Resonant optical transmission from a one-dimensional relief metalized subwavelength grating

We have studied one-dimensional (1D) relief metalized subwavelength gratings, which support resonant optical transmission. We have used pregrooved DVD stampers, metalized with a thin Al layer. The sensitivity of resonant transmission of the gratings to the cladding environment was investigated by the help of matching fluids. We have shown that the shift of the spectral position of the resonance peak can be used for sensor applications, e.g., for determination of very low concentrations of nanosized dielectric particles in distilled water.     

An inverse boundary problem for one-dimensional heat equation with a multilayer domain

In this paper, we propose a regularization method for determining a moving boundary from Cauchy data in one-dimensional heat equation with a multilayer domain. The numerical scheme is based on the use of the method of fundamental solutions and a discrete Tikhonov regularization technique. The generalized cross validation rule for the choice of a regularization parameter is applied to obtain a stable numerical approximation to the moving boundary. Numerical experiments for five examples show that our proposed method is effective and stable.     

Reconstruction of time-dependent boundary heat flux by a BEM-based inverse algorithm

The objective of this study is to reconstruct an unknown time-dependent heat flux distribution at a surface whose temperature history is provided by a broad-band thermochromic liquid crystal (TLC) thermographic technique. The information given for this inverse problem is the surface temperature history. Although this is not an inverse problem, it is solved as such in order to filter the errors in input temperatures which are reflected in errors in heat fluxes. We minimize a quadratic functional which measures the sum of the squares of the deviation of estimated (computed) temperatures relative to measured temperatures provided by the TLC thermography. The objective function is minimized using the Levenberg–Marquardt method, and we develop an explicit scheme to compute the required sensitivity coefficients. The unknown flux is allowed to vary in space and time. Results are presented for a simulation in which a spatially varying and time-dependent flux is reconstructed over an airfoil.     

Computer-aided inverse panorama on a conical projection surface

The aim of this study is to develop a practical method of direct mapping of an inverse conical panorama with computer aid. The panoramic image is a central projection onto a conical surface from the centres dispersed on a circular or straight path located outside the projection surface. The proposed method is a nonlinear projection in which the resulting image is treated as a sequence of stitched pictures of zero width taken from a moving view point. Geometric data and relations between the projected points are utilised to formulate algorithms for drawing of inverse panoramic images of straight lines, which further enables drawing of wire frame models of represented forms. Images are drawn as plots of a function in the Mathcad software. However, in order to make drawing more efficient and convenient, as well as for the practical applications of them, the algorithms can be implemented in any graphical package.     

Reconstruction of long-period fiber gratings from their core-to-core transmission function

In order to reconstruct the structure of a long-period grating, both the complex core-to-core transmission function and the complex core-to-cladding transmission function should be known. However, in practice, only the core-to-core transmission function of the grating can be measured. We demonstrate theoretically the reconstruction of long-period gratings from only the core-to-core transmission function. The reconstruction is performed by extracting the complex core-to-cladding transmission function of the grating from its core-to-core transmission function. Generally, the extraction is not unique; however, we show that by writing an additional grating in cascade to the interrogated grating, a unique reconstruction can be obtained. In weak long-period gratings, only the amplitude of the core-to-core transmission function is needed to reconstruct the grating. The results of our work can enable the experimental reconstruction of long-period gratings from their transmission function as well as the development of novel distributed sensors.     

Solution of the linear one-dimensional inverse heat-conduction problem on the basis of a hyperbolic equation

The linear problem of determining the temperature in an infinite one-dimensional plate with a stationary heat sensor and a stationary boundary is solved. The allowable approximation time steps in the calculations can be diminished by using a hyperbolic heat-conduction equation with a suitably chosen hyperbolicity parameter.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 6, pp. 1093–1098, June, 1981.     

Reconstruction of myocardial current sources from measured surface potentials

An algebraic algorithm is proposed for the reconstruction of the density of equivalent current sources on a spherical surface enclosing the myocardium. The characteristics of the measurement system are considered together with the electrode placing scheme. Reconstruction results are given from actual recordings of surface potentials as maps of the density distribution for the equivalent sources for various times in the cardiac cycle.     

Effects of uncertainty on background permittivity in one-dimensional linear inverse scattering

We discuss the role of uncertainties in the knowledge of the background in inverse scattering for a buried object under the distorted Born approximation. In particular, we focus on the role played by inaccuracy in the knowledge of the dielectric permittivity of the host medium, with reference to both a lossless half-space and a lossless three-layered medium. This investigation allows us to show how reconstruction of an inhomogeneity in a three-layered medium is more critical than in the case of a half-space (two-layered) geometry.     

Reconstruction of the thermal conductivity coefficient from the solution of the nonlinear inverse problem

We consider the iteration algorithm for the solution of the nonlinear inverse problem of non-steady-state heat conduction.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 4, pp. 587–592, October, 1981.     

大粗糙度起伏下一维海面声散射建模与分析

针对起伏海面高频声散射计算问题,提出了一种改进的基尔霍夫(Kirchhoff)近似方法。该方法考虑了海面的阴影区和亮区之间的多次散射声场,可对小入射角下大粗糙度起伏海面的散射声场进行计算。以一维余弦和高斯谱海面散射声场的有限元计算结果为标准解验证了所提方法的准确性和适用性。利用该方法计算了一维余弦海面的散射强度,分析了不同入射声波频率和角度下海面散射强度的分布情况,并解释了Bragg散射的产生机理,同时讨论了不同海面均方根高度和相关长度情况下高斯谱海面散射强度的变化规律。     

Reconstruction of nonstationary temperatures from the results of measurements on a heat-insulated wall surface

The problem of boundary temperature determination from the results of its measurement on a heat-insulated wall surface is analyzed. A solution is based on solving the corresponding direct problem in the form of a Duhamel integral.Kuban State Technological University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 5–6, pp. 483–488, November–December, 1994.     

