Some applications of the discrete fourier transform to problems of crystal lattice deformation II

The method elaborated in [1] is applied to the solution of some problems for a plane lattice and the linear chain. The method can be used to investigate deformations around crystal lattice defects.

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, [1] . .

     

Swept source optical coherence tomography based on non-uniform discrete fourier transform

A high-speed high-sensitivity swept source optical coherence tomography （SSOCT） system using a high speed swept laser source is developed. Non-uniform discrete fourier transform （NDFT） method is introduced in the SSOCT system for data processing. Frequency calibration method based on a Mach-Zender interferometer （MZI） and conventional data interpolation method is also adopted in the system for comparison. Optical coherence tomography （OCT） images from SSOCT based on the NDFT method, the MZI method, and the interpolation method are illustrated. The axial resolution of the SSOCT based on the NDFT method is comparable to that of the SSOCT system using MZI calibration method and conventional data interpolation method. The SSOCT system based on the NDFT method can achieve higher signal intensity than that of the system based on the MZI calibration method and conventional data interpolation method because of the better utilization of the power of source.     

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

We have developed a model and realized an algorithm for the calculation of the coefficient of coherent (direct) transmission of light through a layer of liquid crystal (LC) droplets in a polymer matrix. The model is based on the Hulst anomalous diffraction approximation for describing the scattering by an individual particle and the Foldy-Twersky approximation for a coherent field. It allows one to investigate polymer dispersed LC (PDLC) materials with homogeneous and inhomogeneous interphase surface anchoring on the droplet surface. In order to calculate the configuration of the field of the local director in the droplet, the relaxation method of solving the problem of minimization of the free energy volume density has been used. We have verified the model by comparison with experiment under the inverse regime of the ionic modification of the LC-polymer interphase boundary. The model makes it possible to solve problems of optimization of the optical response of PDLC films in relation to their thickness and optical characteristics of the polymer matrix, sizes, polydispersity, concentration, and anisometry parameters of droplets. Based on this model, we have proposed a technique for estimating the size of LC droplets from the data on the dependence of the transmission coefficient on the applied voltage.     

Dynamic holographic joint fourier transform correlator based on a CdF2:Ga crystal

A joint Fourier transform correlator based on a bulk holographic medium—a CdF₂:Ga crystal serving a dynamic matched spatial-frequency filter—is implemented. Specific features of the correlator design are discussed. Correlatorf’s possibilities for selective recognition of objects of different type are demonstrated. Experimental data, results of mathematical modeling, and their analysis are reported. Suggestions for modifying the correlator scheme in order to improve its characteristics (operating speed, stability with respect to orientational and scale changes in objects, signal-to-noise ratio, correlation peak sharpness) are formulated.     

Study of lattice vibrational modes in CuGaS2 by using fourier transform spectroscopy

The lattice dynamics of a single crystal of CuGaS₂, grown by iodine transport technique, have been studied by using far IR absorption spectroscopy. All the absorption maxima caused by the phonon excitation are compared with the lattice vibrational modes obtained by Raman spectroscopy and by IR reflection techniques. An absorption maximum located at 175 cm^?1 cannot be explained with the help of phonon excitation; however this peak can be attributed to the defect frequency originating from the replacement of gallium atom by sulphur in the v₁₇ mode of vibration. The frequency of this defect-induced vibrational mode is calculated by taking a modified molecular model approach, and is found to be 166.9 cm^?1, which is in reasonably good agreement with the experimentally observed value of 175 cm^?1.     

High resolution fourier transform spectroscopy using infrared synchrotron radiation: I. Instrumentation

A compact high resolution (.002 cm^–1) vacuum Fourier transform spectrometer for use with far infrared synchrotron radiation was constructed at the National Synchrotron Light Source at Brookhaven National Laboratory. The spectrometer may be operated using a gas cell of path length of 2 m and a He cooled bolometer with NEP of 10^–13. The pure rotational spectrum of Ammonia was used to test the spectrometer.     

Applications of near-infrared spectroscopy to process analysis using fourier transform spectrometer

The applications of near-IR spectroscopy to process analysis using a Fourier transform spectrometer are described. In recent years, process analysis based on near-IR spectroscopy has received keen interest from a growing number of industries. Some configurations of Fourier transform near infrared (FT-NIR) interferometers used for process analysis are introduced as special optical systems for the realization of stable and reproducible performance. Moreover, the applications of NIR spectroscopy to process analysis using FT-NIR spectrometers are overviewed and two examples of applications are described in more detail. Furthermore, process analytical technology (PAT) for the pharmaceutical industry is introduced as a future trend of the application of FT-NIR spectroscopy, and a dual-wavelength system that can combine NIR and IR spectra is discussed as a newly proposed PAT tool for understanding processes.     

