This PDF file contains the front matter associated with SPIE Proceedings Volume 8083, including the Title Page, Copyright information, Table of Contents, Introduction, and the Conference Committee listing.

Metallo-dielectric structured materials, or in other words metamaterials (MTM), are in principle a well established composite to improve efficiency, functionality, and weight of micro-wave components. In recent times, it has been demonstrated that the functionalities of metamaterials can be scaled down to optical frequencies by nano structuring techniques. Examples include negative index materials in the near infrared and visible frequency range, cloaking structures, filters, and structures for improved sensing of environmental gases. The physical processes in plasmonic metamaterials depend strongly on the excitation of surface plasmons and the interaction between them. We have learned how to control the plasmon-photon and the plasmon-plasmon interaction for manipulating the electromagnetic response in a metamaterial at wavelengths well below the vacuum wavelength. Many interesting and novel optical applications and devices are expected. For instance sub-wavelength imaging, compact communication devices as polarisation splitters, slow light media structures, compact colour filters, and resonators. All-plasmonic circuits are also the basis for ultra-dense photonic integration not achievable through the conventional optical integration. With examples of several metamaterial structures we try to illustrate the application potential of MTMs and comment on their fabrication feasibility to show whether metamaterials can hold their promise. Their investigation is in any case a rewarding adventure.

It has been shown that surface plasmon polaritons (SPPs) have a dominant influence on the unique properties of negative index materials (NIMs). Consequently, one could replace bulk NIMs by resonantly coupled surfaces that allow the propagation of SPPs. We show that a metallic meander structure is perfectly suited as such a resonant surface due to the tunability of the short range SPP (SRSPP) and long range SPP (LRSPP) frequencies by means of geometrical variation. Furthermore, the pass band between the SRSPP and LRSPP frequencies of a single meander sheet, induced by two Fanotype resonances, retains its dominant role when being stacked. In this report we demonstrate how a stack consisting of two meander structures can mimic perfect imaging known from Pendry's lens within this pass band region. On the other hand, to observe sub-wavelength features in the far-field more than (perfect) near-field imaging is necessary. We propose a stack of meander structures with successively increasing periodicity capable to decrease the lateral wave vector until near-field to far-field transformation is achieved. When stacking multiple meander structures with different periodicities, the pass band shifts in frequency for each sheet in a different way. We rigorously calculate the spectra of various meander designs and show that this shift can be compensated by changing other geometrical parameters of each single sheet. Such meander stacks can transfer energy resonantly over large distances with a high transmission and might enable sub-wavelength imaging.

Layered media Green's functions are introduced as an additional expansion set for the Multiple Multipole Program (MMP). By using these new expansions, the necessity of matching the boundary conditions along the infinite boundaries in the layered geometry is eliminated. As the result, OpenMaX, the open-source platform that includes the latest version of MMP, becomes more user friendly and robust when handling photonic structures in layered media. A description of both MMP and the layered media Green's functions, together with various numerical examples are introduced to demonstrate the efficiency of the method.

An approach is proposed of near field introscopy of a left-handed material (LHM) layer, i.e. Veselago's lens, without using any waveguides: the near field image of an inhomogeneity in a tested homogeneous LHM layer appears on the wave receiver placed near a wave source provided that this layer is illuminated by source in a way that inside Veselago's lens focus appears near inhomogeneity considered. We extend the traditional potential wave multiple scattering theory to analytical study an inhomogeneous and absorbing LHM slab focusing properties by the Green function method. A specific multiplicative quasistatic singularity of the Green function is revealed provided a weak and thin linelike inhomogeneity is placed near focus inside perfect LHM slab. This sort of singularity is directly linked with concept about spatial transformation media. Modelling the linelike scatterer by non-local separable scattering potential reveals a resonance property of the scattering amplitude related to singular behaviour of the Green function for waves propagated inside perfect LHM slab. These resonance properties were previously lost in the Born's approximation.

