Fringe Width Research Articles

Scattering of an electromagnetic light wave from a quasi-homogeneous medium with semisoft boundary

Based on the first-order Born approximation, the scattering of an electromagnetic plane wave from a relatively more realistic random medium, a quasi-homogeneous medium with semisoft boundary, has been investigated. The analytic expressions for the spectral density, the spectral degree of coherence and the spectral degree of polarization have been derived, and the effects of the characteristics of the medium and the polarization of the incident light wave on the far-zone scattered field are determined. The numerical simulations indicate that, with the increasing of the edge softness M of the medium, the spectral density presents a pattern with interference fringes, and the number, position and width of interference fringes can be modified by the parameter. It is also found that there is an obvious value saltation in the coherence profile. Besides, unlike the intensity and the coherence are significantly affected by the properties of the medium, the polarization of the scattered field is irrelevant to them due to the quasi-homogeneity and isotropy of the medium, and it is only connected with the polarization of the incident light.

Improvements of measuring the width of Fraunhofer diffraction fringes using Fourier transform

In this paper, we proposed an improved method for calculating the fringe width of Fraunhofer diffraction. Because the diffraction patterns are equidistant when the diffraction angle is small, the width of fringes can be determined through finding out the spatial frequency of the fringes using Fourier transform. To make the result more precise, the experimental data are compared with the theoretical values having the same range of the image in the frequency domain to get the modified frequency. We applied this method to calculate the diameters of some filaments by measuring their Fraunhofer diffraction fringes.

Residual stress analysis of swage autofrettaged gun barrel via finite element method

Residual stress analysis of swage autofrettaged gun barrel is performed in this study via finite element (FE) method. The swage autofrettage technique is one of the modernized pre-stressing methods to enhance the load bearing capacity and fatigue life of all gun barrels. An oversized moving mandrel is forced inside the gun barrel, which deforms the material through physical interference. The process is analyzed by evaluating residual stresses using a commercially available software package. The deformation effects caused by the mandrel and the geometrical variation of the mandrel on the gun barrel are analyzed in this study. This field has been insufficiently researched, but the effect of pre-stressing on the barrel, and at the start and mid-length for the swaging process, is not well examined. Thus, further analysis is required. The variations and effectiveness of the designed pressure band model are shown to define the problem easily. Results are evaluated at mid-length using a fixed fringe width percentage (A defined percentage of gun barrel axial length). The desired effects are well validated through numerical investigation using FE analysis. This study reveals that the geometry should be designed very thoroughly to determine the after effects. If too many variations occur, then the initial force requirement is extremely high; otherwise, the desired swaging effect cannot be achieved.

N−atomcollective-state atomic clock withN−foldincrease in effective frequency andN−foldreduction in fringe width

We describe a collective state atomic clock with Ramsey fringes narrowed by a factor of $\sqrt{N}$ compared to a conventional clock, N being the number of non-interacting atoms, without violating the uncertainty relation. This narrowing is explained as being due to interferences among the collective states, representing an effective $\sqrt{N}$ fold increase in the clock frequency, without entanglement. The detection process, which measures a collective state, can be used to increase the quantum efficiency of detection significantly, yielding a net improvement in stability by as much as a factor of 10.

Beyond the partial light intensity imager: Eliminating Moiré patterns

A partial light intensity imager (PLII) was proposed in our previous research for enhancing the dynamic range to 2.2×105lx in strong light. Moiré patterns may occur, however, since the PLII employs both a liquid crystal display (LCD) and a charge-coupled device (CCD) camera as its key devices, which can be regarded as two gratings. This research calculates the fringe widths and spectra for both the LCD and the CCD, and analyzes the relationship between the fringe width and the applied voltage on each pixel of the LCD. According to the theoretical results, we find that changing the rotational angle of the liquid crystal (LC) molecule by regulating the applied voltage is an effective method to eliminate the Moiré patterns in the PLII. Based on this principle, an experiment has been designed, and the Moiré patterns fringe width is alleviated from 20 pixels to10 pixels distance before and after, and the results verify the correctness of the theoretical analysis.