Non-unitary representations and fourier transform on the poincaré group

Two families of representations of the Poincaré group $\text{P}$ associated to complex orbits (with complex linear momenta) are introduced. The conditions for equivalence and irreducibility are stated. Fourier transforms related to them are defined and inversion formulas obtained for functions infinitely differentiable and of compact support on $\text{P}$.     

Ellipsometry with fourier transform spectrometer: An application to TaSi2 films

Summary Ellipsometric measurements on TaSi₂ polycrystalline films are presented in this paper. The optical functions are directly obtained in the wavenumber range from 400 to 3000 cm⁻¹ using an infrared ellipsometer coupled with a Fourier transform spectrometer. The analysis of the results provides the spectral range where the infrared response has a Drude-like behaviour. Finally, the optical resistivity at zero frequency is evaluated from the Drude parameters.     

Some examples and applications of Fedosov's star products and deformation quantization

We develop a simple example of Fedosov's method of constructing star products and we suggest a generalization of the method to the framework of Poisson supermanifolds. It is also shown how it is possible to construct a strict flabby quantization using Connes' concept of tangent groupoid.     

Uncertainty relation for the discrete Fourier transform

We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation.     

The use of the fast fourier transform in high resolution spectroscopy

Journal of Applied Spectroscopy -     

Theory of fourier hyperfunctions and its applications to quantum field theory

A new type of Fourier hyperfunctions is introduced. The axiomatic quantum field theory in terms of Fourier hyperfunctions is shown to include Wightman's formulation of tempered fields and its generalizations. The complete equivalence is established between the axioms for Wightman Fourier hyperfunctions and those for Green's functions by eliminating from the latter the linear growth condition of Osterwalder and Schrader.     

On the correlation between flux line lattice and crystal lattice

For pure type-II superconductors with κ slightly above 1/√2 it is shown that the preferential orientations of the flux-line lattice relative to the crystal lattice are related to the anisotropy of the coherence length.     

Some approximate solutions to the discrete master equation

Recent mathematical developments on approximate diffusionlike solutions to the master equation are summarized. The technique is applied to two master equations of physical interest-one that describes the phenomenon of superradiance and a second that characterizes generation-recombination noise in semiconductors. For this second case, some previously obtained equilibrium results are found and the extension of these results to finite times is given.     

Speckle reduction by a rotating aperture at the fourier transform plane

Statistical properties of the time-averaged speckle-reduced pattern at the image plane of a coherently illuminated uniform diffuse object are theoretically and experimentally studied. The diffuse object is assumed to be approximated by a deep random phase screen and zero-mean circular complex Gaussian statistics is also assumed to hold for the formation of speckles. The time-averaging process is performed by using a rotating aperture at the Fourier transform plane of the object. A theoretical study of the speckle reduction is conducted for a rotating Gaussian soft aperture at the Fourier transform plane. Expressions are analytically derived for the mean, autocorrelation function, power spectrum, and contrast of the time-averaged speckle pattern at the image plane. In particular, the contrast of the time-averaged speckle pattern is theoretically evaluated and its characteristics are discussed in detail. The theoretical results for the contrast are experimentally confirmed using a TV/film recording system. Excellent agreement between theoretical and experimental results is obtained.     

High-resolution infrared spectra of air pollutants with fourier transform spectroscopy

A Fourier transform spectrometer coupled with a long-path cell was used to record high resolution infrared spectra of air pollutants at very low concentrations. The spectral transmittance curves of CO were measured at room temperature, at a constant resolution of 0·5 cm^-1, at partial pressures from 2·32 to 0·004 torr, N₂ being the diluent. Apparent absorption coefficients were tabulated at 0·2-cm^-1 intervals. The techniques and data are applicable to studies of our contaminated atmosphere.     

Diffraction limitations of the lamellar grating interferometer in far-infrared fourier transform spectroscopy

The prediction of scalar diffraction theory that the effect of varying the groove depth of a lamellar grating illuminated by a plane wave at near-normal incidence is to modulate sinusoidally the intensity of specularly reflected flux is herein submitted to a critical re-evaluation.