Previous work has shown that the reconstruction of geometric parameters describing the profile of an attenuated phase shift (MoSi) photomask is possible by a least-square minimization of the difference between measurement data and simulation results. Modelling work on other related systems, in particular EUV scatterometry, has revealed a strong influence of the uncertainties assigned to the input data. Their choice may introduce a systematic bias to the determination of the reconstructed geometric quantities like line height, top- and bottom CDs or side-wall angles. Here we employ a maximum likelihood estimation (MLE) to obtain the profile parameters as well as consistent uncertainty estimates for the input data. The method is applied to a set of goniometric scatterometry measurements at a wavelength of 193nm on a state-of-the-art MoSi mask.

We present a method to combine measurements from different techniques that reduces uncertainties and can improve measurement throughput. The approach directly integrates the measurement analysis of multiple techniques that can include different configurations or platforms. This approach has immediate application when performing model-based optical critical dimension (OCD) measurements. When modeling optical measurements, a library of curves is assembled through the simulation of a multi-dimensional parameter space. Parametric correlation and measurement noise lead to measurement uncertainty in the fitting process with fundamental limitations resulting from the parametric correlations. A strategy to decouple parametric correlation and reduce measurement uncertainties is described. We develop the rigorous underlying Bayesian statistical model and apply this methodology to OCD metrology. We then introduce an approach to damp the regression process to achieve more stable and rapid regression fitting. These methods that use a priori information are shown to reduce measurement uncertainty and improve throughput while also providing an improved foundation for comprehensive reference metrology.

Optical metrology by scatterometry usually bases on the comparison of experimental and modeled light field data. When solving inverse scatterometric problems, often not only a single simulation has to be carried out, but multiple electromagnetic field solutions have to be computed for varying material and geometrical parameters of the system under consideration. Then, high computational times for a single forward solution can make the complete simulation task infeasible. Table based parameter reconstruction on the other hand has the disadvantage of long offline computational times for creation of the library. Also an increasing number of variable parameters can not be handled efficiently. In this contribution we introduce the reduced basis method for creation of highly accurate reduced order models of parametrized electromagnetic scattering problems. We apply our method to a real-world EUV metrology application and show speed up factors of about 3000 in reconstruction time. Instead of several minutes or hours EUV mask parameters can now be obtained in seconds, i.e., in real-time. Comparison to direct microscopical measurements of the reconstructed geometry demonstrate the good performance and maturity of our method.

Finite element methods (FEM) for the rigorous electromagnetic solution of Maxwell's equations are known to be very accurate. They possess a high convergence rate for the determination of near field and far field quantities of scattering and diffraction processes of light with structures having feature sizes in the range of the light wavelength. We are using FEM software for 3D scatterometric diffraction calculations allowing the application of a brilliant and extremely fast solution method: the reduced basis method (RBM). The RBM constructs a reduced model of the scattering problem from precalculated snapshot solutions, guided self-adaptively by an error estimator. Using RBM, we achieve an efficiency accuracy of about 10^-4 compared to the direct problem with only 35 precalculated snapshots being the reduced basis dimension. This speeds up the calculation of diffraction amplitudes by a factor of about 1000 compared to the conventional solution of Maxwell's equations by FEM. This allows us to reconstruct the three geometrical parameters of our phase grating from "measured" scattering data in a 3D parameter manifold online in a minute having the full FEM accuracy available. Additionally, also a sensitivity analysis or the choice of robust measuring strategies, for example, can be done online in a few minutes.

We pursue the objective of developing a scatterometer based on focused-beam illumination and back-focal plane imaging which is suitable for characterization of truly three-dimensional objects and provides locally-resolved measurements unlike most of the state-of-the-art scatterometry tools. In this paper a full-scale simulation model for the scatterometry is proposed, comprising vector description for the illumination and imaging in terms of physical optics, and rigorous calculation of light-object interaction in the near field by a finite-difference-in-time-domain solver. Using the model we optimize the scatterometry technique to get higher sensitivity to nano-scale dimensional variations of the profile of test patterns. It has been demonstrated that asymmetry of the scattered field distribution allows one to determine separately different parameters of test structures, including refractive index, height, width, side wall, and orientation. Finally, we present a comparison of our approach with the through-focus scanning optical microscopy method.

