parameters are temperature, heat flux, and pressure changes. Their optimization is necessary to maintain both speed and print quality. Difficulty in analyzing the relationship among these parameters occurs because of the complexity of two-dimensional phenomena in a rotating field and the rapidity of changes. Experimental equipment to measure relative heat flux in the nip region during rapid temperature changes was designed. Two sensors are installed in the heat roller. An adiabatic piece is buried under sensor 1. Sensor 2, without an adiabatic piece, detects temperature. Sensor 1 is electrically heated and always at the same temperature as sensor 2. Heat flux changes are obtained by noting the electric power supplied to sensor 1. The equipment was fabricated and measurements were made. They indicate an intermittent two-dimensional heat flux. Because of this, temperature decreases rapidly before the entrance to the nip region. Estimates of two-dimensional effects are made and modified for a one-dimensional case. From them, the temperature field in the nip region for actual fixing conditions is calculated.

Seepage flow in unconfined aquifers

1975 ◽  
Vol 71 (1) ◽  
pp. 181-192 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Flow Rate ◽  
Seepage Flow ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Unconfined Aquifers ◽  
Source Line ◽  
Theory Yield ◽  
The Relationship

The paper concerns one- and two-dimensional models of steady seepage flow in unconfined aquifers and the relationship between them. The first part gives a new proof of Charnyi's result that one- and two-dimensional theory yield the same value for the flow rate in a horizontal aquifer or porous bed between vertical ends and shows the extent to which it can be generalized to non-uniform or anisotropic media. The second part solves the highly two-dimensional problem of flow from a line source (line of springs) in an otherwise impermeable, sloping stratum and compares the result with the predictions of a one-dimensional Dupuit–Pavlovsky approach. Confirmatory experiments using the Hele Shaw analogue of seepage flow are also reported.

Multivariate analysis of montmorillonite

Clay Minerals ◽  
1965 ◽  
Vol 6 (1) ◽  
pp. 59-70 ◽  
Author(s):  
J. H. Rayner
Keyword(s):  
Multivariate Analysis ◽  
Similarity Coefficient ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
The Relationship

AbstractVarty & White's application of multivariate analysis to Grim & Kulbicki's measurements on montmorillonites has been re-examined and extended. Inconsistencies between their table of scored data and derived similarity table, and some unexplained errors in the similarity table, have only a small effect on their results. Similarities calculated from Grim & Kulbicki's data, using a different similarity coefficient, lead to a two dimensional representation which separates the groups of montmorillonites more clearly. The groups can be clearly separated even in a one dimensional representation, by changing the relationship between distance and similarity.

The relation of wavelength dispersion and scan mode in X-ray diffractometry with a monochromator

1985 ◽  
Vol 18 (6) ◽  
pp. 506-508
Author(s):  
A. M. Mathieson
Keyword(s):  
Bragg Reflection ◽  
Constant Width ◽  
Full Range ◽  
Measurement Procedure ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
Dimensional Measurement ◽  
Monochromator Crystal

The contribution to the size of a Bragg reflection due to the interaction of the wavelength dispersion of a monochromator crystal, M, and of a specimen crystal, c, is considered from the two-dimensional Δω, Δ2θ viewpoint. Its variation with change in scan mode is demonstrated. For the ω/θ scan mode, the contribution in respect of Δ2θ [i.e. (Δλ/λ)tan θc ] is independent of the monochromator used and is the same as for the non-monochromator case. For the ω/2θ scan mode, the corresponding contribution [(Δλ/λ)tan θM ] is constant and so, for the conventional one-dimensional measurement procedure, a receiving aperture of constant width may be used to collect intensities over the full range of θc .

PUSHDOWN RECOGNIZERS FOR ARRAY PATTERN

1989 ◽  
Vol 03 (03n04) ◽  
pp. 377-392
Author(s):  
H. J. LIN ◽  
P. S. P. WANG
Keyword(s):  
Two Dimensional ◽  
One Dimensional ◽  
Array Pattern ◽  
The Relationship ◽  
Context Free ◽  
Pushdown Automata

We investigate the factors that make it difficult to generalize pushdown automata for one-dimensional strings to two-dimensional arrays. Then we resolve the problems and construct two-dimensional pushdown array automata (PDAA). The relationship between isometric context-free array languages and pushdown array automata is established. Several examples of array automata are presented, and a pushdown array automaton is tested on VAX8650/VMS using PASCAL.

THE EFFECT OF INKDOTS FOR TWO-DIMENSIONAL AUTOMATA

1995 ◽  
Vol 09 (05) ◽  
pp. 777-796 ◽  
Author(s):  
AKIRA ITO ◽  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI ◽  
YUE WANG
Keyword(s):  
Turing Machine ◽  
Open Problem ◽  
Complexity Classes ◽  
Two Dimensional ◽  
Turing Machines ◽  
Input Tape ◽  
One Dimensional ◽  
Finite State ◽  
Relationship Of ◽  
The Relationship

Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.

Palatal Surface Area of Maxillary Plaster Casts—A Comparison between Two-Dimensional and Three-Dimensional Measurements

2007 ◽  
Vol 44 (4) ◽  
pp. 381-390 ◽  
Author(s):  
Tron A. Darvann ◽  
Nuno V. Hermann ◽  
Bjarne K. Ersbøll ◽  
Sven Kreiborg ◽  
Samuel Berkowitz
Keyword(s):  
Surface Area ◽  
Three Dimensional ◽  
Area Ratio ◽  
Two Dimensional ◽  
Surface Area Ratio ◽  
Dimensional Measurement ◽  
Interobserver Error ◽  
Dimensional Measurements ◽  
The Relationship ◽  
Plaster Casts

Objective: To investigate the relationship between corresponding two-dimensional and three-dimensional measurements on maxillary plaster casts taken from photographs and three-dimensional surface scans, respectively. Materials and Methods: Corresponding two-dimensional and three-dimensional measurements of selected linear distances, curve lengths, and (surface) areas were carried out on maxillary plaster casts from individuals with unilateral or bilateral cleft lip and palate. The relationship between two-dimensional and three-dimensional measurements was investigated using linear regression. Results and Conclusions: Error sources in the measurement of three-dimensional palatal segment surface area from a two-dimensional photograph were identified as photographic distortion (2.7%), interobserver error (3.3%), variability in the orientation of the plaster cast (3.2%), and natural shape variation (4.6%). The total error of determining the cleft area/palate surface area ratio was 15%. In population studies, the effect of using two-dimensional measurements is a decrease of discriminating power. In well-calibrated setups, a two-dimensional measurement of the cleft area/palate surface area ratio may be converted to a three-dimensional measurement by use of a multiplication factor of 0.75.

On Ship Wave Patterns and Their Spectra

1971 ◽  
Vol 15 (01) ◽  
pp. 11-21 ◽  
Author(s):  
E. O. Tuck ◽  
J. I. Collins ◽  
W. H. Wells
Keyword(s):  
Wave Pattern ◽  
Wave Resistance ◽  
Two Dimensional ◽  
One Dimensional ◽  
Ship Wave ◽  
Wave Patterns ◽  
The One ◽  
Relationship Of ◽  
The Relationship

The one dimensional and two dimensional spectra of a ship wave pattern have been derived. It is shown that the spectra have distinct signatures containing information on speed, direction, shape, size, and wave resistance of the ship. The speed and direction are readily determined but the relationship of the spectrum to other ship characteristics requires further investigation. Some examples of detailed wave patterns in the wake of a parabolic sided ship have been computed.

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