This article reviews standard and advanced modeling techniques in lithography simulation. Rigorous electromagnetic field solvers such as the Waveguide Method and finite-difference time-domain (FDTD) algorithms in combination with vector imaging models predict the image formation inside the photoresist. Semi-empirical macroscopic and microscopic models describe physical and chemical phenomena during the processing of resists. Various local and global optimization techniques are applied to identify the best exposure and process parameters. Several examples demonstrate the application of predictive simulation for the exploration of future lithography options and for the optimization of existing technologies. This includes the consideration of mask material parameters in source/mask optimization, the evaluation and comparison of different options for double exposure and double patterning techniques, and the investigation of mask-induced imaging artifacts in EUV-lithography. Selected examples illustrate the application of lithography simulation for the modeling of cost efficient alternative exposure techniques for special applications of micro- and nanotechnology.

The effect of a metal layer with negative permittivity on the behavior of nonlinear-magnetoopic isolator is studied. The isolator consists of Metal film, nonlinear cladding, and magnetooptic substrate. It is found that difference between forward and backward propagation for TM₀ mode increases with increasing the absolute value of the tuning parameter which is the permittivity of the metal film, ε_f. It is also found that the maximum cutoff thickness of the isolator occurs in selfdefocusing case around η=0.65 and at the highest assumed value of ε_f = -8. The results are interesting since they assure the possibility to get maximum optimization of the isolator behavior by adding metallic materials.

We have investigated the uncertainty sources that affect the traceability of dimensional measurements using the VIScan of the Zeiss F25 coordinate measuring machine (CMM). Our experimental results on line-width measurements are promising, having a repeatability below 120 nm and moreover they are reproducible for all light settings investigated. The comparison with the measurements performed on a facility used for line-scale calibrations provides very good agreement. At present we can report an uncertainty below 0.45 μm for line-width calibrations. This would be the first traceable F25 VIScan, and to our knowledge one of the first truly traceable vision systems for line-width calibrations.

We present an optical design and describe the way to build and test a new model of the human eye. This model is intended to work specifically with wide field angles featuring invariant aberrations across the field. Our model is a compromise between the simplicity of the design (using only two plano-convex lenses) and its ability to imitate the real properties of ocular aberrations. The position of the aperture stop in the system as well as the concentricity of the first and the last surfaces allowed us to control the field aberrations. We model the artificial eye using the optical design software Zemax. Our ray-tracing analysis and experimental results are discussed in relation to the inverse optical design, which enables us to find the imperfections in the artificial eye with interferometric testing. Measuring wavefront aberrations in double pass on axis we could identify the manufacturing errors in lens characteristics as well as find their misalignment errors. The inverse optical design involves modification of the original eye model parameters (thickness, radius of curvatures, asphericity, lens centration and tilts) to match the experimental measurements of the wavefront aberrations. We identified the sources of errors and verified that the overall performance of the artificial eye is comparable with the theoretical wide-field eye model, which is based on the average properties of the real human eye.

The misalignment of a particular optic in lens assembly will induce aberrations and deteriorate the performance. For the purpose of failure analysis, there are requirements from optic manufactures for the development of measurement tool to address the misaligned element. This paper presents a method for the quantitative measurement and analysis of misalignment in lens assembly, which may figure out the misaligned element and its misalignment factors. Since there are several optical elements in lens assembly, and there are different misalignments, such as decenter, tilt etc, a multiparameter tool need to be employed in the analysis. Wavefront can be expressed with Zernike polynomials, which are selected for the analysis. We choose a positive lens assembly with four elements for the study. A point light source is placed in the front focus point of lens assembly; the collimated emergent wavefront is analyzed with Zernike polynomials. We use Zeemax to simulate the propagation of wavefront, calculate Zernike coefficients correspondent to various misalignment. The results show there is a group of Zernike polynomials correspond to each misalignment. Each polynomial increase/decrease progressively against the magnitude of misalignment. It is difficult to tell the misalignment only by the analysis of Zernike coefficients. To further address the misaligned elements, we present a concept - the contrast value of Zernike coefficients, which is a series of constant even though the magnitude of misalignment changes. The method and procedure is presented to measure the contrast value with the employment of dual directional wavefront sensing.

Fiber-Bragg-grating (FBG) sensors have become commercially available sensors for the measurement of temperature, strain and many other quantities. The sensor information is encoded in the spectral reflection characteristic of these devices. Their usage as strain sensors is one of the most prominent fields of application. Strains from a structure which is to be monitored are transferred into the fiber-Bragg-grating, by surface bonding or embedding. In general an arbitrary state of strain may thus occur within the FBG, represented by a full strain tensor with normal strain components, as well as with shear strain components. The influence of normal strains is well understood and has been treated theoretically by many authors. The influence of shear strains is however not well understood. As we were recently able to theoretically demonstrate by a full tensor coupled mode analysis, shear strains do influence the spectral response of fiber-Bragg-sensors and thus have to be considered. In this work, an introduction to the modeling of shear strains within fiber-Bragg-gratings is given. We discuss reasonable approximations for the simplification of the theoretical model. We compute, to our knowledge for the first time, the direct influence of shear strains on the output of a FBG measurement system and show the cases when shear strain effects are relevant. Furthermore, we compare the sensitivity of different interrogation algorithms towards shear strain influences on the measurement system output.

