Measurements of coating density using ultrasonic reflection coefficient phase spectrum

A nondestructive method to determine the density of coating has been proposed in this paper based on the ultrasonic reflection coefficient phase spectrum (URCPS). A model was set up first to represent the ultrasonic waves reflected from a coating system at normal incident, and the relation between the extremum of URCPS and the coating density was established to provide the principle of determining the density. The ultrasonic method was validated on a series of ZrO2-7 wt.%Y2O3 (YSZ) coatings with various density. The specimens were prepared by electric beam physical vapor deposit (EB-PVD). After deposition, the specimens were irradiated using high-intensity pulsed ion beam (HIPIB) at different ion current density of 100 and 200 A/cm2 to change coating density. The coating densities of as-deposited and post irradiation by HIPIB were derived to be 4940-5030, 5200-5320 and 5390-5470 kg/m3, respectively. The relative error between the coating density measured by the ultrasonic method and Archimedean principle ranging from 2.53% to 6.11%, indicates that the proposed ultrasonic quantification method provides a reliable nondestructive way to determine coating density.     

Multisoliton phase shifts in the case of a nonzero reflection coefficient

We study multisoliton solutions of the Korteweg-de Vries equation in the case of a nonzero reflection coefficient. An explicit phase shift formula is derived that clearly displays the nature of the interaction of each soliton with the other ones and with the dispersive wavetrain. In particular, this formula shows that each soliton experiences in addition to the ordinary N-soliton phase shift an extra phase shift to the left caused by the collision with the dispersive wavetrain.     

Attenuation and reflection coefficient nomogram

A nomogram is described for the determination of the sound pressure reflection coefficient R and the round-trip loss 2αL when using the pulse-echo buffer rod technique.     

Lateral shift of X-ray beams and determination of phase in reflectometry of multilayer periodic structures

Lateral shift of X-ray beams during Bragg’s reflection from a multilayer periodic structure (MS) is studied analytically and numerically. The field distribution in the MS, as well as the displacement of reflected and transmitted beams are determined. Analytic expressions for the shifts are derived in the approximation of spectrally narrow beams. Since the shift is controlled by the phase of the reflectance (transmittance), it is possible in principle to extract information concerning the phase of reflection (transmission) by measuring the spatial shift.     

Reflective phase shift measurement of the Mo/Si multilayer mirror in extreme ultraviolet region

The reflective phase shift of multilayer mirror is one important property required in EUV lithography and attosecond pulses experiments. The reflective phase shift of the periodic Mo/Si multilayer mirror was characterized by combining the reflectivity with total electron yield signal at the synchrotron radiation in Hefei. The multilayer was fabricated using direct current magnetic sputtering method. Using the wavelet transform approach, the period and each layer thickness were obtained, the small angle X-ray reflective data from X-ray diffractometer were fitted using these data as the mutilayer's initial structure. The TEY signal of the multilayer is coincided with the surface electron field of the multilayer. A thick Si layer was used to eliminate the effect of the multilayer's surface layer on the TEY signal. The retrieved difference in reflected phase from the incident phase was obtained combining the reflectivity with the total electron yield signal and it is similar with the calculated phase shift of the multilayer.     

Coherent and incoherent reflection and transmission of multilayer structures

The complex-amplitude reflection and transmission coefficientsr andt of a pile of films are represented as a product of matrices. The matrices describe the transformation of two plane waves travelling in opposite directions between the films, and their development within the films.If one of the films is significantly thicker than the other layers (e.g., several films on a substrate), the calculated reflectanceR=rr ^* and transmittanceTt ^* show narrow Fabry-Perot oscillations which, in a lot of cases, are not observed in the experiment. Since the matrix method is equivalent to the representation of the amplitudesr andt as a coherent superposition of multiple reflected waves within the thick slab, we are able to suppress, in the calculation, the interference within this thick film by adding the absolute squares of the partial waves corresponding to an incoherent treatment. This procedure is shorter and more simple than averaging over an appropriate interval of frequency or thickness, which, in most cases, leads to the same results.     

Full wave-field reflection coefficient inversion

This paper develops a Bayesian inversion for recovering multilayer geoacoustic (velocity, density, attenuation) profiles from a full wave-field (spherical-wave) seabed reflection response. The reflection data originate from acoustic time series windowed for a single bottom interaction, which are processed to yield reflection coefficient data as a function of frequency and angle. Replica data for inversion are computed using a wave number-integration model to calculate the full complex acoustic pressure field, which is processed to produce a commensurate seabed response function. To address the high computational cost of calculating short range acoustic fields, the inversion algorithms are parallelized and frequency averaging is replaced by range averaging in the forward model. The posterior probability density is interpreted in terms of optimal parameter estimates, marginal distributions, and credibility intervals. Inversion results for the full wave-field seabed response are compared to those obtained using plane-wave reflection coefficients. A realistic synthetic study indicates that the plane-wave assumption can fail, producing erroneous results with misleading uncertainty bounds, whereas excellent results are obtained with the full-wave reflection inversion.     

