Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources. (c) 2006 Elsevier GmbH. All rights reserved.

A new beam propagation method based on least-squares expansion approximating

A new finite difference wide-angle beam propagation method is developed by introducing the least-squares expansion approximant in the propagator expansion. In this new method it is not necessary to select the reference index point because of the whole region approaching the lease-square expansion. This method avoids the problems induced by error selection of the reference index in the old methods based on Taylor or Pade expansion. Several typical structures are simulated by the new method and the results prove the validity of it.

Determination of ethenzamide and acetoaminophen in quaternary powdered samples by near infrared spectroscopy and searching combination moving window partial least squares algorithm: effects of spectral resolution and signal-to-noise ratio

The present study reports an application of the searching combination moving window partial least squares (SCMWPLS) algorithm to the determination of ethenzamide and acetoaminophen in quaternary powdered samples by near infrared (NIR) spectroscopy. Another purpose of the study was to examine the instrumentation effects of spectral resolution and signal-to-noise ratio of the Buchi NIRLab N-200 FT-NIR spectrometer equipped with an InGaAs detector. The informative spectral intervals of NIR spectra of a series of quaternary powdered mixture samples were first located for ethenzamide and acetoaminophen by use of moving window partial least squares regression (MWPLSR). Then, these located spectral intervals were further optimised by SCMWPLS for subsequent partial least squares (PLS) model development. The improved results are attributed to both the less complex PLS models and to higher accuracy of predicted concentrations of ethenzamide and acetoaminophen in the optimised informative spectral intervals that are featured by NIR bands. At the same time, SCMWPLS is also demonstrated as a viable route for wavelength selection.

LEAST-SQUARES POLYNOMIAL SMOOTHING FOR INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTRA

The use of least-squres polynomial smoothing in ICP-AES is discussed and a method of points insertion into spectral scanning intervals is proposed in the present paper. Optimal FWHM/SR ratio can be obtained, and distortion of smoothed spectra can be avoided by use of the recommended method.

Calculation of light delay for coupled microrings by FDTD technique and Pade approximation

The Pade approximation with Baker's algorithm is compared with the least-squares Prony method and the generalized pencil-of-functions (GPOF) method for calculating mode frequencies and mode Q factors for coupled optical microdisks by FDTD technique. Comparisons of intensity spectra and the corresponding mode frequencies and Q factors show that the Pade approximation can yield more stable results than the Prony and the GPOF methods, especially the intensity spectrum. The results of the Prony method and the GPOF method are greatly influenced by the selected number of resonant modes, which need to be optimized during the data processing, in addition to the length of the time response signal. Furthermore, the Pade approximation is applied to calculate light delay for embedded microring resonators from complex transmission spectra obtained by the Pade approximation from a FDTD output. The Prony and the GPOF methods cannot be applied to calculate the transmission spectra, because the transmission signal obtained by the FDTD simulation cannot be expressed as a sum of damped complex exponentials. (C) 2009 Optical Society of America

Decomposition of circular dichroism of norepinephrine by singular value decomposition-least square method

Singular value decomposition - least squares (SVDLS), a new method for processing the multiple spectra with multiple wavelengths and multiple components in thin layer spectroelectrochemistry has been developed. The CD spectra of three components, norepinephrine reduced form of norepinephrinechrome and norepinephrinequinone, and their fraction distributions with applied potential were obtained in three redox processes of norepinephrine from 30 experimental CD spectra, which well explains electrochemical mechanism of norepinephrine as well as the changes in the CD spectrum during the electrochemical processes.

Shape effects on the yield stress and deformation of silicon nanowires: A molecular dynamics simulation

The tension and compression of single-crystalline silicon nanowires (SiNWs) with different cross-sectional shapes are studied systematically using molecular dynamics simulation. The shape effects on the yield stresses are characterized. For the same surface to volume ratio, the circular cross-sectional SiNWs are stronger than the square cross-sectional ones under tensile loading, but reverse happens in compressive loading. With the atoms colored by least-squares atomic local shear strain, the deformation processes reveal that the failure modes of incipient yielding are dependent on the loading directions. The SiNWs under tensile loading slip in {111} surfaces, while the compressive loading leads the SiNWs to slip in the {110} surfaces. The present results are expected to contribute to the design of the silicon devices in nanosystems.

In situ surface topography measurement method of granite base in scanning wafer stage with laser interferometer

Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

Intensity-moments characterization of general pulsed paraxial beams with the Wigner distribution function

On the basis of the space-time Wigner distribution function (STWDF), we use the matrix formalism to study the propagation laws for the intensity moments of quasi-monochromatic and polychromatic pulsed paraxial beams. The advantages of this approach are reviewed. Also, a least-squares fitting method for interpreting the physical meaning of the effective curvature matrix is described by means of the STWDF. Then the concept is extended to the higher-order situation, and what me believe is a novel technique for characterizing the beam phase is presented. (C) 1999 Optical Society of America [S0740-3232(99)001009-1].