Polarimetry is an optical technique currently used in many research fields as biomedicine, polarimetric metrology or material characterization, where the knowledge of the state of polarization of light beams and the polarizing properties of polarizing samples is required. As a consequence, in such as applications it is necessary to use polarimeters which by means of radiomentric measurements, lead to the obtaining of some important polarimetric information. As is known, polarimeters include a state of polarization detector (PSD), which is typically formed by combinations of waveplates and polarizers. Then, intensity measurements corresponding to the projection of the analyzed state of polarization upon different configurations of the PSD used, leads to the determination of the polarimetric properties of light beams. Here, we have studied and optimized a polarimeter based on PSD system containing two electronically variable retardance waveplates. The variable waveplates are based on the Liquid Crystal Display technology, allowing the implementation of a complete polarimeter without mechanical movements.

We propose a new setup established to measure the light polarization state and the birefringent media parameters. This setup consists of two pairs of the linear Wollaston compensators and special circular compensators which form a set of two spatially modulated elliptical compensators. These compensators can be used separately as a spatial generator of all polarization states and as an elliptical spatial analyzer. When analyzing the light polarization state the singular minimum points in the output light intensity appear. The coordinates of these points depend linearly on the azimuth and ellipticity angles of the examined light. When combining both elements (generator and compensator) we can obtain a special spatial elliptical polariscope. It allows measuring the main birefringent media parameters: the azimuth and the ellipticity angle of its both eigenvectors as well as the phase difference, introduced by this medium. All desired quantities could be obtained by some simple intensity measurements and neither movable parts nor active elements are needed and no complicated analysis of output light should be made. We propose also a modification of described setup by using different shearing angles in Wollaston compensators used in generator and analyzer. This should allow using Fourier analysis of the output intensity distribution and makes our devices more suitable to real time measurements.

Optical sensors have wide range of application such as in medicine, astronomy, industry, and others. Sensitivity of symmetric three layered optical waveguide sensor is investigated. The proposed sensor consists of dielectric slab surrounded by metamaterial (MTM) cladding and MTM substrate. MTMs are new artificial materials which have simultaneously negative permittivity ε and negative permeability μ. Different values of MTMs parameters ε and μ are chosen to optimize the sensitivity of the sensor. However, the value of ε_μ is kept content and equal to 4. The dispersion equation which represents the effective index n_e for transverse electric modes (TE) as a function of slab thickness has been derived. A close form solution of the sensitivity (S) which is defined as the variation of the effective index with respect to Temperature variation is introduced. The sensitivity then numerically calculated as function of the film thickness at different values of Metamaterial parameters. It is found that sensitivity varies with the film thickness and depends on the MTMs parameters. These results are important for designing sensors.

Recently, we proposed a new approach of a noncollinear correlation technique for ultrashort-pulsed coherent optical signals which was referred to as Bessel-autocorrelator (BAC). The BAC-principle combines the advantages of Bessellike nondiffracting beams like stable propagation, angular robustness and self-reconstruction with the principle of temporal autocorrelation. In comparison to other phase-sensitive measuring techniques, autocorrelation is most straightforward and time-effective because of non-iterative data processing. The analysis of nonlinearly converted fringe patterns of pulsed Bessel-like beams reveals their temporal signature from details of fringe envelopes. By splitting the beams with axicon arrays into multiple sub-beams, transversal resolution is approximated. Here we report on adaptive implementations of BACs with improved phase resolution realized by phase-only liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs). Programming microaxicon phase functions in gray value maps enables for a flexible variation of phase and geometry. Experiments on the diagnostics of few-cycle pulses emitted by a mode-locked Ti:sapphire laser oscillator at wavelengths around 800 nm with 2D-BAC and angular tuned BAC were performed. All-optical phase shift BAC and fringe free BAC approaches are discussed.

In this paper the concept of a so-called assistance system for interferometric and confocal sensor systems is presented. Goal of the research described here is the development of a software-based user friendly tool for three-dimensional optical topography measurements. With this assistance system the user will be enabled to use his measurement system in an optimal way for his special task. Additionally a reliable usage of these systems in the production environment is provided. This assistance system will be developed in the project "OptAssyst", where five research institutes are collaborating with commercial partners from the automobile industry and their suppliers as "users" of the considered systems. Furthermore several manufacturers of optical measurement systems are involved.

Two wavelength contouring is used especially for the shape measurement and testing of steep objects. Conventional and digital holographic techniques can be utilized for this. But both these methods require the interference of the test wavefront with a known background or reference wavefront. This makes the adjustment of the two beams intensities to get high contrast fringes necessary. These methods are also prone to external noise like vibrations. Phase retrieval from intensity sampling at multiple axial planes offer an attractive alternative for whole field imaging. Diffusively reflecting objects produce volume speckle field when exposed to highly coherent radiation like laser. This volume speckle field has appreciable intensity variation both in the transverse as well as axial direction, which is the necessary condition to reconstruct the complex amplitude of the object wavefront from the intensity values. The reconstruction process uses the angular spectrum propagation approach to the scalar diffraction theory. This paper explores the use of phase retrieval in two wavelength contouring. The method can be used for the shape measurement of steep diffuse objects and the optical path length measurement of transparent objects. The method is explained using simulations. Some experimental observations are also provided to validate the simulation results.