The optical function generated by a real optical system differs typically from the simulation result. Differences are caused for example by light source radiation tolerances, by alignment tolerances or deviations of the fabricated surfaces from ideal surfaces. In order to simulate the influence of surface deviations of a real system on the optical function it is required to import surface measurement data into optics software. These measurement data contain often the profile height at discrete data points. In order to do a simulation it is required to import these data into optics software and to create a continuous surface profile with the help of a suitable interpolation method. Surfaces deviations can have high spatial frequencies. This requires often a simulation of light propagation including diffraction, interference and vectorial effects. In general different models of light propagation are needed depending on the required physical simulation accuracy. The authors show the modelling of refractive, diffractive and hybrid surfaces from discrete data sets. It turns out that for the description of these different surface types different interpolation methods are required to allow an efficient construction of a continuous surface from measurement data. In addition the authors introduce the Field Tracing concept that allows using different light propagation models from geometrical optics to rigorous. It enables the adjustment of the physical modelling accuracy in every part of an optical system. The simulation of the effect of measured surface deviations will be demonstrated on the examples of a refractive beam shaping element and of a diffraction grating. It will be shown that it is important to include diffraction and interference effects in the simulation.

Metrology is of paramount importance in submicron patterning. Particularly, line width and overlay have to be measured very accurately. Appropriated metrology techniques are scanning electron microscopy and optical scatterometry. The latter is non-invasive, highly accurate and enables optical cross sections of layer stacks but it requires periodic patterns. Scanning laser focus sensors are a viable alternative enabling the measurement of non-periodic features. Severe limitations are imposed by the diffraction limit determining the edge location accuracy. It will be shown that the accuracy can be greatly improved by means of rigorous modeling. To this end, a fully vectorial 2.5-dimensional model has been developed based on rigorous Maxwell solvers and combined with models for the scanning and various autofocus principles. The simulations are compared with experimental results. Moreover, the simulations are directly utilized to improve the edge location accuracy.

This paper studies the convergence behavior of the vectorial modal method (VMM) recently applied to model diffraction from gratings. Results of the VMM are compared with the well established Fourier modal method (FMM) commonly used to analyze interaction of the electromagnetic waves from periodic structures. Numerical simulations carried out for the VMM and FMM demonstrate practically identical convergence of the diffraction efficiencies for the case of incident illumination being TE polarized. However for TM polarization the convergence of VMM is poor as compared to the FMM for metallic gratings. The reason for this is the formulation of the eigenvalue method used to find the fields in the grating region. An alternate formulation of the eigenvalue equation for the VMM for TM polarization is devised which provides the same level of convergence as the FMM. Numerical simulations are carried out to confirm the validity of this formulation.

The well-established Abbe formulation is one of today's most common approaches for the accurate image simulation of partial coherent projection systems used in semiconductor lithography. The development and application of lithographic imaging systems close to the theoretical resolution limits and the desire for the simulation of larger mask areas with high accuracy require several extensions of the classical Abbe approach. This paper presents the basics of the Abbe approach including the so-called Hopkins assumption. For the accurate simulation of today's lithography systems important physical effects like strong off-axis illumination, small feature sizes, ultra-high NAs, a polarization dependent behavior, imaging demagnification, aberrations, apodizations, and Jones pupils have to be described and taken into account. The resulting extensions of the Abbe approach are presented. The accuracy, flexibility, and computational performance of the new approach are demonstrated by application examples.

Simulation of grating spectrometers constitutes the problem of propagating a spectrally broad light field through a macroscopic optical system that contains a nanostructured grating surface. The interest of the simulation is to quantify and optimize the stray light behaviour, which is the limiting factor in modern high end spectrometers. In order to accomplish this we present a simulation scheme that combines a RCWA (rigorous coupled wave analysis) simulation of the grating surface with a selfmade GPU (graphics processor unit) accelerated nonsequential raytracer. Using this, we are able to represent the broad spectrum of the light field as a superposition of many monochromatic raysets and handle the huge raynumber in reasonable time.

