Position Of Intensity Maximum Research Articles

INTERFERENCE PATTERN OF THE WAVE FIELD OF TWO SOURCES IN THE NEAR FIELD OF OBSERVATION

The paper considers the problem of an approximate wave field in the so-called near, middle and far zones of observation. The possibility of introducing a more accurate than the Fresnel approximation, the so-called quasi-exact approximation, is indicated. For the interference problem usually considered in the Fresnel approximation, the intensity distribution in the near field of observation is obtained. It is shown that the positions of intensity maxima in the near zone of observation are determined by a cubic equation.

Shift of the interference extrema of low-frequency acoustic propagations near the axis of a deep sound channel

Broadband interference patterns measured from acoustic propagations near the axis of a deep sound channel are interpreted. Analyses using mode theory for the waveguide with bilinear sound speed profiles show that the increase in sound speed without gradient variation shifts the positions of intensity maxima to higher frequencies in a fixed range whereas the increase in the gradient shifts the maxima to lower frequencies. Analytic results imply that the frequency shift of intensity extrema appearing in the measurements could be explained by the increase in the sound speed gradient above the axis of the deep sound channel.

Study of the Diffraction Grating on a Convex Surface as a Dispersive Element

A dispersive element in the form of the diffraction grating on a convex mirror surface is investigated. The groove profile of the grating is measured and the intensity distribution between the diffraction orders is calculated as a function of wavelength for the visible spectrum. Optomechanical elements for the required alignments of the spectrometer elements are designed and fabricated. Adjustment of a prototype optical scheme is implemented and point images for three monochromatic incident wavelengths are obtained. The energy distribution between the diffraction orders and the intensity maxima positions are in agreement with the simulation results.

Evolution of decentred laser beams propagating through atmospheric turbulence

The changes of the average intensity, the centre of beam gravity and the position of intensity maximum of decentred laser beams propagating through atmospheric turbulence are examined in detail. It is shown that the decentred intensity distribution is amended gradually with increasing the propagation distance and the strength of turbulence, and it becomes an off-axis Gaussian-like beam when the propagation distance and the strength of turbulence become large enough. The centre of beam gravity is independent of both the propagation distance and the strength of turbulence. On the other hand, there are two intensity maxima, and their positions are symmetrical around the propagation z-axis when the propagation distance z is small. With increasing z, there is only one intensity maximum. As z further increases, position of the intensity maximum is further shifted towards the z-axis. When z is large enough, the position of the intensity maximum is unchanged. The unchanged position of the intensity maximum moves further away from the z-axis with an increase in the refraction index structure constant, the decentred parameter and the waist width.

X-ray diffraction in a uniformly bent crystal in reflection geometry

The features of the intensity distribution over the exit surface of a uniformly bent crystal have been investigated in reflection geometry. Experiments have been performed using thin-layer heterostructures Si(1−x)Gex/Si. For heterosystems, internal stresses induced in the film and substrate lead to an elastic bending of the whole system. The section topographs exhibit deformation interference fringes. It is important that the contrast of this interference pattern is almost one order of magnitude higher than the contrast in the case of Bragg scattering in a perfect crystal. The observed interference pattern depends on the radius of bending of the crystal. As the bending radius increases, all maxima shift toward the basic Bragg peak. Correspondingly, all distances between the interference fringes decrease. It has been shown that the positions of intensity maxima do not depend on the sign of the crystal bending. For a negative sign of the radius of the crystal bending (positive strain gradient), the integrated intensity increases. The results of the numerical simulation of the diffraction images agree well with the experimental topographs. A comparison of the numerical simulation of the interference pattern with the experimental topographs makes it possible to exactly determine the radius of the crystal bending (4%). The formulas describing the positions of interference maxima as a function of the bending radius of the sample have been obtained using the results of the numerical simulation of the experiment.

Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel number N F = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.

Line Formation in a Purely Scattering, Optically Thick Atmosphere

A model problem in the theory of line formation in an optically thick, purely scattering, stellar atmosphere is considered. The integral equation of radiation transfer at line frequencies is solved numerically for a two-level atom in the approximation of complete frequency redistribution in scattering. The numerical results are compared with those calculated from equations of the asymptotic theory. On the basis of the asymptotic theory, the positions of intensity maxima in a line are found for different absorption profiles.

