Diffraction field computation from arbitrarily distributed data points in space

Cataloged from PDF version of article.Computation of the diffraction field from a given set of arbitrarily distributed data points in space is an important signal processing problem arising in digital holographic 3D displays. The field arising from such distributed data points has to be solved simultaneously by considering all mutual couplings to get correct results. In our approach, the discrete form of the plane wave decomposition is used to calculate the diffraction field. Two approaches, based on matrix inversion and on projections on to convex sets (POCS), are studied. Both approaches are able to obtain the desired field when the number of given data points is larger than the number of data points on a transverse cross-section of the space. The POCS-based algorithm outperforms the matrix-inversion-based algorithm when the number of known data points is large. (C) 2006 Elsevier B.V. All rights reserved

Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm

We use a three-dimensional Gerchberg–Saxton algorithm (Shabtay (2003) Opt. Commun. 226 33) to calculate the Fourier-space representation of physically realizable light beams with arbitrarily shaped three-dimensional intensity distributions. From this representation we extract a phase-hologram pattern that allows us to create such light beams experimentally. We show several examples of experimentally shaped light beams

Reconstructing Detailed Line Profiles of Lamellar Gratings from GISAXS Patterns with a Maxwell Solver

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerically solving Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, due to the discrepancy between incident wavelength and finite-element size. This drawback vanishes for GISAXS due to the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop dimensional metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art e-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows a detailed reconstruction of the grating line shape also for thick, non-homogeneous substrates. The reconstructed geometrical line shape models are statistically validated by applying a Markov chain Monte Carlo (MCMC) sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nm uncertainty

Modelling of multiple impacts for the prediction of distortions and residual stresses induced by ultrasonic shot peening (USP)

During a manufacturing process, the ultrasonic shot peening (USP) technique can be used as the final surface treatment. The aim of this operation is to introduce surface compressive residual stresses in order to prevent crack propagation advancement. Although the numerical simulation method is able to predict the level of residual stresses in a peened part, the 3D modelling of the real USP process, in which many successive and shifted impacts take place, is very delicate to perform and costly in terms of computing time and memory space required. In this paper, a two step method based at first on the calculation of the averaged plastic strain tensor in a half-space by using a semi-analytical method and in a second time on the transfer of this plastic strain field to a finite element model is proposed in order to simulate the effects of the USP process in thin structures. The accuracy and advantages of the semi-analytical method are validated by a benchmark with several finite element codes. Experiments, similar to the Almen test, are performed on thin plates of Inconel 600. Numerical results in terms of distortions and residual stresses are compared with the experimental data

Exact diffraction calculation from fields specified over arbitrary curved surfaces

Cataloged from PDF version of article.Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface. © 2011 Elsevier B.V. All rights reserved

Three-dimensional quasi-periodic shifted Green function throughout the spectrum--including Wood anomalies

This work presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near "Wood anomaly frequencies". At these frequencies, one or more grazing Rayleigh waves exist, and the lattice sum for the quasi-periodic Green function ceases to exist. We present a modification of this sum by adding two types of terms to it. The first type adds linear combinations of "shifted" Green functions, ensuring that the spatial singularities introduced by these terms are located below the grating and therefore outside of the physical domain. With suitable coefficient choices these terms annihilate the growing contributions in the original lattice sum and yield algebraic convergence. Convergence of arbitrarily high order can be obtained by including sufficiently many shifts. The second type of added terms are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on the this new Green function for the problem of scattering by doubly periodic three-dimensional surfaces at and around Wood frequencies. We believe this is the first solver in existence that is applicable to Wood-frequency doubly periodic scattering problems. We demonstrate the proposed approach by means of applications to problems of acoustic scattering by doubly periodic gratings at various frequencies, including frequencies away from, at, and near Wood anomalies