Design and analysis of modified version of double aperture speckle interferometer consisting of holographic optical element: Application to measurement of in plane displacement component

Duffy's double aperture speckle interferometer consists of two apertures placed symmetrically over an imaging lens and is used to measure in plane displacement component parallel to the line joining the two apertures using speckle photography. Diffraction limited imaging performance almost free from all monochromatic aberration over the two apertures is desirable for accurate measurement. In present work twin apertures are placed over a compact holographic lens (hololens) system. Lens system consists of two properly recorded and played back holographic lenses cemented together with proper alignment. Recording and play back geometry of holographic lenses has been designed for ease of alignment similar that of an on-axis imaging performance obtained by a conventional lens. Experimental results on measurement of in plane displacement along a line joining the two apertures using the designed interferometer is presented and compared with the actual displacement given to a diffuser between the two exposures. Further, results on measurement of in-plane displacement by analyzing speckle correlation fringes contained in zero order and ±1st order are presented to show that measurement made by analyzing fringes contained in ±1st order give better result than that of results obtained by analyzing speckle correlation fringes contained in zero order. In plane displacement measurement carried out by measuring fringe width of young's fringes contained in ±1st order provides an experimental technique to avoid cumbersome mathematical calculation for correction in the measured value of fringe spacing as suggested by several researchers.

Synthesis of vanadium pentoxide (V2O5) nanobelts with high coverage using plasma assisted PVD approach

Cost-saving, easy-handling, and eco-affable plasma assisted sublimation process (PASP) is proposed to synthesize vanadium pentoxide (V2O5) nanobelts (NBs) with excellent coverage on Si [100] wafer using oxygen plasma without using surfactants/catalysts. Pure orthorhombic V2O5 NBs having average length of few hundred of microns with quite uniform width nearly of 100nm are formed at 500°C. No film is deposited on Si in presence of oxygen gas without exciting plasma at 500°C. HRTEM analysis with SAED pattern confirm that all V2O5 NBs are single crystalline in nature with the fringe width of 0.33nm corresponding to [010] crystal plane. The XPS analysis shows the compositional purity and sub-stoichiometric nature of V2O5 NBs. The sub-stoichiometric nature of NBs is manifested through an appearance of low intensity peak corresponding to low oxidation state of V (i.e. V4+) at the binding energy of 514.8eV. The micro-Raman and FTIR analysis of NBs are carried out to study the different vibrational modes exhibited by V and O atoms coordinated in distinct fashions. The nanobelts exhibit room temperature PL emission in UV–visible realm with a broad hump in the range of 450–750nm, which confirms the presence of oxygen defects in NBs and strongly supports the XPS results as well. The possible growth mechanism of α-V2O5 NBs is proposed in this paper briefly.

Uncertainty formulations for multislit interferometry

In the context of (far-field) multislit interferometry we investigate the utility of two formulations of uncertainty in accounting for the complementarity of spatial localization and fringe width. We begin with a characterization of the relevant observables and general considerations regarding the suitability of different types of measures. The detailed analysis shows that both of the discussed uncertainty formulations yield qualitatively similar results, confirming that they correctly capture the relevant tradeoff. One approach, based on an idea of Aharonov and co-workers, is intuitively appealing and relies on a modification of the Heisenberg uncertainty relation. The other approach, developed by Uffink and Hilgevoord for single- and double-slit experiments, is readily applied to multislits. However, it is found that one of the underlying concepts requires generalization and that the choice of the parameters requires more consideration than was known.

Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection

We examine thermal light diffracted through a double slit using photon-number-resolved detection to directly measure high-order spatial correlations, and we see sinusoidal modulations of those correlations. The fringe width can, in principal, be made arbitrarily small, and we have experimentally obtained fringe widths as small as 30 nm with 800 nm wavelength light. This extreme sub-wavelength resolution, along with this direct detection technique, offers potential for high precision measurement applications.

Spatial shift unwrapping for digital fringe profilometry based on spatial shift estimation

An approach is presented to solve the problem of spatial shift wrapping associated with spatial shift estimation-based fringe pattern profilometry (FPP). This problem arises as the result of fringe reuses (that is, use of fringes with periodic light intensity variance), and the spatial shift can only be identified without ambiguity within the range of a fringe width. It is demonstrated that the problem is similar to the phase unwrapping problem associated with the phase-detection-based FPP, and the proposed method is inspired by the existing ideas of using multiple images with different wavelengths proposed for phase unwrapping. The effectiveness of the proposed method is verified by comparing experimental results against several objects, with the last object consisting of more complex surface features. We conclude by showing that our method is successful in reconstructing the fine details of the more complex object.

Calibration for medium resolution off-axis electron holography using a flexible dual-lens imaging system in a JEOL ARM 200F microscope.

In this work the calibration of a medium resolution off-axis electron holography using a dual-lens imaging system in a JEOL ARM 200F is shown. The objective dual-lens configuration allows adjusting the field of view from 35nm to 2.5μm. Subsequently, the parameters used in phase shift reconstruction were calibrated considering biprism voltage versus fringe spacing (σ) and versus fringe width (W). The reliability of the transmission electron microscope performance using these parameters was achieved using gold nanoparticles of known size and adjusting the excitation voltage of the lenses.