A Shack-Hartmann wavefront sensor (SHWS) uses a lenslet array to sample incoming wavefront on an image sensor, which is usually a Charge Coupled Device (CCD). By measuring the shift of centroids on CCD compared to reference spots, wavefront profile is reconstructed and therefore test surface shape is revealed. There are various factors that affect the performance of SHWS. In order to study how and to which extend does each factor affect reconstruction result, we established a simulation platform for SHWS in MATLAB. Through this platform, detailed properties and affecting factors were analyzed. Based on the system-oriented platform, we obtained some interesting findings, which are very important in the design of S-H wavefront sensors. In this paper, the performance-affecting significance of the key properties of the light beam, the diverging angle, the intensity distribution, and the intensity of the light beam, is simulated, analyzed and concluded. The simulation results are useful guide for the selection, design and preparation of the sensing light beam.

A novel method for full-field absolute phase measurements in the heterodyne interferometer with an electro-optic modulator is proposed in this paper. Instead of the commonly-used half-wave voltage to drive the electro-optic modulator, a saw-tooth voltage signal with the amplitude being lower than its half-wave voltage is used. The interference signals become a group of periodical sinusoidal segments. The initial phase of each sinusoidal segment depends on the phase difference induced by the test sample. In real measurements, each segment is taken by a fast camera and becomes discrete digital points. After a series of operations, the starting point of the sampled sinusoidal segment can be determined accurately. Next, the period of the sampled sinusoidal segments is lengthened and they can be modified to a continuous sinusoidal wave by using a least-square sine fitting algorithm. The initial phase of the continuous sinusoidal wave can also be estimated. Subtracting the characteristic phase of the modulator from the initial phase, the absolute phase measured at the pixel can be obtained without the conventional reference signals. These operations are applied to other pixels, and the full-field absolute phase measurements can be achieved. The phase retardation of a quarter-wave plate is measured to show the validity of this method.

Based on the Fresnel's equations and the heterodyne interferometry, an alternative method for measuring the refractive index distribution of a GRIN lens is presented. A light coming from the heterodyne light source passes through a quarterwave plate and is incident on the tested GRIN lens. The reflected light passes through an analyzer and an imaging lens; finally it enters a CMOS camera. The interference signals produced by the components of the s- and the p-polarizations are recorded and they are sent to a personal computer to be analyzed. In order to measure the absolute phases of the interference signals accurately, a special condition is chosen. Then, the interference signals become a group of periodic sinusoidal segments, and each segment has an initial phase ψ with the information of the refractive index. Consequently, the estimated data of ψ are substituted into the special equations derived from Fresnel's equations, and the refractive index distribution of the GRIN lens can be obtained. Because of its common-path optical configuration, this method has both merits of the common-path interferometry and the heterodyne interferometry. In addition, the phase can be measured without reference signals.

Light transmission through a 2D-periodic array of small rectangular apertures in a film of highly conductive material is simulated using a finite-element method. It is demonstrated that well converged results are obtained using higher-order finite-elements. The influence of the array periodicity and of corner roundings on transmission properties is investigated.

Numerical design inverse reconstruction and parameter estimation of optical systems usually involves the multiple solution of an e.g. geometrically parameterized system. Long computational times however can rule out many possible applications like inverse scatterometry. The reduced basis method allows to split up the solution process of an e.g. geometrically parameterized system into an expensive offline and a cheap online part. In the offline phase the reduced basis is computed selfadaptively by solving the underlying model several times. During the real-time application the reduced system is solved in the order of seconds even for 3D problems. Error estimators assure the reliability of the reduced basis solutions. In our contribution we explain general ideas of the reduced basis method and apply it to the simulation of light scattering from 2D and 3D parameterized photo masks. We compare computational times and accuracy of reduced basis and rigorous finite element simulations.

Plasmonic nano antennas are highly attractive at optical frequencies due to their strong resonances - even when their size is smaller than the wavelength - and because of their potential of extreme field enhancement. Such antennas may be applied for sensing of biological nano particles as well as for single molecule detection. Because of considerable material losses and strong dispersion of metals at optical frequencies, the numerical analysis of plasmonic antennas is very demanding. An additional difficulty is caused when very narrow gaps between nano particles are utilized for increasing the field enhancement. In this paper we discuss the main difficulties of time domain solvers, namely FDTD and FVTD and we compare various frequency domain solvers, namely the commercial FEM packages JCMsuite, Comsol, HFSS, and Microwave Studio with the semi-analytic MMP code that may be used as a reference due to its fast convergence and high accuracy. The current version of this paper has had a correction made to it at the request of the author. Please see the linked Errata for further details.

Reflection spectra of one dimensional diffraction gratings are calculated on the basis of an exact, fast approach, uniting several modern methods, to the theory of electromagnetic wave multiple scattering in two dimensional inhomogeneous dielectric media which uses the technique of matrix Riccati equation. The sensitivity of computed reflection spectra to distortions of a grating shape (strip like, triangular, trapezoidal) for metal and dielectric structures is demonstrated. Distortions of the lamellar grating shape are simulated by the roundness of sharp edges of the grating. In particular, the computations shows that the roundness of grating ruling (150 nm wide and 300 nm hegh) edges with a curvature radius as small as 10 nm can be detected by changing the intensity of specular reflected light (500 nm wavelength) provided that the grating has a subwavelength period (300 nm) even in the case of low dielectric contrast.