Dispersion of second-order nonlinear optical coefficient

A simple, approximate relation between the dispersion of the second-order nonlinear optical (SNLO) coefficient and first-order susceptibility has been derived using the well-known results of density-matrix calculation of quantum-mechanical theory. A new tensor of SNLO coefficient has been defined, which retains symmetries when the input beams are in the spectral range of transparency while the generated beam can also be in the spectral range of absorption. The validity of the relation has been checked for three ferroelectric crystals, KTP, LiNbO₃ and KNbO₃, which are transparent in the visible and near infrared, and for two semiconductors, GaP and GaAs, which absorb in the visible. Contrary to Miller’s law, the presented relation is in good agreement with measurements. Received: 8 February 2001 / Revised version: 2 July 2001 / Published online: 10 October 2001     

Omnidirectional complete reflection from multilayer dielectric structures

Formulas for determining the boundaries of the high-reflectance zone of a dielectric multilayer system at all angles of oblique incidence of light are derived. The optimal conditions for a possible extension of the boundaries of omnidirectional complete reflection for all polarizations in a given spectral range are discussed.     

In-situ monitoring of interface formation using the phase shift of reflection high-energy electron diffraction intensity oscillations

A novel phase shift of Reflection High-Energy Electron Diffraction (RHEED) intensity oscillations during heterointerface formation allows direct monitoring of segragation at GaAs/Al _x Ga_1–x As interfaces. The effect should be applicable to other materials systems as it is due to the reconfiguration of the surface structure at the heterointerface.     

Causes of phase variations in the air–ice boundary reflection coefficient in the microwave range

We study phase variations in the coefficient of reflection from a flat air–ice boundary at the ice melting point. The measurements were performed by different methods at frequencies 3.3, 6, 13, and 32 GHz. The experimental data were compared with simple theoretical models. It was found that ice wettening in thin layers leads to a phase variation in the reflection coefficient by up to a few ten degrees with satisfactory agreement between the experiment and the theory. However, anomalies of the transmission properties of the samples unexplainable in terms of the model of effective dielectric permittivity of the melting layers were observed in a narrow temperature range before the ice destruction. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 3, pp. 260–266, March 2009.     

Studies of the ocean-bottom reflection coefficient at angles of total internal reflection

For practical-purpose studies in underwater acoustics, a new method is proposed to determine the bottom reflection coefficient on the basis of multiple bottom-surface reflections. The method allows one to obtain the angular dependence of the bottom reflection coefficient at grazing angles from several degrees to several tens of degrees in the audio and infrasonic frequency bands. The sound field structure is studied in deep-water regions of the Black (2000 m) and Arabian (4000 m) seas at frequencies within 10–400 Hz. For the regions under investigation, the frequency-angular dependence of the reflection coefficient is obtained with the use of the proposed method. The data for the Black Sea are compared with those provided by the conventional method based on the use of single and double bottom and bottom-surface reflections. Experimental data on the values and variations of the bottom reflection coefficient are presented for different deepwater and shallow-water regions of the World Ocean. The presence of shear waves in the bottom sediments is revealed, and the effect of these waves on the frequency-angular dependence of the reflection coefficient is demonstrated.     

A method for measuring the phase of the reflection coefficient in the visible range of the spectrum

A method for measuring the phase of the reflection coefficient in the optical wavelength range is proposed. The method is simple in experimental implementation and is based on measuring the energyreflection coefficients of a sample in two media with different refractive indices. Analytical and numerical estimates show that the measurement accuracy of the phase is on the order of 1°. The possibilities of using the results of the phase measurement in practice for a more complete characterization of materials and structures under investigation are considered.     

A mirror with an intensity-dependent reflection coefficient

A device exhibiting a power-dependent reflection coefficient with fast time response and no frequency shift is proposed and analysed. It utilizes a combination of a nonlinear crystal for second harmonic generation and a dichroic mirror with high reflectivity for the second harmonic and partial transmission for the fundamental wavelenth. This device has been successfully used in a preliminary experiment to modelock a Nd:YAG laser.Department of Physics, Sofia University, BG-1126, Sofia, Bulgaria.     

Zakharov-Shabat inverse problem with meromorphic reflection coefficient

We analyze the Zakharov-Shabat-type inverse problem when the reflection coefficient contains poles in the eigenvalue plane, as an extension of the earlier work by Atkinson in the case of the Schrödinger problem. It is demonstrated that due to the mutual influence of such a pole and the usual bound-state pole, a discontinuous solitary wave profile is generated. Furthermore, we also examine the form of the nonlinear field only due to the pole of the reflection coefficient. A different approach is necessary to convert the GLM equation into a purely differential one for its solution.     

Measuring the reflection coefficient for ultrasonic interfaces

The lack of quantitative information about the properties of the tissue interface is one shortcoming in imaging biological structures with the echo-ranging ultrasonic technique. A multitransducer configuration offers a method for experimentally evaluating a reflection coefficient for arbitrarily oriented interfaces. Mathematical analysis indicates that this is feasible. Experiments with interfaces formed by water and aluminium, and acrylic plastics and polyethylene have demonstrated accuracies of 20% for orientations ranging between ±1 degree from the normal.     

Dispersion of the linear electrooptic coefficient in ZnS

The measured values and the analysis of the dispersion of the unclamped linear electrooptic coefficient r^T₄₁ in cubic ZnS single crystals operating as optical modulator are presented. The spectral dispersion of the non-linear optical coefficient d₄₁(ω, ω, 0) is also reported and the weak dependence on the light frequency, observed for d₄₁, is discussed by taking into account the opposite sign of ionic and electronic contributions.