The quality test is one of the main components of a production process. The main task of the quality test is the inspection of the relevant geometry parts concerning the predefined tolerance range. To verify, that the relevant geometry parts can be detected with a measurement uncertainty, which is less than the predefined tolerance range, multiple measurements of an appropriate reference specimen have to be done. The related time and money effort is very high and can be reduced using a numerical simulation of the whole measurement process. The measurement uncertainty can be estimated using a virtual measurement process and Monte-Carlo methods. Using the combination of the simulation and Monte-Carlo methods, it is, for example, possible, to calculate the optimal alignment of the workpiece within the measurement volume. Thereby, the optimality criterion can be defined as a minimum of the measurement uncertainty or as a hollistic measurement. In addition to the estimation of uncertainties, it is possible to use the virtual measurement system as part of an assistance system. The assistance system should provide measurement strategies with respect to different criteria, like the minimisation of the measurement uncertainty. This is the field of research of the subproject B5 of the collaborative research centre 489 (CRC 489), funded by the German Research Foundation (DFG). The main task is the setup of a virtual multisensor assistance system for the calculation of optimised work piece adapted measurement strategies. In this paper the virtual measurement system and process of a shadow projection system will be explained in detail. Besides the mathematical model, a verification of the simulation and a concept for the estimation of measurement uncertainties will be given.

In this paper, we describe a theoretical model, which allows simulating speckle pattern in an imaging system and its detection by an image sensor with a limited number of pixels. This simulation tool is based on the Fourier Optics theory. Preliminary tests show a very good agreement between simulations and experiments. We have demonstrated experimentally and theoretically that sub-micrometer displacement resolution is possible by means of the crosscorrelation of speckle patterns, over a range limited to half of the field-of-view of the imaging system.

We present in this paper our results regarding the modeling of the modulation functions of the light flux of optical choppers working with top-hat (constant) light beam distributions. Two configurations of chopper wheels are considered: with windows with linear and with circular margins (the latter, to the best of our knowledge, we have introduced, works as an "eclipse" chopper). A rigorous analytical modeling has been performed for each type of device. For the first configuration, of windows with linear margins, all the four possible relationships between the diameter of the beam in the plane of the wheel and the dimensions of the window of the chopper have been considered and are discussed: (i) large wing and focused beam [in the plane of the wheel]; (ii) large wing and beam of finite diameter in the plane of the wheel, but with a wing large enough to cover the section of the beam; (iii) narrow wing, finite diameter beam and large windows, so there is only one wing at a time in front of the beam section; (iv) narrow wings and windows, so there are more wings at a time in front of the beam section. A recent study covered experimentally case (ii) presented above, obtaining a particular signal function (with an approximate trapezoidal profile). The second and more general wheel configuration that we have proposed in a previous study, with windows with circular margins (for which by example choppers with circular windows are a particular case) is also discussed. Both outwards and inwards circular margins are considered. The modulation functions of this second type of devices are also derived, studied and compared to those for the first, classical types of wheels (with windows with linear margins), which are but a particular case of this second type of chopper. From this study, the various profiles of the function of the transmitted flux are obtained: rectangular, approximate trapezoidal, approximate triangular, sinusoidal, and with nonnull values. The possible geometries of chopper wheels that may generate a required modulation function are thus concluded. An insight in the experimental part we are currently working on, with the stall we have developed to study the different configurations of chopper wheels, is also presented.

The determination of interesting parameters is very often performed through curves fitting, like in scatterometry for example. Classically, the problem is solved by means of least-squares. Although optimal in an ideal context of Normal errors, this assumption is not valid mainly because of modeling and calibration errors, and induce some uncontrolled biases. In this paper, we propose radically different principles of fitting techniques, based on an Entropy criterion instead of the Maximum Likelihood Principle. Combining simple implementation and high performance, we show that this technique is optimal for pure Normal noise and dramatically reduces bias on parameters for corrupted data, outperforming conventional robust M-Estimators. We also provide tests on real scatterometry samples which demonstrate a bias reduction of a factor 4.