The 2-dimensional Power Spectral Density (PSD) can be used to characterize the mid- and the high-spatial frequency components of the surface height errors of an optical surface. We found it necessary to have a complete, easy-to-use approach for specifying and evaluating the PSD characteristics of large optical surfaces, an approach that allows one to specify the surface quality of a large optical surface based on simulated results using a PSD function and to evaluate the measured surface profile data of the same optic in comparison with those predicted by the simulations during the specification-derivation process. This paper provides a complete mathematical description of PSD error, and proposes a new approach in which a 2-dimensional (2D) PSD is converted into a 1-dimensional (1D) one by azimuthally averaging the 2D-PSD. The 1D-PSD calculated this way has the same unit and the same profile as the original PSD function, thus allows one to compare the two with each other directly.

The appearance of an object is strongly influenced by the reflective properties of its surface. These properties are governed by the optical constants of the material, its roughness and the thickness and optical properties of the coatings. In this paper we study rough steel substrates covered with thermal grown oxide layers. The optical constants, thickness and roughness of the sample were measured and they were used as parameters in a model to simulate the reflection of the samples. These simulated reflections correspond well with experimental scatterometry measurements. Using these data we were able to predict the colour and the gloss of the samples. This opens the possibility to design the colour and the gloss of coated steel according to the wishes of the users.

The performance of synchrotron beamline optics is often limited by the accuracy in the figuring and finishing of the optical surfaces. In consequence, a very sensitive and accurate characterization of the optics is required during manufacturing and testing. Such characterization can only be done with instruments like long trace profilometers or Fizeau interferometers. In the case of the Fizeau interferometer, the accuracy is mainly limited by the quality of the reference surface. In this work, we propose a new method for improving the accuracy of the surface reconstruction by using the lateral shearing technique. It consists on measuring the sample surface several times, applying different displacements. By subtracting these measurements each other, the error introduced by the reference surface can be removed and the profile of the sample mirror can be reconstructed. Then, the accuracy of the reconstruction is limited by the imprecisions of the linear stage used to shift the sample mirror. The positioning error is analyzed regarding the shearing transfer function and the Natural Extension. Small displacements are more sensitive to the positioning error, not only because the error is comparatively bigger, but also because the error using Natural Extension is bigger than using large displacements. Using the proposed technique, a statistical analysis regarding the positioning error has been performed. Its conclusion is that the accuracy in metrology of x-ray mirrors is improved by at least a factor of 18 compared to that achieved with the Fizeau interferometer and a standard λ/20 reference surface, giving a reconstruction error lower than 1.8 nm peak to valley.

The Nanometer Comparator is the PTB reference length measuring machine for high precision calibrations of line scales and encoder systems. Up to now the Nanometer Comparator allows to measure the position of line structures in one dimension only. For high precision characterisations of masks, scales and incremental encoders, the measurement of the straightness of graduations is a requirement from emerging lithography techniques. Therefore the Nanometer Comparator will be equipped with an additional short range measurement system in the Y-direction, realized as a single path plane mirror interferometer and supposed to achieve sub-nm uncertainties. To compensate the topography of the Y-mirror, the Traceable Multi Sensor (TMS) method will be implemented to achieve a reference-free straightness measurement. Virtual experiments are used to estimate the lower accuracy limit and to determine the sensitive parameters. The virtual experiments contain the influence of the positioning devices, interferometer errors as well as non-perfect adjustment and fabrication of the machine geometry. The whole dynamic measurement process of the Nanometer Comparator including its influence on the TMS analysis, e.g. non-equally spaced measurement points, is simulated. We will present the results of these virtual experiments as well as the most relevant error sources for straightness measurement, incorporating the low uncertainties of the existing and planned measurement systems.

This paper introduces recent advances in scatterfield microscopy using improved normalization and fitting procedures. Reduced measurement uncertainties are obtained through the use of more accurate normalization procedures in combination with better parametric fitting algorithms. A new approach to embed atomic force microscopy (AFM) or other reference metrology measurements directly into the uncertainty analysis and library-fitting process is used to reduce parametric uncertainties. We present both simulation results and experimental data demonstrating this new method, which is based on Bayesian analysis as applied to library-based regression. We develop the statistical methods to implement this approach of nested uncertainty analysis and give several examples that demonstrate reduced uncertainties in the final combined measurements. The approach is also demonstrated in a combined reference metrology application using multiple independent measurement methods.

The solution of the inverse problem in scatterometry employing deep ultraviolet light (DUV) is discussed, i.e. we consider the determination of periodic surface structures from light diffraction patterns. With decreasing dimensions of the structures on photo lithography masks and wafers, increasing demands on the required metrology techniques arise. Scatterometry as a non-imaging indirect optical method is applied to periodic line structures in order to determine the sidewall angles, heights, and critical dimensions (CD), i.e., the top and bottom widths. The latter quantities are typically in the range of tens of nanometers. All these angles, heights, and CDs are the fundamental figures in order to evaluate the quality of the manufacturing process. To measure those quantities a DUV scatterometer is used, which typically operates at a wavelength of 193 nm. The diffraction of light by periodic 2D structures can be simulated using the finite element method for the Helmholtz equation. The corresponding inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Fixing the class of gratings and the set of measurements, this inverse problem reduces to a finite dimensional nonlinear operator equation. Reformulating the problem as an optimization problem, a vast number of numerical schemes can be applied. Our tool is a sequential quadratic programing (SQP) variant of the Gauss-Newton iteration. In a first step, in which we use a simulated data set, we investigate how accurate the geometrical parameters of an EUV mask can be reconstructed, using light in the DUV range. We then determine the expected uncertainties of geometric parameters by reconstructing from simulated input data perturbed by noise representing the estimated uncertainties of input data. In the last step, we use the measurement data obtained from the new DUV scatterometer at PTB to determine the geometrical parameters of a typical EUV mask with our reconstruction algorithm. The results are compared to the outcome of investigations with two alternative methods namely EUV scatterometry and SEM measurements.