Quantitative structure-property relationships for octanol-air partition coefficients of polychlorinated naphthalenes, chlorobenzenes and p,p '-DDT

The octanol-air partition coefficient (K-OA) is a key descriptor of chemicals partitioning between the atmosphere and environmental organic phases. Quantitative structure-property relationships (QSPR) are necessary to model and predict KOA from molecular structures. Based on 12 quantum chemical descriptors computed by the PM3 Hamiltonian, using partial least squares (PLS) analysis, a QSPR model for logarithms of K-OA to base 10 (log K-OA) for polychlorinated naphthalenes (PCNs), chlorobenzenes and p,p'-DDT was obtained. The cross-validated Q(cum)(2) value of the model is 0.973, indicating a good predictive ability of the model. The main factors governing log K-OA of the PCNs, chlorobenzenes, and p,p'-DDT are, in order of decreasing importance, molecular size and molecular ability of donating/accepting electrons to participate in intermolecular interactions. The intermolecular dispersive interactions play a leading role in governing log K-OA. The more chlorines in PCN and chlorobenzene molecules, the greater the log K-OA values. Increasing E-LUMO (the energy of the lowest unoccupied molecular orbital) of the molecules leads to decreasing log K-OA values, implying possible intermolecular interactions between the molecules under study and octanol molecules. (C) 2002 Elsevier Science Ltd. All rights reserved.

Quantitative relationships between molecular structures, environmental temperatures and octanol-air partition coefficients of PCDD/Fs

A concise quantitative model that incorporates information on both environmental temperature M and molecular structures, for logarithm of octanol-air partition coefficient (K-OA) to base 10 (logK(OA)) of PCDDs, was developed. Partial least squares (PLS) analysis together with 14 quantum chemical descriptors were used to develop the quantitative relationships between structures, environmental temperatures and properties (QRSETP) model. It has been validated that the obtained QRSETP model can be used to predict logK(OA) of other PCDDs. Molecular size, environmental temperature (T), q(+) (the most positive net atomic charge on hydrogen or chlorine atoms in PCDD molecules) and E-LUMO (the energy of the lowest unoccupied molecular orbital) are main factors governing logK(OA) of PCDD/Fs under study. The intermolecular dispersive interactions and thus the size of the molecules play a leading role in governing logK(OA). The more chlorines in PCDD molecules, the greater the logK(OA) values. Increasing E-LUMO values of the molecules leads to decreasing logK(OA) values, implying possible intermolecular interactions between the molecules under study and octanol molecules. Greater q(+) values results in greater intermolecular electrostatic repulsive interactions between PCDD and octanol molecules and smaller logK(OA) values. (C) 2002 Elsevier Science B.V. All rights reserved.

Quantitative structure-property relationships for octanol-air partition coefficients of polychlorinated biphenyls

Based on nine quantum chemical descriptors computed by PM3 Hamiltonian, using partial least squares analysis, a significant quantitative structure-property relationship for the logarithm of octanol-air partition coefficients (log K-OA) of polychlorinated biphenyls (PCBs) was obtained. The cross-validated Q(cum)(2) value of the model is 0.962, indicating a good predictive ability. The intermolecular dispersive interactions and thus the size of the PCB molecules play a key role in governing log K-OA. The greater the size of PCB molecules, the greater the log K-OA values. Increasing E-LUMO (the energy of the lowest unoccupied molecular orbital) values of the PCBs leads to decreasing log K-OA values, indicating possible interactions between PCB and octanol molecules. Increasing Q(Cl)(+) (the most positive net atomic charges on a chlorine atom) and Q(C)(-) (the largest negative net atomic charge on a carbon atom) values of PCBs results in decreasing log K-OA values, implying possible intermolecular electrostatic interactions between octanol and PCB molecules. (C) 2002 Elsevier Science Ltd. All rights reserved.

Quantitative structure-property relationships (QSPRs) on direct photolysis of PCDDs

By the use of partial least squares (PLS) method and 27 quantum chemical descriptors computed by PM3 Hamiltonian, a statistically significant QSPR were obtained for direct photolysis quantum yields (Y) of selected Polychlorinated dibenzo-p-dioxins (PCDDs). The QSPR can be used for prediction. The direct photolysis quantum yields of the PCDDs are dependent on the number of chlorine atoms bonded with the parent structures, the character of the carbon-oxygen bonds, and molecular polarity. Increasing bulkness and polarity of PCDDs lead to decrease of log Y values. Increasing the frontier molecular orbital energies (E-lumo and E-homo) and heat of formation (HOF) values leads to increase of log Y values. (C) 2001 Elsevier Science Ltd. All rights reserved.

Quantitative structure-property relationship study on reductive dehalogenation of selected halogenated aliphatic hydrocarbons in sediment slurries

In this study, by the use of partial least squares (PLS) method and 26 quantum chemical descriptors computed by PM3 Hamiltonian, a quantitative structure-property relationship (QSPR) model was developed for reductive dehalogenation rate constants of 13 halogenated aliphatic compounds in sediment slurry under anaerobic conditions. The model can be used to explain the dehalogenation mechanism. Halogenated aliphatic compounds with great energy of the lowest unoccupied molecular orbital (E-lumo), total energy (TE), electronic energy (EE), the smallest bond order of the carbon-halogen bonds (BO) and the most positive net atomic charges on an atom of the molecule (q(+)) values tend to be reductively dehalogenated slow, whereas halogenated aliphatic compounds with high values of molecular weight (Mw), average molecular polarizability (a) and core-core repulsion energy (CCR) values tend to be reductively dehalogenated fastest. (C) 2001 Published by Elsevier Science Ltd.