Number of degrees of freedom in inverse diffraction

The problem of inverse diffraction from plane to plane is considered in the case where a finite aperture exists in the boundary plane. Singular values and singular functions for the problem are introduced, and the number of degrees of freedom is defined in terms of the distribution of the singular values. Numerical computations are presented for the one-dimensional problem, and it is shown that the effect of evanescent waves disappears at a distance of approximately one wavelength from the boundary plane, even when the dimension of the slit is comparable with the wavelength of the diffracted field. © 1983 Taylor & Francis Group, LLC.

Particle size distributions from Fraunhofer diffraction

info:eu-repo/semantics/published

Stability Problems in Inverse Diffraction

Inverse diffraction consists in determining the field distribution on a boundary surface from the knowledge of the distribution on a surface situated within the domain where the wave propagates. This problem is a good example for illustrating the use of least-squares methods (also called regularization methods) for solving linear ill-posed inverse problem. We focus on obtaining error bounds For regularized solutions and show that the stability of the restored field far from the boundary surface is quite satisfactory: the error is proportional to ∊(ðŗ‚ ≃ 1) ,ðŗœ being the error in the data (Hölder continuity). However, the error in the restored field on the boundary surface is only proportional to an inverse power of │In∊│ (logarithmic continuity). Such a poor continuity implies some limitations on the resolution which is achievable in practice. In this case, the resolution limit is seen to be about half of the wavelength. Copyright © 1981 by The Institute of Electrical and Electronics Engineers, Inc.

Intermetallic phase detection in lead-free solders using synchrotron X-ray diffraction

The high-intensity, high-resolution x-ray source at the European Synchrotron Radiation Facility (ESRF) has been used in x-ray diffraction (XRD) experiments to detect intermetallic compounds (IMCs) in lead-free solder bumps. The IMCs found in 95.5Sn3.8Ag0.7Cu solder bumps on Cu pads with electroplated-nickel immersion-gold (ENIG) surface finish are consistent with results based on traditional destructive methods. Moreover, after positive identification of the IMCs from the diffraction data, spatial distribution plots over the entire bump were obtained. These spatial distributions for selected intermetallic phases display the layer thickness and confirm the locations of the IMCs. For isothermally aged solder samples, results have shown that much thicker layers of IMCs have grown from the pad interface into the bulk of the solder. Additionally, the XRD technique has also been used in a temperature-resolved mode to observe the formation of IMCs, in situ, during the solidification of the solder joint. The results demonstrate that the XRD technique is very attractive as it allows for nondestructive investigations to be performed on expensive state-of-the-art electronic components, thereby allowing new, lead-free materials to be fully characterized.

An Electron-Microscope X-Ray-Diffraction And Amino-Acid-Analysis Study Of The Opercular Filament Cuticle Calcareous Opercular Plate And Habitation Tube Of Pomatoceros Lamarckii Quatrefages (Polychaeta Serpulidae)

The structure, X-ray diffraction and amino acid compositions of the opercular filament cuticle, calcareous opercular plate and habitation tube of the polychaete serpulid, Pomatoceros lamarckii quatrefages, are reported. The opercular filament cuticle is made up of protein and chitin. The chitin is probably in the crystallographic α form. The structure and amino acid composition of the organic components of the opercular filament cuticle and calcareous opercular plate have similarities but are distinctly different from those of the calcareous habitation tube. The opercular plate and habitation tube are composed of different polymorphs of calcium carbonate, aragonite and calcite respectively. Comparisons are made with other chitin-protein systems, structural and calcified proteins.