We investigate some prospects of scatterometric methods for quantitative dimensional metrology of periodic micro- and nanostructures like e. g. parameter sensitivity. Additionally we discuss some limitations with respect to numerical or metrological constrains of different scatterometric methods.

We have developed a set of techniques, referred to as scatterfield microscopy, in which the illumination is engineered at a sufficiently large Conjugate Back Focal Plane (CBFP) of the microscope. A primary advance of our new scatterfield microscope is the use of 193 nm excimer laser light. Sophisticated configurations have been implemented to allow measurement of both the image plane and the Fourier plane using full-field and angleresolved illumination. Here, the microscope is primarily used in an angular mode by engineering the CBFP to enable angle-resolved scatterometer measurements with a numerical aperture (NA) range from 0.08 to 0.74. Electromagnetic models - the Finite Element Method (FEM) and the Modal Method of Fourier Expansion (MMFE) were used to model the experimental light scattering and evaluate the sensitivity to the geometrical parameters and correlations. In addition, experimental results obtained on line gratings for unpolarized illumination will be presented and discussed. measurements.

Scatterometry, the analysis of light diffracted from a periodic structure, is a versatile metrology tool for characterizing periodic surface structures, regarding the critical dimension (CD) and other properties of the surface profile. For extreme ultraviolet (EUV) masks, only EUV radiation provides direct information on the mask performance comparable to the operating regime in an EUV lithography tool. With respect to the small feature dimensions on EUV masks, the short wavelength of EUV is also advantageous since it provides a large number of diffraction orders from the periodic structures irradiated. We present measurements at a prototype EUV mask with large fields of periodic lines-space structures using an EUV reflectometer at the Berlin storage ring BESSY II and discuss the corresponding reconstruction results with respect to their measurement uncertainties. As a non-imaging indirect optical method scatterometry requires the solution of the inverse problem, i.e., the determination of the geometry parameters describing the surface profile from the measured light diffraction patterns. In the time-harmonic case the numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution of the two-dimensional Helmholtz equation. Restricting the solutions to a class of surface profiles and fixing the set of measurements, the inverse problem can be formulated as a nonlinear operator equation in Euclidean space. The operator maps the profile parameters to special efficiencies of diffracted plane wave modes. We employ a Gauss-Newton type iterative method to solve this operator equation, i.e., we minimize the deviation of the calculated efficiencies from the measured ones by variation of the geometry parameters. The uncertainties of the reconstructed geometry parameters depend on the uncertainties of the input data and can be estimated by statistical methods like Monte Carlo or the covariance method applied to the reconstruction algorithm. The input data of the reconstruction are very complex, i.e., they consists not only of the measured efficiencies, but furthermore of fixed and presumed model parameters such as the widths of the layers in the Mo/Si multilayer mirror beneath the line-space structure. Beside the impact of the uncertainties on the measured efficiencies, we analyze the influence of deviations in the thickness and periodicity of the multilayer stack on the measurement uncertainties of the critical dimensions.

Investigation of nanoscale objects is becoming increasingly important with development of modern nanotechnology related industries. Under certain conditions, some information on the investigated object can be obtained in the forward scattering far field when the object is scanned by a focused beam. The sensitivity of the far field based measurements depends on a number of factors including the shape of the investigated object. In this work we present a case study comparing far field response in scanning mode. The response sensitivity for nano-scale phase objects of different shapes and different phase volumes under various illuminating conditions is discussed. We perform a paraxial simulation with investigated phase objects represented as thin optical elements: free standing and as a part of a surface.

The present work deals with a comprehensive numerical analysis of x-ray grazing-incidence scattering from single- and double-boundary, finite-conducting rough surfaces with asperities of different statistics, performed with the use of a mid-end workstation in a reasonable computation time. Multiple and multi-wave diffraction, refraction, absorption, and resonances influence significantly x-ray and neutron scattering. These are pure dynamic effects, which require application of a rigorous theory to correctly describe the power change in the specular order and to describe nonspecular distribution. Despite the impressive progress attained in developing a rigorous theory with account for random roughness, the author is aware only of approximate and asymptotic approaches in the case of neutron and x-ray scattering even by 1D surfaces, such as the Born approximation, the distorted-wave Born approximation, parabolic equation methods, etc. The PCGrate®-SX v.6.3 software developed on the basis of a modified boundary integral equation method and the Separating solver allows one to operate with exact models, e.g., those involving Maxwell's equations and rigorous boundary conditions, and appropriate radiation conditions. In order to compute the scattering properties of a rough surface using the forward electromagnetic solver, Monte Carlo simulation is employed to average the deterministic scattered power due to individual surfaces over an ensemble of realizations. The difference between approximate and rigorous approaches can be clearly seen in cases where grazing incidence occurs at close to or larger than the critical angle. This difference may give rise to wrong estimates of rms roughness and correlation length if they are determined by comparing experimental data with calculations. Besides, the rigorous approach permits taking into account any known roughness statistics, including quasi-periodicity of quantum dot ensembles.