Analysis of composition fluctuations in Al xGa 1 −xN

Composition fluctuations in Al x Ga 1 −x N-layers ( x=0.25 and 0.35) are investigated on an atomic scale by high-resolution transmission electron microscopy (HRTEM). The samples were grown by plasma induced molecular beam epitaxy on Al 2O 3 (0001). A strain state analysis of the cross-sectional HRTEM micrographs is performed with the digital analysis of lattice images (DALI) program package. Composition profiles on an atomic scale are derived by the measurement of the distances between intensity maxima positions in the HRTEM image. The analyses revealed different areas in the Al x Ga 1 −x N-layers with either homogeneous or ‘striped’ contrast. In the striped areas the analyses indicate a strong decomposition that leads to the formation of self-organized superlattice structures.

Analysis of composition fluctuations on an atomic scale in Al0.25Ga0.75N by high-resolution transmission electron microscopy

Composition fluctuations in the Al0.25Ga0.75N layer of an AlGaN/GaN transistor structure grown by plasma induced molecular beam epitaxy on Al2O3(0001) at a growth temperature of 870 °C were studied by digital analysis of lattice images (DALI) of high-resolution transmission electron microscopy (HRTEM) cross-section images. DALI exploits the linear dependence of the lattice parameters on the Al content by applying Vegard’s law. Detecting the distances between intensity maxima positions in the micrograph which can be considered as a fingerprint of the local lattice parameters quantitatively derives composition profiles on an atomic scale. In the HRTEM cross-section image different areas were observed in the Al0.25Ga0.75N layer with either homogeneous or “striped” contrast. In the striped areas the analyses indicate a strong periodic decomposition with a period of 1 nm consisting of 1 ML Al0.8Ga0.2N and about 3 ML Al0.07Ga0.93N. The regions with homogeneous contrast do not exhibit significant composition fluctuations.

Sensitivity limits of strain mapping procedures using high‐resolution electron microscopy

Strain detection limits achieved by several approaches of strain mapping differing in the procedure of determining positions of intensity maxima have been compared. Algorithms which simultaneously take into account the two‐dimensional intensity distribution around maximum positions yield similar detection limits and are superior to those performing successive one‐dimensional cuts. Investigations of the effect of image recording imply that the use of photographic plates is superior to direct image recording using a slow‐scan CCD camera because of larger sampling rates and a larger field of view. It is finally shown that the choice of specimen preparation technique substantially affects the strain detection limit with cleaved samples yielding results which are a factor of about three better than ion‐milled samples.

Radiation from creeping waves on micrometer-size perfectly conducting fibers

The asymptotic solution of light scattering from a perfectly conducting circular cylinder is derived using the Watson transformation method first applied by Franz. It is clearly demonstrated that the scattered pattern is a superposition of a reflected wave and radiation from two creeping waves propagating around the cylinder in opposite directions. An He-Ne laser was used as a light source with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ field parallel to the axis of an aluminum-coated quartz fiber at normal incidence. The positions of intensity maxima and minima of the scattered light predicted by the Franz theory were not fully in agreement with experiment. We found it necessary to consider the phase change of the reflected wave in order to obtain satisfactory agreement.

Detection of direction of motion and zero order fringe identification in holographic displacement measurement

Two methods have been suggested to detect the direction (forward or backward) of uniform velocity motion along with identification of no motion positions with other intensity maxima positions in the reconstruction. The first method requires two continuous exposures while the other is a combination of one static and one continuous recording.

Band Structure and the Titanium LII, III X-Ray Emission and Absorption Spectra from Pure Metal, Oxides, Nitride, Carbide, and Boride

The titanium LII, III x-ray emission and absorption spectra (λ∼27.5 Å) from pure metal, oxides, nitride, carbide, and boride have been investigated using a plane-crystal vacuum spectrometer with electron-beam excitation and flow-proportional counter detection. Emission spectra were studied over a wide range of accelerating voltages and takeoff angles, showing that satellite emission and self-absorption effects can significantly distort the band shapes and energy positions of intensity maxima. A replica of the LII, III absorption spectrum can be constructed solely from emission spectra affiicted with widely different amounts of self-absorption. The LII, III emission spectra from the oxides, nitride, and carbide exhibit an important crossover transition from the 2p level of the anion to the LII and LIII levels of titanium. Results indicate formation of a 3d band in titanium compounds which is only partially filled, giving rise to metallic conduction. X-ray data is compared to density of states calculations for TiO, TiN, and TiC. The energy shifts of emission bands and absorption edges indicate a transfer of charge from titanium to anion in the oxides, nitride, and boride but that in TiC there is a transfer of charge from carbon to titanium. Energy separations between anion 2p band and titanium 3d band are measured and it is shown that both bands contribute significantly to the TiLII, III spectra from the compounds.