• Journal of the Semiconductor & Display Technology
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• v.9 no.1
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• pp.11-16
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• 2010

Wafer Pre-Alignment is to find the center and the orientation of a wafer and to move the wafer to the desired position and orientation. In this paper, an area camera based pre-aligning method is presented that captures 8 wafer images regularly during 360 degrees rotation. From the images, wafer edge positions are extracted and used to estimate the wafer's center and orientation using least squares circle fitting. These data are utilized for the proper alignment of the wafer. For accurate alignments, camera calibration methods using high order polynomials are used for converting pixel coordinates into real-world coordinates. A complete pre-alignment system was constructed using mechanical and optical components and tested. Experimental results show that alignment of wafer center and orientation can be done with the standard deviation of 0.002 mm and 0.028 degree, respectively.

• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.11-13
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• 2008

This study proposes the method to use existing digital maps as one of the technologies to exclude individual differences that occur in the process of manually determining GCP for the geometric correction of KOMPSAT images and applying it to the images and to automate the generation of ortho-images. It is known that, in case high-resolution satellite images are corrected geometrically by using RPC, first order polynomials are generally applied as the correction formula in order to obtain good results. In this study, we matched the corresponding objects between 1:25,000 digital map and a KOMPSAT image to obtain the coefficients of the zero order polynomial and showed the differences in the pixel locations obtained through the matching. We performed proximity corrections using the Boolean operation between the point data of the surface linear objects and the point data of the edge objects of the image. The surface linear objects are road, water, building from topographic map.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1997.10a
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• pp.213-218
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• 1997

Thermal deformation of machine origin of machine tools due to internal and external heat sources has been the most important problem to fabricate products with higher accuracy and performance. In order to solve this problem, GMDH models were constructed to estimate thermal deformation of machine origin for a vertical machining ceneter through measurement of temperature data of specific points on the machine tool. These models are nonlinear equations with high-order polynomials and implemented in a multilayered perceptron type network structure. Input variables and orders are automatically selected by correlation and optimization procedure. Sensors with small influence are deleted automatically in this algorithm. It was shown that the points of temperature measurement can be reduced without sacrificing the estimation accuracy of $\pm$5${\mu}{\textrm}{m}$. From the experimental result, it was confirmed that GMDH methodology was superior to least square models to estimate the thermal behavior of machine tools.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.148-153
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• 1998

In order to control thermal deformation of machine origin of machine tools due to internal and external heat sources, the real-time compensation system has been developed. First, GMDH models were constructed to estimate thermal deformation of machine origin for a vertical machining center through the measurement of deformation data and temperature data of specific points on the machine tool. Thermocouples and gap sensors are used respectively for measurement. These models are nonlinear equations with high-order polynomials and implemented in a multilayered perceptron type network structure. Secondly, work origin shift method were developed by implementing digital I/O interface board between CNC controller and IBM-PC. The work origin shift method is to shift the work origin by the compensation amounts which is calculated by pre-established GMDH model. From the experimental result, thermal deformation of machine origin was reduced to below $\pm$5${\mu}{\textrm}{m}$.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.173-174
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• 2006

High power amplifier (HPA), which is used in transmitter of wireless communication systems, usually works in near saturation point in order to achieve maximum efficiency. In this region, HPA can introduce undesirable nonlinear effects. In this paper, we present a polynomial modeling method for efficient techniques to compensate for nonlinear distortion introduced by nonlinear HPA. Proposed polynomial predistorter inverses actual amplifier. Namely, we derive polynomials of amplifiers from analytical method and the electrical parameters in the data sheet of an actual amplifier and then can derive polynomial predistorter by inversing them. It is an effective and a simple method to compensate nonlinear distortion. SSPA(Solid-state power amplifier) is considered. We also analyze the effects of predistortion on the SER performance of communication system with 16-QAM modulation format. The results have shown the efficiency of this model.

• Journal of the Semiconductor & Display Technology
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• v.9 no.3
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• pp.47-51
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• 2010

This paper presents a wafer pre-alignment system which is improved using the image of the entire wafer area. In the previous method, image acquisition for wafer takes about 80% of total pre-alignment time. The proposed system uses only one image of entire wafer area via a high-resolution CMOS camera, and so image acquisition accounts for nearly 1% of total process time. The larger FOV(field of view) to use the image of the entire wafer area worsen camera lens distortion. A camera calibration using high order polynomials is used for accurate lens distortion correction. And template matching is used to find a correct notch's position. The performance of the proposed system was demonstrated by experiments of wafer center alignment and notch alignment.

• Journal of Welding and Joining
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• v.30 no.6
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• pp.74-79
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• 2012

It depends on the joint configuration, dimensions and constraints of the joint whether the residual stress at the root of single-sided butt weld is tensile or not. Therefore, recommendation is generally made that high R ratio should be used in the fatigue test of welded joint in order to prevent excessively long life caused by compressive residual stress. In this research, the residual stress profile in butt weld joint was obtained through compliance method, using successive extension of a slot and measurement of the variation of strain during the slot extension. The residual stress profile was firstly assumed to be the linear summation of Legendre polynomials up to 9th order excluding 0th and 1st order. Strain variation on the surface was measured while the slot was being extended by cutting to find out the 8 unknown coefficients of each polynomial term. The cut was made by the electric discharge machine. It was concluded that the residual stress near the surface is positive valued, however, it turned into the negative value as soon as it passed through 2 or 3 mm of the depth.

• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.151-168
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• 2005

In this paper an energy method is presented for the linear buckling analysis of first order shear deformable plates. The displacement fields are defined in terms of the shape functions, which correspond to a set of predefined points and are composed of significantly high order polynomials. The locations of these points are found by mapping the geometry using the naturalized coordinates and bilinear shape functions. In order to evaluate the method, fully clamped and simply supported rectangular plates subjected to uniform uniaxial compressive loading on two opposite edges of the plate are investigated thoroughly and the results are compared with the exact solution given in the monograph of Timoshenko and Gere (1961). The method is extended to the analysis of perforated plates, wherein the negative stiffness computed over the opening area from in-plane and out-of-plane deformation modes is superimposed to the stiffness of the full plate. Numerical results are then favorably compared with those obtained by finite element methods. Other cases such as; rectangular plates with eccentrically located openings of different shapes are studied and reported in this paper with regards to the effect of aspect ratio, hole size, and hole position on the buckling. For a square plate with a large circular opening at the center, diameter being 80 percent of the length, the present method yields buckling coefficient 12.5 percent higher than the one from the FEM.