Modeling microlenses by use of vectorial field rays and diffraction integrals

A nonparaxial vector-field method is used to describe the behavior of low-f-number microlenses by use of ray propagation, Fresnel coefficients and the solution of Maxwell equations to determine the field propagating through the lens boundaries, followed by use of the Rayleigh-Sommerfeld method to find the diffracted field behind the lenses. This approach enables the phase, the amplitude, and the polarization of the diffracted fields to be determined. Numerical simulations for a convex-plano lens illustrate the effects of the radii of curvature, the lens apertures, the index of refraction, and the wavelength on the variations of the focal length, the focal plane field distribution, and the cross polarization of the field in the focal plane.     

Large-area avalanche photodiodes for the detection of soft x rays

The charge-collection efficiency of beveled-edge-type silicon avalanche photodiodes has been determined for soft x rays in the 50-300-eV range. An efficiency of greater than 80% is measured for energies below the Si L absorption edge. The measured efficiency is well described by a model that accounts for absorption in an oxide overlayer and recombination at the front surface of the diode. The avalanche photodiodes are shown to be significantly more sensitive compared with other detectors for pulsed sources such as a laser-produced plasma source. These results are also very encouraging for soft-xray/ extreme-UV applications involving synchrotron radiation.     

Experimental study of the phenomenon of 1 x N spectral switch due to diffraction of partially coherent light

Spectral properties of a class of partially coherent light with spectral profiles of varying bandwidths are studied on diffraction by a circular aperture in the far zone for different diffractive angles, i.e., for on-axis and off-axis points on the observation plane. It is found that the spectrum of the light in the far zone is different from that at the aperture plane. This change in the spectrum is termed spectral shift, which is found to be different at different diffractive angles. The spectral shift for a fixed diffactive angle shows a gradual change. However, for a critical value of the coherence at the aperture plane, the spectral shift shows a rapid transition, termed spectral switch. For different diffractive angles the coherence that causes the spectral switch also differs. Therefore the phenomenon of 1 x N spectral switch (consisting of one input port and N output ports) is studied experimentally.     

X-ray microtomography using a laboratory source: Measurement technique and comparison of reconstruction algorithms

A method of measuring the projections recorded by a laboratory-scale x-ray tomograph device is described. Numerical realizations of several methods that employ the apparatus of morphological image analysis are used to reconstruct images of a test object. It is shown that the estimators of the mean values of the coefficients of linear attenuation of media that are obtained are in good agreement with the requirements imposed on modern industrial, medical, and laboratory tomograph devices. __________ Translated from Izmeritel’naya Tekhnika, No. 2, pp. 19–24, February, 2008.     

Implications of stimulated resonant X-ray scattering for spectroscopy,imaging, and diffraction in the regime from soft to hard X-rays

The ultrahigh peak brilliance available at X-ray free-electron lasers opens the possibility to transfer nonlinear spectroscopic techniques from the optical and infrared into the X-ray regime. Here, we present a conceptual treatment of nonlinear X-ray processes with an emphasis on stimulated resonant X-ray scattering as well as a quantitative estimate for the scaling of stimulated X-ray scattering cross sections. These considerations provide the order of magnitude for the required X-ray intensities to experimentally observe stimulated resonant X-ray scattering for photon energies ranging from the extreme ultraviolet to the soft and hard X-ray regimes. At the same time, the regime where stimulated processes can safely be ignored is identified. With this basis, we discuss prospects and implications for spectroscopy, scattering, and imaging experiments at X-ray free-electron lasers.     

Variational methods in irreversible thermoelasticity: theoretical developments and minimum principles for the discrete form

A variational approach for fully coupled dynamic irreversible thermoelasticity is developed for continua, which considers both the conservative and dissipative character in terms of mixed variables. By introducing a consistent variational scheme for the spatial and temporal discretization of the governing equations, a mixed continuum element is established under the Hamiltonian-Lagrangian formalism. The proposed method leads to the development of minimum principles in discrete form with the proper selection of state variables and temporal action sum operators. Consequently, this novel mixed variational formulation can provide the basis for a class of optimization-based methods for irreversible thermomechanics. Several applications are considered to demonstrate the robustness of the proposed variational approach, including transient dynamic response of thermoelastic media due to surface heating caused by ramp- and step-type heat fluxes, and a sequence of laser pulses.     

Variational approaches for dynamics and time-finite-elements: numerical studies

This paper presents general variational formulations for dynamical problems, which are easily implemented numerically. The development presents the relationship between the very general weak formulation arising from linear and angular momentum balance considerations, and well known variational priciples. Two and three field mixed forms are developed from the general weak form. The variational principles governing large rotational motions are linearized and implemented in a time finite element framework, with appropriate expressions for the relevant tangent operators being derived. In order to demonstrate the validity of the various formulations, the special case of free rigid body motion is considered. The primal formulation is shown to have unstable numerical behavior, while the mixed formulation exhibits physically stable behavior. The formulations presented in this paper form the basis for continuing investigations into constrained dynamical systems and multi-rigid-body systems, which will be reported in subsequent papers.     