Optical reflectance and transmission of a textured surface

The reflectivity of a solar thermal or solar electric device is a key parameter in efficiency. In the recent solar device literature, highly “textured” surfaces have been shown to reduce the reflectivity appreciably. The theoretical model used to describe this phenomenon is light trapping by multiple reflections. Surface roughness has also been considered by others through statistical scattering theory. The range of validity of either model is limited to a scale of texture larger than the wavelength of the light. For the micron scaled texture which is of interest, however, both approaches fall into the category of approximate solutions to approximate models of the surface.We approached the problem differently. We obtained the effects of texture on reflectivity and transmission through an exact calculation of a boundary layer whose complex dielectric constant is an appropriate average of the bulk dielectric constant of the material and air. The calculations were made for arbitrary angles of incidence, polarization and wavelength, as well as for arbitrary spatial variation of the dielectric constant through the boundary layer. We developed the spatial variation through effective medium models for a discontinuous surface layer. Finally, we compared the computer calculation with an exact analytic treatment for normal incidence, as well as with experimental reflectivities on several textured surfaces.     

Reconstruction of nonlinearly distorted signals with regularized inverse characteristics

A signal distorted by a system having static, invertible, nonlinear characteristics can be exactly restored in the absence of noise. In this case, the inverse of the characteristics can be used. When noise is superimposed to the distorted signal, the inverse characteristics may not be proper because the noise is strongly amplified. This noise has to be suppressed in the reconstructed signal, which can be accomplished only at the price of bias. This article presents a method to compensate the effect of static nonlinearities in the presence of noise. This method is based on Tikhonov's regularization operators and provides a compromise between noisy and biased estimates.     

Quantitative characterization of flaws near a surface using inverse born approximation

Quantitative reconstruction of volumetric flaws near a surface of an elastic solid has been carried out experimentally by analyzing the scattered ultrasonic waves. The inverse Born approximation (developed for flaws in bulk materials) was tested for the first time in the determination of the size, shape, and orientation of near-surface flaws. We have studied spherical solid inclusions at various depths below the surface. In addition we examined an approximately 2:1 prolate spheroidal inclusion which was located one major axis below the surface. The determination of the flaw's size, shape, and orientation in terms of an equivalent ellipsoid is realized by performing nonlinear least-squares iteration of the one-dimensional Born inversion results obtained at various scattering directions within a finite aperture. The reconstruction is in good agreement with the actual parameters of the flaw.     

Reconstruction of the net emission distribution from the total radiance distribution on a reflecting surface

The problem is considered of reconstructing, from a measurement of the total radiance distribution on an emitting surface, the radiance distribution that would be observed in the absence of reflected radiation. An explicit solution of the implied inverse problem is derived for the case in which the reflective properties of the surface are given in terms of a bidirectional reflection distribution function. Also considered are the limiting cases of diffuse and specular reflection. Practical considerations are discussed for application of the theory to the nonintrusive and remote measurement of temperatures and pressures on concave surfaces, either by traditional radiometry or by the use of thermographic phosphors and temperature- and pressure-sensitive paints.     

Gap modes of one-dimensional photonic crystal surface waves

The finite-difference time-domain method is employed for the analysis of coupling of the surface modes of two truncated one-dimensional photonic crystals separated by a gap. The wave vector, field distributions, and existence conditions of the coupled surface modes are investigated. The wave vector of symmetric gap modes increases with decreasing gap width, while that of antisymmetric modes decreases-exactly opposite of the situation for surface plasmons on metallic half-spaces separated by a dielectric gap. Photonic crystal gap modes could easily and effectively be used as nondissipating gap-mode waveguides.     

Analytical solution of the one-dimensional nonlinear inverse heat conduction problem and its applications

An analytical solution of the nonlinear inverse heat conduction problem is obtained and its application to identification of the boundary conditions on the components of the flow-through part of a gas turbine engine is demonstrated.Ufa Aircraft Institute. Institute of Mechanical Engineering, Russian Academy of Sciences, Ufa, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 6, pp. 735–739, December, 1993.     

Origin of the positional offset of FP-like enhanced transmission peaks in a one-dimensional gold grating

General transmission characteristics of a one-dimensional optically thick gold grating were investigated as functions of the grating structural parameters (period, slit width and grating thickness) in the spectral range from 0.4 μm to 9.9 μm. The positions (resonant wavelengths) of the Fabry–Perot (FP)-like enhanced transmission (ET) peaks depend not only on the grating’s period and thickness, but also on the slit width. These numerically calculated FP-like resonant positions are different from the simple FP predictions. The physical origin of these positional offsets is ascribed to the additional phases produced by the special ‘reflecting planes’, which are caused by oscillating dipoles located at the entrances and exits of the slits. For a particular order of FP-like resonance, the additional phase is found to be independent of the refractive index of the surrounding, but dependent on the grating’s structural parameters.     

Reconstruction of causal characteristics of the thermal conductivity process from the solution of the combined inverse problem

An algorithm is suggested for solving the combined inverse problem of heat exchange on the basis of using uniqueness theorems.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No.5, pp. 839–844, May, 1987.