A novel method for measuring the coma of a lithographic projection system by use of mirror-symmetry marks

A novel method for measuring the coma of a lithographic projection system is proposed and the principle of the method is described. By utilizing mirror-symmetry marks, the adverse effects of axial aberrations on the coma measurement are avoided. Experimental results demonstrated that the method has high accuracy. Compared with TAMIS, the conventional technique used for coma measurement, the method is more reliable because the influences of the process factors on the lateral displacements have been considered. (c) 2006 Elsevier Ltd. All rights reserved.

Transonic wind tunnel for investigation of turbomachinery blades

The design of a two-stream wind tunnel was undertaken to allow the simulation and study of certain features of the flow field around the blades of high-speed axial-flow turbomachineries. The mixing of the two parallel streams with designed Mach numbers respectively equal to 1.4 and 0.7 will simulate the transonic Mach number distribution generally obtained along the tips of the first stage blades in large bypass-fan engines.

The GALCIT hypersonic compressor plant will be used as an air supply for the wind tunnel, and consequently the calculations contained in the first chapter are derived from the characteristics and the performance of this plant.

The transonic part of the nozzle is computed by using a method developed by K. O. Friedrichs. This method consists essentially of expanding the coordinates and the characteristics of the flow in power series. The development begins with prescribing, more or less arbitrarily, a Mach number distribution along the centerline of the nozzle. This method has been programmed for an IBM 360 computer to define the wall contour of the nozzle.

A further computation is carried out to correct the contour for boundary layer buildup. This boundary layer analysis included geometry, pressure gradient, and Mach number effects. The subsonic nozzle is calculated {including boundary layer buildup) by using the same computer programs. Finally, the mixing zone downstream of the splitter plate was investigated to prescribe the wall contour correction necessary to ensure a constant-pressure test section.

A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method

The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

Coma measurement by use of an alternating phase-shifting mask mark with a specific phase width

The correlation between the coma sensitivity of the alternating phase-shifting mask (Alt-PSM) mark and the mark's structure is studied based on the Hopkins theory of partially coherent imaging and positive resist optical lithography (PROLITH) simulation. It is found that an optimized Alt-PSM mark with its phase width being two-thirds its pitch has a higher sensitivity to coma than Alt-PSM marks with the same pitch and the different phase widths. The pitch of the Alt-PSM mark is also optimized by PROLITH simulation, and the structure of p - 1.92 lambda/NA and pw = 2p/3 proves to be with the highest sensitivity. The optimized Alt-PSM mark is used as a measurement mark to retrieve coma aberration from the projection optics in lithographic tools. In comparison with an ordinary Alt-PSM mark with its phase width being a half its pitch, the measurement accuracies of Z(7) and Z(14) apparently increase. (C) 2009 Optical Society of America

Even aberration measurement of lithographic projection system based on optimized phase-shifting marks

In the present paper, we propose a novel method for measuring the even aberrations of lithographic projection optics by use of optimized phase-shifting marks on the test mask. The line/space ratio of the phase-shifting marks is optimized to obtain the maximum sensitivities of Zernike coefficients corresponding to even aberrations. Spherical aberration and astigmatism can be calculated from the focus shifts of phase-shifting gratings oriented at 0 degrees, 45 degrees, 90 degrees and 135 degrees at multiple illumination settings. The PROLITH simulation results show that, the measurement accuracy of spherical aberration and astigmatism obviously increase, after the optimization of the measurement mark. (C) 2008 Elsevier B.V. All rights reserved.

Um problema inverso na modelagem da difusão do calor

O presente trabalho aborda um problema inverso associado a difus~ao de calor em uma barra unidimensional. Esse fen^omeno e modelado por meio da equac~ao diferencial par- cial parabolica ut = uxx, conhecida como equac~ao de difus~ao do calor. O problema classico (problema direto) envolve essa equac~ao e um conjunto de restric~oes { as condic~oes inicial e de contorno {, o que permite garantir a exist^encia de uma soluc~ao unica. No problema inverso que estudamos, o valor da temperatura em um dos extremos da barra n~ao esta disponvel. Entretanto, conhecemos o valor da temperatura em um ponto x0 xo no interior da barra. Para aproximar o valor da temperatura no intervalo a direita de x0, propomos e testamos tr^es algoritmos de diferencas nitas: diferencas regressivas, leap-frog e diferencas regressivas maquiadas.

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases. (C) 2005 Elsevier B.V. All rights reserved.

Nd3+螯合物的含氢有机溶液光谱性能研究

Tris-thenoyltrifluroacetonate of Nd3+ has been prepared and dissolved in DMF solation with very high concentration, and the contained hydrogen has not been substituted by deuterium. The absorption spectrum, emission spectrum, and fluorescence lifetime of the solution were measured. Very obvious characteristic fluorescence peaks were observed at 898 and 1058 nm. Based on Judd-Ofelt theory, three intensity parameters were obtained: Omega(2) = 4.9 x 10(-20) cm(2), Omega(4) = 5.1 x 10(-20) cm(2) and Omega(6) = 2.5 x 10(-20) cm(2). Line strengths S-cal, oscillator strengths f(cal), radiative transition probabilities A(ed), radiative lifetimes tau(r) and branch ratios beta were calculated too. The measured lifetime tau of 1058 nm peak is 460 mu s, and that of 898 nm 505 mu s. Comparison between theoretically computed radiative lifetime tau(r)(682 mu s) and the measured lifetime indicates that the non-radiative transition probability of the solution is very low and the fluorescence quantum efficiency very high. High values of three intensity parameters prove the high asymmetric surroundings of Nd3+, which is important for Nd3+ to absorb the excitation energy. Spectropic quality factor Omega(4)/Omega(6) > 1 makes radiation at 898 nm stronger than at 1058 nm.

Design and analysis of a kind of large flattened mode optical fibre

In this paper, a refractive index pro. le design enabling us to obtain a. at modal field around the fibre centre is investigated. The theoretical approach for designing such multilayer large flattened mode (LFM) optical fibres is presented. A comparison is made between the properties of a three-layer LFM structure and a standard step-index pro. le with the same core size. The obtained results indicate that the effective area of the LFM fibre is about twice as large as that of the standard step-index fibre, but the LFM fibre has less effective ability to filter out the higher order modes than the standard step-index fibre with the same bending radius.

Motion simulation of annular polishing

Based on the Coulomb friction model, the frictional motion model of workpiece relating to the polishing pad was presented in annular polishing. By the dynamic analysis software, the model was simulated and analysed. The conclusions from the results were that the workpiece did not rotate steadily. When the angular velocity of ring and the direction were the same as that of the polishing pad, the angular velocity of workpiece hoicked at the beginning and at the later stage were the same as that of the polishing pad before contacting with the ring. The angular velocity of workpiece vibrated at the moment of contacting with the ring. After that the angular velocity of workpiece increased gradually and fluctuated at a given value, while the angular velocity of ring decreased gradually and also fluctuated at a given value. Since the contact between the workpiece and the ring was linear, their linear velocities and directions should be the same. But the angular velocity of workpiece was larger than that of the polishing pad on the condition that the radius of the workpiece was less than that of the ring. This did not agree with the pure translation principle and the workpiece surface could not be flat, either. Consequently, it needed to be controlled with the angular velocity of ring and the radii of the ring and the workpiece, besides friction to make the angular velocity of workpiece equal to that of the polishing pad for obtaining fine surface flatness of the workpiece. Copyright © 2007 Inderscience Enterprises Ltd.}