Synchrotron X-ray diffraction study of the phase transformations in titanium alloys

High-resolution synchrotron X-ray diffraction was used to study the phase transformations in titanium alloys. Three titanium alloys were investigated: Ti-6Al-4V, Ti-6Al-2Sn-4Zr-2Mo-0.08Si and beta21s. Both room and high temperature measurements were performed. The room temperature experiments were performed to study the structure of the alloys after different heat treatments, namely as received (AR), furnace cooling (FC), water quenching (WQ) and water quenching followed by ageing. The alpha, alpha', alpha'' and beta phases were observed in different combinations depending on the heat treatment conditions and the alloy studied. A multicomponent hexagonal close packed (hcp) alpha phase, with different c and the same a lattice parameters, was detected in Ti-6Al-4V after FC. High temperature synchrotron X-ray diffraction was used for 'in situ' study of the transformations on the sample surface at elevated temperatures. The results were used to trace the kinetics of surface oxidation and the concurrent phase transformations taking place under different conditions. The influence of the temperature and oxygen content on the lattice parameters of the alpha phase was derived and new data obtained on the coefficients of thermal expansion in the different directions of the hcp alpha phase, for Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo-0.08Si.

Geometry- and diffraction-independent ionization probabilities in intense laser fields: Probing atomic ionization mechanisms with effective intensity matching

We report an experimental technique for the comparison of ionization processes in ultrafast laser pulses irrespective of pulse ellipticity. Multiple ionization of xenon by 50 fs 790 nm, linearly and circularly polarized laser pulses is observed over the intensity range 10 TW/cm(2) to 10 PW/cm(2) using effective intensity matching (EIM), which is coupled with intensity selective scanning (ISS) to recover the geometry-independent probability of ionization. Such measurements, made possible by quantifying diffraction effects in the laser focus, are compared directly to theoretical predictions of multiphoton, tunnel and field ionization, and a remarkable agreement demonstrated. EIM-ISS allows the straightforward quantification of the probability of recollision ionization in a linearly polarized laser pulse. Furthermore, the probability of ionization is discussed in terms of the Keldysh adiabaticity parameter gamma, and the influence of the precursor ionic states present in recollision ionization is observed.

Crystallization and preliminary X-ray diffraction analysis of naphthalene dioxygenase from Rhodococcus sp strain NCIMB 12038

The three-component naphthalene dioxygenase (NDO) enzyme system carries out the first step in the aerobic degradation of naphthalene to (+)-cis-(1R,2S)-dihydroxy-1,2-dihydronaphthalene by Rhodococcus sp. strain NCIMB 12038. The terminal oxygenase component (naphthalene 1,2-dioxygenase) that catalyzes this reaction belongs to the aromatic ring hydroxylating dioxygenase family and has been crystallized. These enzymes utilize a mononuclear nonheme iron centre to catalyze the addition of dioxygen to their respective substrates. In this reaction, two electrons, two protons and a dioxygen molecule are consumed. The Rhodococcus enzyme has only 33 and 29% sequence identity to the corresponding alpha- and beta-subunits of the NDO system of Pseudomonas putida NCIMB 9816-4, for which the tertiary structure has been reported. In order to determine the three-dimensional structure of the Rhodococcus NDO, diffraction-quality crystals have been prepared by the hanging-drop method. The crystals belongs to space group P2(1)2(1)2(1), with unit-cell parameters a = 87.5, b = 144, c = 185.6 Angstrom, alpha = beta = gamma = 90degrees, and diffract to 2.3 Angstrom resolution.

An EXAFS, X-ray diffraction, and electrochemical investigation of 1-alkyl-3-methylimidazolium salts of [{UO2(NO3)(2)}(2)(mu(4)-C2O4)](2-)

The structure of the 1-alkyl-3-methylimidazolium salts of the dinuclear mu(4)-(O,O,O',O'-ethane-1,2-dioato)-bis[bis(nitrato-O,O)dioxouranate(VI)] anion have been investigated using single crystal X-ray crystallography. In addition, EXAFS and electrochemical studies have been performed on the [C(4)mim](+) salt which is formed following the oxidative dissolution of uranium(IV) oxide in [C(4)mim][NO3]. EXAFS analysis of the solution following UO2 dissolution indicates a mixture of uranyl nitrate and mu(4)-(O,O,O',O'-ethane-1,2-dioato)-bis[bis(nitrato-O,O)dioxouranate(VI)] anions are formed.