Affect of interference fringe width for processing accuracy and its recognition in measuring form deviation of tooth flank with laser interferometry

When an oblique-incidence interferometry is employed to measure the form deviation of helical tooth flank, the fringe width of collected interferogram varies greatly in practice. The processing accuracy in zones of narrow fringe is poorer than that of other zones generally. Two parameters are used to indicate the processing accuracy in this paper: the wrapped phase error led by random error and the discontinuous pixels after phase unwrapping. The corresponding relationships between the fringe width and the processing accuracy are summarized: the processing accuracy of interferogram is in inverse proportion to the width of interference fringe, and it is unreliable if the fringe width is less than four pixels. This paper employs the pseudocorrelation (PSD) algorithm to recognize the width of interference fringe. The experimental results are given to verify the feasibility of the recognition method.

Dual-Lens Electron Holography for Junction Profiling and Strain Mapping of Semiconductor Devices

Electron microscopes have been used extensively to look at structure at the nanometer scale. Most of the information obtained from electron microscopes is amplitude information. Yet, the phase information of electron microscopy, which can be obtained from off-axis electron holography, provides unique information on electronic structure and structural changes in a wide variety of materials.For the semiconductor industry, junction profiling and strain mapping in Si at high spatial resolution provide information that is critical for further scaling of semiconductor devices. Because of the complex process conditions involved to control the junction position relative to the gate position, determination of junction position at high spatial resolution can help to reduce the cost and cycle time of development. Bright-field holography can measure the phase change of electrons traversing the materials, which is directly related to the mean inner potential of Si, indicating the junction position at the nanometer scale. Furthermore, in recent years stressors have been incorporated into devices to change the semiconductor lattice constant in the channel region and thereby enhance hole and electron mobility. Like the junction definition, the extra processing steps involved to add strain in a device have increased development and manufacturing costs. One way to minimize development cycle time is to monitor, at a nanometer scale, changes in channel deformation resulting from process changes. In 2008, Hytch et al. reported that dark-field holography can provide a promising path to nanometer scale strain mapping [1]. Cooper et al. reported using dark-field holography to measure strain related to different process conditions [2, 3].The requirements of electron holography to inspect the current generation of semiconductor devices are: (1) a fringe width (fringe overlap) in the range of about 100 to 800 nm for an adequate field of view (FOV), (2) fringe spacing between 0.5 and 10 nm for meaningful spatial resolution, (3) visibility of the fringe contrast (10–30%) for useful signal-to-noise ratio, and (4) adjust-ability of both the FOV and the fringe spacing relative to the sample. In previous papers and patent disclosures, we reported that we had developed a dual-lens electron holography method on a JEOL instrument to meet the above requirements, and later we implemented the same method on FEI instruments to provide a similar operational range for electron holography [4–6]. This dual-lens operation allows electron holography to be performed from low to high magnification and provides the FOV and fringe spacing necessary for two-dimensional (2D) junction profiling and strain measurements for devices with various sizes.In this article, we describe the electron optics for this method. We also describe several examples of junction profiling and strain mapping to show how to use dual-lens electron holography to resolve semiconductor device issues at high spatial resolution.

Theoretical analysis of two-color ghost interference

Recently demonstrated ghost interference using correlated photons of different frequencies, has been theoretically analyzed. The calculation predicts an interesting nonlocal effect: the fringe width of the ghost interference depends not only on the wave-length of the photon involved, but also on the wavelength of the other photon with which it is entangled. This feature, arising because of different frequencies of the entangled photons, was hidden in the original ghost interference experiment. This prediction can be experimentally tested in a slightly modified version of the experiment.

Investigation of Thermal Expansion Coefficient of Metals from Light Diffraction Pattern