Nonlinear diffraction tomography: The use of inverse scattering for imaging

Our recent inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an efficient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear theory is that it accounts for multiple scattering effects within the scatterers which often give rise to distortions in an image. A new method to invert strong scatterers, such as metallic scatterers, is presented. © 1996 John Wiley & Sons, Inc.     

Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion

Holographic interferometry (HI) has proved to be a useful tool for nonintrusive temperature measurements in flames (and thereafter for inference of the local composition based on the state relationship approach) with high spatial and temporal resolution. Digital holographic interferometry (DHI) is a relatively new imaging and measurement technique that electronically records a hologram (e.g., on a CCD) and reconstructs it by a numerical method. Cumbersome chemical processing of the hologram is avoided in DHI, which thereby provides greater flexibility, speed, and the potential for real-time processing. In conventional holography, fringes that are neither bright nor dark on a hologram cannot be accurately resolved. The DHI technique has not yet to our knowledge been used for combustion applications. Herein we evaluate its efficacy for making temperature measurements in flames and assess its applicability through a simulation. Each part of a double exposure associated with the holographic technique is considered to be recorded by a hypothetical CCD sensor at a separate time from the other part. We applied the principles of Fourier optics to develop two numerical methods for hologram reconstruction, and we show that both methods provide an accurate reconstruction of the phase image associated with a flame. Because of the periodic nature of the wave function, the reconstructed phase values are limited to the interval [-pi/2, pi/2]. Thus an unwrapping algorithm is provided that produces a continuous phase distribution based on the condition that the reconstructed phase is jumped by a value of -pi or pi. We have also developed an iterative calculation method to adjust the value of the digital reference wave parameters that determines the phase imaging reconstruction in DHI.     

Spectral changes and 1 X N spectral switches in the diffraction of partially coherent light by an aperture

The off-axis and on-axis spectra in the far zone of an aperture for the case in which a particular class of partially coherent light with a broad spectrum is diffracted by an aperture are studied. It is shown that the spectrum in the far zone is generally different from that at the aperture; i.e., the spectrum is split into two or more peaks. Moreover, the spectrum varies with the diffractive angle. For a fixed diffractive angle, the spectral shift, defined as the difference between the frequencies at which the observed spectrum and the spectrum at the aperture take their maximum, shows a gradual change with the change in the coherence at the aperture. However, as the coherence reaches some critical values, the spectral shift exhibits a rapid transition; i.e., spectral switch occurs. The coherence that causes the spectral switch to take place is different for different diffractive angles. Therefore we propose a new kind of 1 x N spectral switch, where N detectors (output ports) are placed at different diffractive angles in the far zone, and the spectral shifts at different detectors are measured. By adjusting the coherence of the aperture (input port) to the desired values, we obtain a rapid transition of the spectral shift in the desired output ports.     

Two-dimensional nonradiating currents for imaging systems: theoretical development and preliminary assessment

An analytical orthonormal set of basis functions for 2D nonradiating current is derived. Preliminary numerical investigation shows the capabilities of this set of currents in enhancing the solution to an inverse scattering problem.     

Nucleation of recrystallization in compressed aluminium: studies by electron microscopy and Kikuchi diffraction

Following the earlier investigation of recrystallization of aluminium by Bellier and Doherty [1] by transmission Kossel diffraction, the details of the nucleation process were studied by transmission electron microscopy and Kikuchi electron diffraction. This showed that nucleation appeared to occur via a sub-grain coalescence process that occurred selectively at deformation bands and at deformation band, grain boundary junctions. Nucleation occurred only at grain boundaries and at deformation bands. The condition for continued growth, of enlarged sub-grains of length 2L, along the grain boundary L>2r( _s/ _g) where _s is the sub-boundary energy and _g the grain-boundary energy, was found to be obeyed. The values of the stored energy calculated from the measured sub-grain sizes and misorientations were less than the reported experimental value, indicating that in as-deformed aluminium the dislocation arrays in the sub-boundaries may not have the lowest energy structure assumed in the calculation.     

Reflectance enhancement in the extreme ultraviolet and soft x rays by means of multilayers with more than two materials

Sub-quarterwave multilayer coatings with more than two different materials are shown to provide a reflectance enhancement compared with the standard two-material multilayer coatings when reflectance is limited by material absorption. A remarkable reflectance enhancement is obtained when the materials in the multilayer are moderately absorbing. A simple rule based on the material optical constants is provided to select the most suitable materials for the multilayer and to arrange the materials in the correct sequence in order to obtain the highest possible reflectance. It is shown that sub-quarterwave multilayers generalize the concept of multilayers, of which the standard two-material multilayers are a particular case. Various examples illustrate the benefit of sub-quarter-wave multilayer coatings for highest reflectance in the extreme ultraviolet. Applications for sub-quarterwave multilayer coatings are envisaged for astronomy in the extreme ultraviolet (EUV) and soft x rays and also for future EUY lithography.     