Scatterometry is a common technique for the characterization of nano-structured surfaces. It is an indirect measuring method, where a chosen set of parameters describing the scattering object is fitted numerically to the data obtained from a scattering experiment. In order to detect several diffraction orders with an angular resolved measurement, it is necessary to choose the wavelength of the light to be of the same order or smaller than the size of the scattering structure. At PTB, detailed scatterometric investigations of an EUV photomask with periodic absorber line gratings on an EUV multilayer mirror have been performed using EUV and DUV radiation. Multiple propagating diffraction orders could be observed and it was possible to derive information about the line profile by means of rigorous numerical modeling. A comparison with microscopic measurements yields consistent results regarding the line width. The sidewall angle of the line profile, however, as determined in the scatterometry measurements performed in the EUV spectral range as well as in the DUV, was distinctly lower than the angle provided by atomic force microscopy. Analyzing different sources of uncertainty, it could be shown that structure disturbances such as line edge or line width roughness cause significant impact on the angular distribution of the diffraction intensity. This effect can be formulated analytically. On the one hand, this can be used to investigate the consequences of roughness for the structure reconstruction algorithm. For instance, a considerable variation of the reconstructed sidewall angle can be observed as a function of roughness. On the other hand, it is possible to determine a roughness parameter through an appropriate evaluation of the scatterometry experimental data. In this paper we will sum up the sources of uncertainty involved in scatterometry and focus on the line roughness and on how it affects the profile reconstruction.

The paper reports on development of an integral and nondestructive technique of characterization of low-dimensional periodically arranged nanocrystals (LDPAN) by spectroscopic scatterometry in the UV-IR ranges. Some approaches to the solution of direct and inverse problems in scatterometry are addressed. For the solution of the direct problem, the author has chosen the universal method of boundary integral equations, which has demonstrated a broad range of applicability and a high accuracy. Cases are analyzed in which a complicated three-dimensional diffraction problem involving 2D gratings can be reduced to a two-dimensional one with 1D gratings, or multilayer mirrors with plane boundaries. An algorithm is proposed for the solution of a system of nonlinear operator equations with an arbitrary, but limited set of unknown LDPAN structural parameters, and a given set of measured values of diffraction efficiency. The functional to be minimized in the course of solution of the inverse problem is identified, and methods of its regularization and for monitoring the accuracy of the solution are proposed. A Fortran code written with the use of the Löwenberg-Markwardt gradient method has turned out an efficient way to the solution of model problems for a Si grating with a trapezoidal profile.

Recently Fourier-Scatterometry has become of increasing interest for quantitative wafer metrology. But also in other fields the fast and precise optical characterization of periodical gratings of sub 100 nm size is of great interest. We present the application of Fourier-Scatterometry, extended by the use of the coherent properties of white light for the characterization of sub-wavelength periodic gratings of photosensitive material structured by two-photon polymerization. First a simulation-based sensitivity comparison of Fourier-Scatterometry at one fixed wavelength, Fourier-Scatterometry using a white light light source and also additionally using a reference-branch for white-light-interference has been carried out. The investigated structures include gratings produced by two-photon polymerization of photosensitive material and typical semiconductor test gratings. The simulations were performed using the rigorous-coupled-waveanalysis included in our software package MicroSim. A sensitivity comparison between both methods is presented for the mentioned structure types. We also show our experimental implementation of the measurement setup using a whitelight- laser and a modified microscope with a high-NA (NA: 0.95) objective as well as a Linnik-type reference branch for the phase sensitive measurements. First measurements for the investigation of the performance of this measurement setup are presented for comparison with the simulation results.

The task of solving the inverse problem of scatterometry is considered. As a non-imaging indirect optical metrology method the goal of scatterometry is, e.g., to reconstruct the absorber line profiles of lithography masks, i.e., profile parameters such as line width, line height, and side-wall angle (SWA), from the measured diffracted light pattern and to estimate their associated uncertainties. The impact of an appropriate choice of the statistical model for the input data on the reconstructed profile parameters is demonstrated for EUV masks, where light with wavelengths of about 13.5 nm is applied. The maximum likelihood method is proposed to determine more reliable estimations of all model parameters, including the sought profile dimensions. Finally, this alternative approach is applied to EUV measurement data and the results are compared to those obtained by a conventional analysis.

