High-resolution frequency estimation technique for recovering phase distribution in interferometers

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms.     

Maximum-likelihood estimator for dual phase extraction in holographic moire

A maximum-likelihood (ML) method based on spectral estimation theory for the extraction of dual phase distributions in holographic moire in the presence of nonsinusoidal waveforms, noise, and the miscalibration of piezoelectric (PZT) devices is proposed. The extraction of these phases requires incorporating two PZTs into the moire setup. ML estimators are asymptotically efficient for sufficient data samples. The approach presented uses a direct stochastic algorithm called probabilistic global search Lausanne for minimizing the ML function.     

Assay of tolnaftate and related impurities by isocratic supercritical fluid chromatography

Tolnaftate, an antifungal drug (TF) and related impurities arising from synthesis, viz., N-methyl-m-toluidine (NMmT) and beta-naphthol-1-chlorothio carbamate (beta-NCTC) can be determined by supercritical fluid chromatography. Even though it was possible to elute TF completely with neat SCF CO2, the peaks of the impurities were found to merge. The chromatographic figures of merit of the three analytes such as retention time (tR), capacity factor (k), selectivity factor (alpha), no. of theoretical plates (N), were optimized. The three compounds can be resolved in 5 min on a Hypersil (250 x 4.0 mm) 5 mu, C18 column with supercritical carbon dioxide, modified with 1.96% methanol as the mobile phase at 9.81 MPa and at 40 degrees C. Detection was carried out at 220 nm. The data as evaluated by the linear regression least squares fit method gave linearity ranges from 0.2 to 10.0 microg/mL for TF and NMmT and 0.3 to 10.0 microg/mL for beta-NCTC with correlation coefficients > 0.99. The method was successfully employed to estimate levels of 0.01% for NMmT and 0.02% for beta-NCTC with respect to TF.     

Alkyne hydroamination triggered cyclizations: A powerful tool for the construction of biologically important structural motifs

This review focuses mainly on recent endeavors in the field of cyclizations triggered by the catalytic hydroamination (formal or direct) of alkynes. The new strategies developed offer an efficient and convenient entry to several heterocycles of biological importance.     

Conditions for the onset of elastic and material instabilities in hyperelastic materials

Several constitutive inequalities have been proposed in the literature to quantify the notion that ‘stress increases with strain’ in an elastic material. Due to some inherent shortcomings in them, which we discuss, we propose a new tensorial criterion for isotropic materials. We also present necessary conditions in terms of elasticity tensors for the onset of elastic instabilities.