Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.

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.

Real-time micro-vibration measurement in sinusoidal phase-modulating interferometry

As there exist some problems with the previous laser diode (LD) real-time microvibration measurement interferometers, such as low accuracy, correction before every use, etc., in this paper, we propose a new technique to realize the real-time microvibration measurement by using the LD sinusoidal phase-modulating interferometer, analyze the measurement theory and error, and simulate the measurement accuracy. This interferometer utilizes a circuit to process the interference signal in order to obtain the vibration frequency and amplitude of the detective signal, and a computer is not necessary in it. The influence of the varying light intensity and light path difference on the measurement result can be eliminated. This technique is real-time, convenient, fast, and can enhance the measurement accuracy too. Experiments show that the repeatable measurement accuracy is less than 3.37 nm, and this interferometer can be applied to real-time microvibration measurement of the MEMS. (C) 2007 Elsevier GmbH. All rights reserved.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Detection of Brillouin scattering temperature signal in Brillouin optical time-domain reflectometer sensing system based on instantaneous frequency measurement technology

We present a simple and practical method for the single-ended distributed fiber temperature measurements using microwave (11-GHz) coherent detection and the instantaneous frequency measurement (IFM) technique to detect spontaneous Brillouin backscattered signal in which a specially designed rf bandpass filter at 11 GHz is used as a frequency discriminator to transform frequency shift to intensity fluctuation. A Brillouin temperature signal can be obtained at 11 GHz over a sensing length of 10 km. The power sensitivity dependence on temperature induced by frequency shift is measured as 2.66%/K. (c) 2007 Society of Photo-Optical Instrumentation Engineers.