The scatterometric and electromagnetic signatures of a pattern are computing with the perturbation method combined with the Fourier Modal Method (FMM) in order to reduce computational time. In electromagnetic point of view, the grating is characterized by its scattering matrix which allows the computation of the reflection and transmission coefficient. A slight variation of profile parameters or electrical ones provides a small fluctuation of the scattering matrix, consequently, an analytical expression of the local behavior of its eigenvectors and eigenvalues can be obtained by using a perturbation method.

A new technique for the phase gradient estimation encoded in a single interferogram is proposed. The gradient is calculated numerically solving a differential equation obtained from the interferogram's derivatives in orthogonal directions. The phase gradient is assumed to vary almost linearly among adjacent pixels in a small window. A regularized term is aggregated to the differential equation which enables us to find the solution for the phase derivatives adjusting a plane in a minimization process. Both phase derivatives terms are obtained simultaneously from a set of linear equations that results from the minimization process. The algorithm requires a small initial region with the phase, the phase derivatives, and the sine of the phase already estimated. The calculated values of the sine of the phase from the initial region are used as a regularized term to solve the differential equation. The phase derivatives solution is then propagated from the initial region until the whole interferogram field is processed. Each value of the sine of the phase found is aggregated in the regularized term which makes the solution stable. The initial region may be easily found applying a band pass filter in the frequency domain as done with the Fourier method. The phase of the interferogram is calculated with a least square method using the information of the phase derivatives found with the proposed technique. The feasibility of the described approach for phase gradient reconstruction is tested in simulated and experimental data.

The usage of stitching technologies in the interferometrical precision optics measurement technique becomes more and more popular. There exist already a few metrology stages providing the stitching principle, such as, for example, the well known Sub-Aperture Stitching Interferometer for Aspheres (SSI-A¹) [1] [2] [3] from QED technologies. For measurements with the SSI-A the greatest measurable diameter of the test object is approximately 280 mm [1]. As a consequence the University of Applied Sciences Deggendorf develops an own measuring system in order to test large telescope mirrors with a diameter of more than one meter which should be ready for application in 2012. The expected positioning accuracy of the measuring patches is significantly lower in comparison with the high-accurate SSI-A. Therefore a cross-correlation based translation detection tool is implemented in our current software solution. Since the metrology system is currently being established the SSI-A and the μPhase2 interferometer from TRIOPTICS are used as input data sources for the software development. Further this paper discusses the robustness of the translation detection tool and presents a stabilisation method of the stitching result with the aid of physical markers.

In this paper, some concepts and results associated with the interferometric concept of effective wavelength have been applied for the evaluation of optical surfaces. This testing technique measures the wavefront slope instead of the contour of the wavefront, like in the conventional interferometry. Therefore in this paper we present two methods of analysis of optical surfaces with the Ronchi test. First, we described a procedure to evaluate surfaces employing the effective wavelength in the Ronchi test [1]. Our results were computationally processed in order to reconstruct the wavefront of a particular mirror by means of the effective wavelength. A second proposal technique of analysis is based on the change of the traditional analysis of a ronchigram to a method by a proper scaling of the shearing interferogram, via the equivalent wavelength. The effective wavelength and equivalent wavelength are distinct concepts and are independent of the wavelengths used in the image registering process. Comparisons of the Zernike Polynomials for each wavefront with a reference wavefront show, the differences between both methods. Finally, we discuss some advantages and disadvantages of each of the proposed analysis and mention the principal factors to improve our results.

