Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.     

The 7th Asian Symposium on Visualization

The 7th Asian Symposium on Visualization (7ASV) was successfully held in Singapore from 3^rd to 7^th November 2003. This event was originally scheduled from 26^th to 30^th May 2003, but had to be postponed because of the outbreak of SARS (Severe Acute Respiratory Syndrome) in some parts of the world. A total number of 122 participants attended the Symposium of which, 107 were foreign participants from 16 countries (excluding Singapore) worldwide. There were 104 papers covering broad range of topics presented at the Symposium which were delivered in 2×7 long sessions, and 9 keynote papers.     

Modification of Spatial Coherence by Means of Low-Order Zernike-Mode Adaptive Optics

Spatial coherence of the field modified by low-order adaptive optics is analyzed to establish a theoretical basis for the recent idea of using adaptive optics as a spatial coherence modifier. In this context low-order adaptive optics has the ability to correct some of the low-order aberrations specified by Zernike polynomials. The initial field to be modified is assumed to be a spatially partially coherent one resulting from phase disturbance. It is demonstrated, as in the previous study, that low-order adaptive optics serves to enhance the spatial coherence of the resultant field and that the effect of the enhancement becomes stronger as the spatial coherence of the initially partially coherent field increases. Potential applications of low-order adaptive optics as a spatial coherence modifier are briefly discussed.     

Elasticity and inelasticity of biomorphic silicon carbide ceramics

The effect of the vibration strain amplitude on the Young modulus and ultrasonic absorption (internal friction) in biomorphic SiC ceramics is investigated in the temperature range 116–296 K. The biomorphic SiC ceramics is prepared through pyrolysis of eucalyptus with subsequent infiltration of silicon. It is demonstrated that the vibration loading of samples in air and under vacuum is accompanied by a number of unexpected effects. The behavior of the studied ceramics is governed by at least two mechanisms, which, to a large extent, are responsible for the elastic and inelastic properties of the material. One mechanism is associated with the adsorption-desorption of environmental molecules (hypothetically, owing to the presence of pores and residual carbon), and the other mechanism involves microplastic deformation due to the motion of dislocations or other (similar) structural units.     

<Emphasis FontCategory="NonProportional">L</Emphasis>-Matrices and solvability of linear complementarity problems by a linear program-Matrices and solvability of linear complementarity problems by a linear program

The classes ofL ₁-matrices,L ₂-matrices,L ₃-matrices andW-matrices are introduced to study solvability of a linear complementarity problem via solving a linear program. Three sufficient conditions are presented to guarantee that a linear complementarity problem is solvable via a linear program. The new sufficient conditions are weaker than the ones introduced by Mangasarian. This fact is also illustrated by an example. Partially supported by NSFC. This author is also with College of Business Administration of Human University as a Lotus chair professor.     

Synchronization in supply chains: implications for design and management

Supply chain management literature calls for coordination between the different members of the chain. Materials should be moved from one supplier to the next according to a just-in-time schedule. In this paper, we show that for many supply chain configurations, complete synchronization will result in some members of the chain being ‘losers’ in terms of cost. We develop an algorithm for optimal synchronization of supply chains and provide some guidelines for incentive alignment along the supply chain. In developing the model, we use the economic delivery and scheduling problem model and analyze supply chains dealing with single and multiple components. For single-component supply chains, we derive a closed-form expression for the optimal synchronized cycle time. For multi-component supply chains, we develop an algorithm for finding the optimal synchronized cycle time. We test the performance of the algorithm and show that it provides optimal solutions for a wide range of problems. We illustrate the models with numerical examples.     

Structure and reflective properties of Al-Cu-Fe quasicrystalline thin film prepared by laser induced arc method

Al-Cu-Fe thin films were prepared by laser induced arc (laser-arc) method from a single source—Al₆₃Cu₂₅Fe₁₂ alloy, which was proved to consist of quasicrystalline phase together with approximant phase. The composition of the deposited films meets the requirement for formation of icosahedral symmetry phase. Quasicrystalline phase was obtained after annealing the amorphous as-deposit film samples. The optical properties of the samples were investigated. Thin film samples of Al, Cu and Fe deposited under the same condition were employed for comparison. The results showed specific reflective properties of Al-Cu-Fe quasicrystal thin film in some wavelength range. The optical conductivity of the films exhibited a negative peak, centered about 440 nm in range of 190 to 800 nm. The Al-Cu-Fe quasicrystal thin films could absorb almost all the ray in the wavelength range from 420nm to 450 nm. The ratio of absorption was greater than 99%.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

The components of the Wired Spanning Forest are recurrent

 We show that a.s. all of the connected components of the Wired Spanning Forest are recurrent, proving a conjecture of Benjamini, Lyons, Peres and Schramm. Our analysis relies on a simple martingale involving the effective conductance between the endpoints of an edge in a uniform spanning tree. We believe that this martingale is of independent interest and will find further applications in the study of uniform spanning trees and forests. Received: 20 April 2001 / Revised version: 23 July 2002 / Published online: 14 November