The paper presents an approach for error estimation for the various steps of an automated 3D vision-based reconstruction procedure of manufactured workpieces. The process is based on a priori planning of the task and built around a cognitive intelligent sensory system using so-called Situation Graph Trees (SGT) as a planning tool. Such an automated quality control system requires the coordination of a set of complex processes performing sequentially data acquisition, its quantitative evaluation and the comparison with a reference model (e.g., CAD object model) in order to evaluate quantitatively the object. To ensure efficient quality control, the aim is to be able to state if reconstruction results fulfill tolerance rules or not. Thus, the goal is to evaluate independently the error for each step of the stereo-vision based 3D reconstruction (e.g., for calibration, contour segmentation, matching and reconstruction) and then to estimate the error for the whole system. In this contribution, we analyze particularly the segmentation error due to localization errors for extracted edge points supposed to belong to lines and curves composing the outline of the workpiece under evaluation. The fitting parameters describing these geometric features are used as quality measure to determine confidence intervals and finally to estimate the segmentation errors. These errors are then propagated through the whole reconstruction procedure, enabling to evaluate their effect on the final 3D reconstruction result, specifically on position uncertainties. Lastly, analysis of these error estimates enables to evaluate the quality of the 3D reconstruction, as illustrated by the shown experimental results.

In this paper we present a way to formulate the holographic reconstruction of a wavefield throughout a volume by means of a sequence of convolutions. The discussion is based on the assumption that the field is generated by a set of real valued scattering sources within the volume. In analogy to two dimensional imaging this enables the application of deconvolution techniques to the holographic scheme. We show, that the proposed formalism can theoretically be used to perform a three dimensional deconvolution of the reconstructed amplitude in order to recover object information, e.g. the position of scattering sources. In the ideal case of an infinite aperture of the hologram the deconvolution may be employed by a simple inverse filter. However, for the more realistic case of finite apertures an iterative technique called Out of Hologram Extrapolation (OHE) is introduced, which is based on the projected Landweber method. Finally, the novel method is applied to a synthetic example in order to recover the positions of a set of distributed point sources.

Measure roughness in some sort of samples can present several problems when it is done in traditional way (with physical contact). For instance, soft samples will present at least two kinds of problem: (a) the value presented by the equipment not represents the sample roughness; (b) the equipment can perform serious damages to the sample. Using a commercial type OCT (Thorlabs Inc.) with 6μm axial resolution (in air) and 6μm lateral resolution, measurements of roughness standards with Ra nominal values of 0.8, 1.6, 3.2, 6.3, 12.5, 25.0 and 50.0 μm. A homemade software analysis the OCT images, and automatically calculates the Ra and Rz values. This procedure was performed to validate this methodology comparing the OCT and roughness standards values.

A shape of a wave-front that is transformed by an optical element (or system) is changed depending on physical and geometric properties of such a system. This fact can be used in many areas of science and technology. For example, various applications can be found in adaptive optics where active optical elements are used for wave-front correction. Our work presents a detailed analysis of aberration properties of a simple deformable planar mirror from both the aspect of modeling the shape of reflecting surface of the mirror and the mechanisms that enable to reach this desired shape for correction of spherical aberration. Finally, a simple experimental device for practical realization of the optical system for partial wave-front correction is proposed.

Polygonal Fresnel zone plates with a low number of sides have deserved attention in micro and nanoptics, because they can be straightforwardly integrated in photonic devices, and, at the same time, they represent a balance between the high-focusing performance of a circular zone plate and the easiness of fabrication at micro and nano-scales of polygons. Among them, the most representative family are Square Fresnel Zone Plates (SFZP). In this work, we propose two different customized designs of SFZP for optical wavelengths. Both designs are based on the optimization of a SFZP to perform as close as possible as a usual Fresnel Zone Plate. In the first case, the criterion followed to compute it is the minimization of the difference between the area covered by the angular sector of the zone of the corresponding circular plate and the one covered by the polygon traced on the former. Such a requirement leads to a customized polygon-like Fresnel zone. The simplest one is a square zone with a pattern of phases repeating each five zones. On the other hand, an alternative SFZP can be designed guided by the same criterion but with a new restriction. In this case, the distance between the borders of different zones remains unaltered. A comparison between the two lenses is carried out. The irradiance at focus is computed for both and suitable merit figures are defined to account for the difference between them.

In this work we report a method for testing a parabolic trough solar collector (PTSC) based on the null screen principles. For surfaces with symmetry of revolution a cylindrical null screen is used, now, for testing the PTSC we use a flat null screen. The design of the null screen with ellipsoidal spots is described; its image, which is formed by reflection on the test surface, becomes an exact square array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. The flat null screen design and the surface evaluation algorithm are presented. Here the surface is tested in sections and the evaluation of the shape of the surface is performed with stitching method. Results of the evaluation for a square PTSC with 1000 mm by side (F/0.49) are shown.