Experimental and numerical studies of the J-integral for a surface flaw

Applied J-integral values for a surface cracked tensile panel are experimentally evaluated by measuring strain and displacement quantities along an instrumented contour located on the longitudinal symmetry plane. Nonlinear, 3-D, finite-element analyses are employed to obtain corresponding estimates of the contour and area integral contributions to a 3-D J-integral. Finite element results indicate that the area integral contribution is negligibly small on the symmetry plane; the fracture driving force is thus adequately characterized by the experimental contour values. Detailed comparisons of the experimental and numerical results (crack mouth opening displacement, J-values, and strains along the contour) reveal that the one-quarter symmetric, finite element model accurately predicts the panel response for overall (gauge length) strains approaching 1.6 times the material yield strain, beyond which the observed deformation patterns exhibited globally asymmetric shear bands.

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Résumé On évalue expérimentalement les valuers de l'intégrale J dans un panneau en traction fissuré en surface, en mesurant les dilatations et les déplacements suivant un contour instrumenté localisé le long du plan de symétrie longitudinale. On utilise une analyse non linéaire par éléments finis à trois dimensions afin d'obtenir des estimations de la manière dont les intégrales de contour et de surface contribuent à l'intégrale J à 3D.Les résultats par éléments finis indiquent que la contribution de l'intégrale de surface est négligeable suivant le plan de symétrie; le déterminant de la rupture peut done être adéquatement décrit par les valeurs expérimentales relatives au contour.Des comparaisons sur le détail des résultats expérimentaux et numériques révèlent qu'un modèle par éléments finis quart-symétriques peut prédire de manière sûre la réaction de la pièce par rapport à des dilatations globales de près de 1,6 fois la dilatation à la limite élastique du matériau, valeur au-delà de laquelle les configurations de la déformation observées font état de bandes de glissement globalement asymétriques.

     

Influence of skew rays on the sensitivity and signal-to-noise ratio of a fiber-optic surface-plasmon-resonance sensor: a theoretical study

We have theoretically analyzed the influence of skew rays on the performance of a fiber-optic sensor based on surface plasmon resonance. The performance of the sensor has been evaluated in terms of its sensitivity and signal-to-noise ratio (SNR). The theoretical model for skewness dependence includes the material dispersion in fiber cores and metal layers, simultaneous excitation of skew rays, and meridional rays in the fiber core along with all guided rays launching from a collimated light source. The effect of skew rays on the SNR and the sensitivity of the sensor with two different metals has been compared. The same comparison is carried out for the different values of design parameters such as numerical aperture, fiber core diameter, and the length of the surface-plasmon-resonance (SPR) active sensing region. This detailed analysis for the effect of skewness on the SNR and the sensitivity of the sensor leads us to achieve the best possible performance from a fiber-optic SPR sensor against the skewness in the optical fiber.     

Optimizing the speckle noise for maximum efficacy of data acquisition in coherent imaging

The impact of multiplicative speckle noise on data acquisition in coherent imaging is studied. This demonstrates the possibility to optimally adjust the level of the speckle noise in order to deliberately exploit, with maximum efficacy, the saturation naturally limiting linear image sensors such as CCD cameras, for instance. This constructive action of speckle noise cooperating with saturation can be interpreted as a novel instance of stochastic resonance or a useful-noise effect.     

Discrete diffraction transform for propagation, reconstruction, and design of wavefield distributions

A discrete diffraction transform (DDT) is a novel discrete wavefield propagation model that is aliasing free for a pixelwise invariant object distribution. For this class of distribution, the model is precise and has no typical discretization effects because it corresponds to accurate calculation of the diffraction integral. A spatial light modulator (SLM) is a good example of a system where a pixelwise invariant distribution appears. Frequency domain regularized inverse algorithms are developed for reconstruction of the object wavefield distribution from the distribution given in the sensor plane. The efficiency of developed frequency domain algorithms is demonstrated by simulation.     

Empirical and theoretical studies of design judgement: a review

This paper presents a review of some observation-based studies of the design activity and attempts two kinds of analysis of them. The first is to show some patterns of designer behaviour which appear to be common to most of the studies. The second is to show how observed behaviour is related to theoretical work on design. In particular the importance of judgement and evaluation in design is stressed. Using the framework of decision making and value theory, a tentative synthesis, compatible with both empirical and theoretical design studies, is proposed.