In this work, an experimental set for determining the linear thermal expansion coefficient (α) of a metal was designed and constructed. It was divided into three parts: metal rod holder, light source, and heating system. A cylindrical plastic pipe with an inner diameter of 16 cm was used as a metal rod holder. The sample metal rod with unknown linear thermal expansion coefficient was inserted vertically into a holder and covered by the first razor blade at one end, while the other end was fixed. The second razor blade was attached with posts. Two razor blades were aligned and separated with a distance of 0.05 cm; therefore, two razor blades were acted as a thin single slit. The steam generated from heating system was transferred into metal rod holder; subsequently, the length of metal rod increased with increasing temperature. The design of the apparatus for this proposed method based on decreasing the width of single slit with the same amount of increasing the metal rod length due to linear thermal expansion. A He-Ne laser with a wavelength of 632.8 nm used as a light source was passed through a single slit and produced a diffraction pattern on a screen. The decrease in slit width was determined by measuring the fringe width. The value of linear thermal expansion coefficient of a metal can be calculated from alteration of fringe width. In our case, stainless steel (314), copper (UNS C11000), and aluminium (6063) rods with the original length of 45.3 cm were used as samples. The experimental values of α for stainless steel, copper, and aluminium are 15.25 × 10-6, 17.74 × 10-6, and 23.13 × 10-6 (°C)-1, respectively. These values are in good agreement with the standard values as reported by the National Metal and Materials Technology Center (MTEC), Thailand. The error of this proposed method is found to be less than 1.2%.

Determination of the surface morphology of gold-decahedra nanoparticles using an off-axis electron holography dual-lens imaging system

The purpose of this paper is to show surface irregularities in gold decahedra nanoparticles extracted by using off-axis electron holography in a JEOL ARM 200F microscope. Electron holography has been used in a dual-lens system within the objective lenses: main objective lens and objective minilens. Parameters such as biprism voltage, fringe spacing (σ), fringe width (W) and optimum fringe contrast have been calibrated. The reliability of the transmission electron microscope performance with these parameters was carried out through a plug-in in the Digital-Micrograph software, which considers the mean inner potential within the particle leading a precise determination of the morphological surface of decahedral nanoparticles obtained from the reconstructed unwrapped phase and image processing. We have also shown that electron holography has the capability to extract information from nanoparticle shape that is currently impossible to obtain with any other electron microscopy technique.

Research on Improving the Measurement Accuracy of Laser Interferometer System

In the laser interferometer system based on the four quadrants photoelectric, phase difference between two quadrants photoelectric is the way of identifying the fringe width and rotating angle, in order to achieving the measurement of two-dimensional small angle. Due to the temperature instability of the laser itself, the system installation error, the electronic device noise, and wave-front error etc, interference fringes prone to bending, and the received optical signal contains unequal amplitude and DC offset error, which will have a serious impact on measurement. Therefore, this paper analysis these impact of the wave-front error on the interferometer system and propose improvement measures. New hardware circuit is designed to eliminate the DC offset and the new algorithm based on multiple linear regression models is proposed to achieve the high-precision extraction of phase difference. The experiment results show that the methods reach the angle accuracy 0.1 arc second.

Measuring the atomic recoil frequency using a modified grating-echo atom interferometer

We describe progress toward a precise measurement of the recoil energy of an atom measured using a perturbative grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, a perturbing sw pulse is used to shift the phase of excited momentum states---producing a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2\omega_q$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures $\lesssim 5$ $\mu$K in a non-magnetic apparatus. We demonstrate a measurement of $\omega_q$ with a statistical uncertainty of 37 parts per $10^9$ (ppb) on a time scale of $\sim 45$ ms in 14 hours. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be $\sim 6$ parts per $10^6$ (ppm). We describe methods of reducing these systematic errors.

Hydrothermal Synthesis and Magnetic Property Studies of Multiferroic YMnO<sub>3</sub> Nanorods

Multiferroic YMnO3nanorods were synthesized by hydrothermal process at 200°C. Hexagonal structure of the synthesized sample was confirmed by powder X-ray diffraction analysis. High resolution scanning electron microscope analysis shows uniform nanorods with average diameter of about 350nm and length of 10µm. Transmission electron microscope and selected area electron diffraction studies reveal the single crystalline nature of nanorods and the lattice fringe width of nanorod is about 0.296nm for the (111) plane with the growth direction along (001) plane (c-axis). The zero-field-cooled and field-cooled magnetization studies show a complicated magnetic transition occurred in the temperature range from 20 to 300K as confirmed by magnetic hysteresis loops.

High-stability compact atomic clock based on isotropic laser cooling

We present a compact cold-atom clock configuration where isotropic laser cooling, microwave interrogation, and clock signal detection are successively performed inside a spherical microwave cavity. For ground operation, a typical Ramsey fringe width of 20 Hz has been demonstrated, limited by the atom cloud's free fall in the cavity. The isotropic cooling light's disordered properties provide a large and stable number of cold atoms, leading to a high signal-to-noise ratio limited by atomic shot noise. A relative frequency stability of $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ has been achieved, averaged down to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ after $5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ s of integration. Development of such a high-performance compact clock is of major relevance for on-board applications, such as satellite-positioning systems. As a cesium clock, it opens the door to a new generation of compact primary standards and timekeeping devices.