Diffraction gratings are one of the most used elements in optics and even in other fields of science. They are used also like part of measurement devices in scientific and industrial applications. As it is well known, self-imaging effect appears when a diffraction grating is illuminated with a coherent beam, such as a plane wave. This effect has been analyzed in depth and its behavior is well known under ideal grating and illumination conditions. Usually, the illumination beam is not perfectly collimated but presents a certain degree of aberration. The motivation of this work is to try to explain the behavior of the self-images of an ideal amplitude grating when it is illuminated by a non-perfect beam, that is, an aberrated beam. The known of this effect can help to understand how much the aberration of the light beam affects to the diffraction pattern, and more in depth, to the self-imaging phenomenon. The results presented in this work can be very useful in metrology applications, since sometimes the contrast obtained experimentally does not correspond to the theoretical predictions, usually due to aberrations in the light beam. For this, we have used a formalism based in the Rayleigh-Sommerfeld approach. We have modeled the aberrations by using the Zernike polynomials. On the other hand, we have considered all kinds of aberrations, spherical, coma, tilt, astigmatism, etc. As it is expected the contrast of the self-images decrease when the order of them increases and also when the aberration degree increase. In some cases, contrast inversion is also produced for high aberrations.

The paper presents selected issues on laser systems for detection and location of underwater objects. Range detection analysis and simulations include influence of: i) parameters of rangefinder; ii) parameters describing properties of the searched under-water object; iii) parameters of water environment, in particular hydro-meteorological conditions and extinction coefficient, characterizing water transmission properties. This transmission undergoes cyclic and strong changes in time and is strongly area-diversified. In the analyzed regions, average extinction coefficient changes from 0.3 m^-1 to 2.4 m^-1, whereas optimal laser wavelength falls into the spectral range of 575-580 nm. The analysis of the background radiation power has shown, that its value varies from several nW to about 25 nW in dependence of the incidence angle of solar radiation. Therefore, in further calculations we assumed the background radiation power equal to its average value of 9 nW. Having already estimated the signal power and the background noise power, signal to noise ratio (SNR) could be determined. The assumption, that the minimal SNR is 17.5 dB, results in the range detection of under-water objects varying from 7 m to 30 m. This range permits effective detecting and position determining of underwater objects like containers or anchor mines.

A MathCad analysis of the mathematical functions and parameters of polygonal scanning heads is achieved. The results of a previous, rigorous analytical study we have performed are used. A scanning system for dimensional measurements has been considered. However, most of the results obtained are valid for any application of polygon mirror (PM) scanners. The characteristic functions and parameters of the PM scanner in the dimensional measurements setup, i.e. i.e. scanning function and velocity, characteristic angles and duty cycle are discussed. The analysis is performed with regard to the constructive parameters of the polygonal scanning system. An experimental stall is designed and constructed, and some of the experimental results concerning the scanning function, relevant for the analysis performed are presented.

In this paper, it is shown theoretically and verified experimentally that the modulation transfer function (MTF) and phase transfer function (PTF) of a printer can be evaluated simultaneously by measuring convolution of transmission function of a couple of printed Ronchi gratings. In practice, two similar printed Ronchi gratings are superimposed inversely to create the Moiré fringes. By measuring the transmittance of moiré fringes, the convolution function can be obtained. Using the latter function, the PTF can be evaluated in addition to MTF, but the measurement of the autocorrelation function of the gratings results in the MTF only. In fact, as superiority this technique does not require a high sensitive detector and a very narrow slit.

In this paper, the forbidden Photonic Band Gaps (PBGs) of a one-dimensional Photonic Crystal (1D PC) with additional regular layer, t for the constant value of the lattice constant A and at normal incident of light beam were investigated. The additional regular layer was formed from both sides of the high-refractive index layer H. The gap map approach and the Transfer Matrix Method were used for numerical analysis of this structure. The limitation of filling fraction values caused by the presence of t-layer was taking into account during calculations of the Stop-Band (SB) regions for threecomponent PC. The red shift of SBs was observed at the introduction of t-layer to conventional two-component 1D PC with optical contrast of N=3.42/1. The blue edge of the first PBG occupied the intermediate position between the blue edges of SBs regions of conventional PCs with different optical contrast N. This gives the opportunity of tuning the optical contrast of PC by introduction of the additional layer, rather than using the filler, as well as fine tuning of the SB edge. The influence of the number of periods m and the optical contrast N on the properties of SBs was also investigated. The effect of the PBG disappearance in the gap map and in the regions of the PBGs of high order was revealed at certain parameters of the additional layer.

The transmission high-speed links requires the control of the phenomenon of polarization mode dispersion because it can limit the bandwidth of the transmitted signal mainly for long distances. This article presents two used methods of modeling in order to calculate the PMD in the single mode optical fiber links and evaluate its influence on the propagated signal. The results obtained in the modeling have been compared with experimental results in order to validate the proposed methods of modeling.

Diffraction gratings are not always ideal but, due to the fabrication process, several errors can be produced. In this work we show that when the strips of a binary phase diffraction grating present certain randomness in their height, the intensity of the diffraction orders varies with respect to that obtained with a perfect grating. To show this, we perform an analysis of the mutual coherence function and then, the intensity distribution at the far field is obtained. In addition to the far field diffraction orders, a "halo" that surrounds the diffraction order is found, which is due to the randomness of the strips height.