When evaluate the quality of the optical systems using the Ronchi test [1], the source and Ronchi ruling should be placed on the axis systems. In order to know the quality of the system in off-axis, we propose use the nodal optical bench. In particularly we use the principal property of this instrument, its consists when we mounted the refractive system in a rotating mount and his mechanical axis coincide with nodal point, we can rotated about the nodal point then the focal point of systems does not have any movement in a focal plane. So, now we can put a Ronchi ruling in the exit pupil and observe the pattern of fringes, without movement of the source and the ruling. For this, we placed the CCD camera in the focal plane of the refractive system and focused in the exit pupil; the principal advantage of this proposal is test the system without auxiliary optics. For implemented this options we use a simple optical system, one positive singlet lens. In particularly the lens are rotated 4, 12, 16, 20, 24, 28 and 32 degrees. In the optical setup we use a Ronchi ruling of 20 lines/inch, 50 lines/inch and 200 lines/inch in each case.

Non-contacting characterisation of finished surface is commonly done by means of optical systems, e.g., 3D microscopy. In case of the confocal white light microscope the topography of the tribological surface is determined by measuring the intensity distribution of the reflected light. In this work the inter- and intra-layer contributions to the complex optical conductivity tensor are quantum mechanically (ab initio) calculated on the microscopic scale. Based on these complex optical layer-resolved conductivity tensors, the Maxwell equations are solved for a proper modeling of the visible light propagation trough and from a layered sample. Applied to semi-infinite bcc Fe/Fe(100), among others, the incidence dependence of the scattered light is also discussed for variously machined surfaces.

In this paper, we propose an optical model of the surface color controlled by Ag nanograin structure. A forming method of Ag nanograin structure on the surface of a silver mirror by chemical conversion treatment was discovered. The surface has not only unique colors but also properties of bulk metal. The result of SEM observation of the Ag surface showed nanograin structure and varying in the grain size depending on the color. The size of the grains was from 20nm to 100nm. We focused on microscopic behavior of electrons in the Ag grain and the permittivity model was formulated based on Drude Lorentz theory. The model was designed on the assumption that the individual grain behaved like a metallic atom with bound electron different from the silver. The analytical values of this proposed model were compared with measurement values in a reflectance spectrum and a chromatic variation.

We propose a new method to compress digital holograms (DHs) using a sparse matrix representation. Using digital holography to numerically manage complex wavefields, we are able to apply an adaptive mask, based on a threshold filter, to the object wavefield. From there, we store the result of this filtering by sparse representation. We demonstrate that the proposed sparse representation gives us the possibility to obtain high compression factor with minimal loss in the quality of the reconstructed image. This technique is efficient for storage and transmission of DHs and we propose a multiplexing structure for storage the compressed data.

Holography can store full wide angle information about a registered object, since during registration process information about amplitude and phase of an optical wave scattered from an object is captured. Because of this unique feature people put hope in holography as the method which can be utilized in a 3D imaging display. In the paper we present the design of a wide viewing angle display system utilizing multiple Spatial Light Modulators (SLMs). The system is capable of displaying objects from both virtual and real worlds. In our system we are using phase only reflective SLMs based on liquid crystal on silicon (LCoS). There are designed to work with normal illumination. However in order to simplify an optomechanical system of the display here the SLMs are used with an inclined plane wave illumination. Therefore in the paper at first we focus on determination of a tilt depended SLM calibration, so thus SLM even with highly off axis inclined illumination is capable of an accurate wave reproduction. Then we focus on obtaining high quality reconstruction of objects from virtual world. We present an algorithm based on Gerchberg-Saxton scheme and diffraction computing between tilted and parallel planes. All of the paper discussions are accompanied with experimental results obtained in the multi SLMs display.

A major issue so far for digital holography has been the limited number of pixels of currently available detectors, such as CCD sensors, which allows a spatial resolution significantly lower than that of a holographic plate. This is an even more sever limitation when IR sensors such as microbolometers are taken into consideration. In order to increase the numerical aperture of such systems, we developed an automatic technique which is capable to record several holograms and stitch them together before reconstruction. This method can cope with some of the inherent differences of the image structures and tone dynamics of recorded holograms. The joint holograms have been applied for reconstruction of an image by means of numerical and optoelectronic reconstruction processes and they show significant increase of quality.