A tunable grating was fabricated with silver nanoparticles in a gradient increase of nanoparticle size along the grating direction in this study. Owing to the gradual increment of the nanoparticle size, the first order diffraction efficiencies of incident light presented as a function of the impinging position of the probe beam. Via a probe of monochromatic light ranged from 450 to 750 nm, the positive and the negative first order diffraction efficiency were measured by rotating the optical detector. It was noted that the maximum positive and negative diffraction efficiency appeared at around 600 and 700 nm, respectively. The difference in the peak wavelength of these two diffraction efficiency exhibited the diffraction property was strongly affected by the gradient variation of the localized surface plasmon effect. The first order diffraction efficiency spectra affected by the various excitations of the localized surface plasmons with the taper size distribution of nanoparticles were the special discovery of the study and may lead to a potential development in light modulation and manipulation.

In order to increase the sharpness of the fringes in the Ronchi test we consider their interferometric interpretation. The advantage of this approach is that we can obtain the irradiance profile directly. In this work we propose to use different kinds of substructured gratings in order to obtain sharp fringes. Each grating period is divided in a number equal width strips which can be transparent or opaque; the transmission coefficients for the strips across the grating period is not periodic but is a chosen binary sequence. We develop the equations to obtain the corresponding irradiance profiles and perform an analysis of these profiles and of the sharpness of the fringes for different sequences and positions of the gratings. Numerical results for a 3000 mm radius of curvature parabolic mirror are shown. We found that the fringes are sharper at the Rayleigh distance and on other planes in and out of focus of the mirror.

The limited depth-of-field is a main drawback of microscopy that prevents from observing, for example, thick semi-transparent objects with all their features in focus. Several algorithms have been developed during the past years to fuse images having various planes of focus and thus obtain a completely focused image with virtually extended depth-of-field. We present a comparison of several of these methods in the particular field of digital holographic microscopy, taking advantage of some of the main properties of holography. We especially study the extended depth-of-field for phase images reconstructed from the hologram of a biological specimen. A criterion of spatial measurement on the object is considered, completed with a visual criterion. The step of distance taken into account to build the stack of images is less than the instrument depth-of-field. Then, preserving the distance of focus associated with each pixel of the image, a three-dimensional representation is presented after automatic detection of the object. The limits of such a method of extraction of 3D information are discussed.

Diffraction microtomography in coherent light is foreseen as a promising technique to image transparent living samples in three dimensions without staining. Contrary to conventional microscopy with incoherent light, which gives morphological information only, diffraction microtomography makes it possible to obtain the complex optical refractive index of the observed sample by mapping a three-dimensional support in the spatial frequency domain. The technique can be implemented in two configurations, namely, by varying the sample illumination with a fixed sample or by rotating the sample using a fixed illumination. In the literature, only the former method was described in detail. In this report, we derive the three-dimensional frequency support that can be mapped by the sample rotation configuration. We found that, within the first-order Born approximation, the volume of the frequency domain that can be mapped exhibits a missing part, the shape of which resembles that of an apple core. A brightfield transmission microscope was modified to form a Mach-Zehnder interferometer that was used to generate phase-shifted holograms recorded in image plane. We report preliminary experimental results.

With ever shrinking feature sizes in semiconductor and photonics industry, the demand and the challenges for optical modelling in terms of accuracy has increased dramatically over the last decade. Rigorous modal diffraction methods such as the RCWA, the Differential method or the C-method provide sufficient accuracy, however, they are rather costly particularly for 3D patterns. In this paper, we are suggesting an approach which is based on the so-called Rayleigh hypothesis. The basic idea of this method is to extend the expansion of the electromagnetic field components into Rayleigh modes inside the grating grooves as opposed to the RCWA where the expansion within the slices is done in so-called Bragg modes. Therefore, the Rayleigh-Fourier method does not need a diagonalization for the decoupling of the modes. It requires only the formation of an interface transition matrix, the elements of which can be computed analytically. As a consequence, it is very fast both for 2D as well as for 3D. Here, we discuss the details of the method and show how it can be combined with other modal methods into one framework. The application limits are discussed in terms of the corrugation depth of the grating, the shape of the grating profile, the pitch and the refraction index contrast. Surprisingly, the method can be applied far beyond the Rayleigh limit in a sort of semi-convergent regime when implemented and utilized carefully. Due to its speed, the method might be an appropriate choice for real time regression particularly for only slightly corrugated multilayer stacks.

We investigate the possibility to multiplexing and de-multiplexing numerically digital holograms recorded by means of a Mach-Zehnder interferometric microscope. The digital holograms are multiplexed and de-multiplexed thanks to the unique property of the digital holography to numerically manage the complex wavefields in different reconstruction planes. Two kind of multiplexing techniques are investigated. The first one allows to multiplex up to hundreds of digital holograms retrieving correctly quantitative information about their amplitude and phase maps. This technique can be used to optimize the storage of a large number of digital holograms or their transmission process from a recording head to a remote display unit. The second method consists in the angular multiplexing and de-multiplexing of several digital holograms. This technique has been performed rotating numerically one hologram at different angles and adding all the rotated holograms to obtain a single synthetic digital hologram. However, for this technique, a multiplexed digital hologram can be also obtained rotating the CCD array during the holograms recording process. The distortions caused by the multiplexing/de-multiplexing procedures has been evaluated for both the techniques.