A new method of adjusting an optical axis of the lens of receiving module (RM) of laser rangefinder (LRF) [1] to the main axis of space vehicle is described. The testing unit for LRF was designed and described [2]. The unit allows to measure the focal plane position of main lens, RM detectivity, level of nonaxis source of light, transmittance of optical system and dynamic range of RM and to make the most of adjustings. The uncertainty of adjusting four laser beams to the main axis of space vehicle consists of uncertainty of adjusting the optical axis of RM to the main axis of space vehicle, uncertainty of adjusting central fiber of fiber-optic coupler (FOC) RM to the optical axis and uncertainty of adjusting laser beams of laser transmitter module (LTM) to all of four fibers of FOC RM. The method and uncertainty of adjusting an optical axis of RM to main axis of space vehicle is determined as ±45 arcsec and described in this paper.

Irregularity of an optical surface is commonly characterized by peak-to-valley or root mean square error after subtraction of low order aberrations. It is sufficient if the surface is fabricated with the help of conventional techniques. Modern manufacturing methods employ undersized polishing tools generating irregularities on sub-aperture scales or mid-spatial frequencies. This is particularly important for the fabrication of aspheric or free-form surfaces. The smoothness of local polishing depends on how uniformly the influence of a tool is distributed and how well the dwell time is controlled over a part. Diamond turning is known for the variety of shapes, however, a single point tool tends to form surface features on the scale determined by the uniformity of feed rate. A deterministic way to quantify and specify mid-spatial irregularity is important for all areas of optical production. Interferometric map of an optical surface is usually obtained from original data by subtraction of the fit of 9 Zernike fringe polynomials corresponding to piston, tilt, focus and third order astigmatism, coma and spherical aberrations. This paper describes how to characterize the spectral content of residual surface height error, which depends on multiple factors during the fabrication. To quantify small scale irregularities, the residual error is regarded as a statistical process. The method of structure function is applied to the surface errors at different spatial scales yielding RMS height difference vs. physically measurable separation on an optical surface.

We present the analysis of a quasi-distributed fibre sensor based on the concatenation of identical low-reflective fiber Bragg gratings (FBGs) taking into account the effect of spectral-shadowing crosstalk. This allows obtaining more realistic values of the design parameters such as the maximum number of sensing points, the reflectivity of the gratings, and the distance between the sensing points.

The mechanical position alignment of aspherical surfaces becomes a difficult challenge when the aspherical departure of the surface is high. An optically obscured aspherical surface is even more difficult to be aligned due to the missing obscured paraxial spherical vertex surface area for implementation of the auto-collimating technique. This research paper aims to develop a method to align an obscured aspherical surface with respect to the mechanical axis of a precision rotational stage by analyzing the multiple off-axis interferograms measured from a phase shifting Fizeau interferometer. The alignment induced linearly varying coma is successfully shown in the simulation results. The method can predict the vector direction of mis-alignment errors by least square fitting. An iterative process is possible to be implemented to bring the misaligned aspherical surface back to aligned status.

It is shown the feasibility of direct fitting of external quantum efficiency for silicon trap detectors which are applied as radiometric transfer standards at several National Institutes of Metrology. The model considers the internal quantum efficiency and the reflectance of the detector, whose parameters are fitted in the measured data of external quantum efficiency. The advantage of the suggested approach is the possibility of pursuing interpolation of spectral responsivity without loss of physical meaning of the fitted parameters.

High performance optical systems pose very strict limits to positioning errors of the optical components inside the system. Identification and suppression of static and dynamic errors, like alignment errors due to drift or structural vibrations, can lead to superior imaging quality. A concept is presented that allows for intra process monitoring of deviations of a lens from its ideal position. It can track the movement of a lens by illumination through the rim such that the light reflects of the optical surfaces of the lens by total internal reflection before exiting the lens on the opposite side. A Shack-Hartmann wavefront sensor is applied to detect the wavefront. The wavefront-error caused by decenter or tilt of the lens is used for the reconstruction of the geometrical perturbations. Two approaches for the reconstruction of the geometrical properties from forward calculation data (model-based and regularization methods) are compared. Different light sources and geometrical setups can have an effect on the wavefront properties. A comparison is made to investigate their influence on the reconstruction quality. As the measurement principle does not interfere with the imaging process of the system, the method should be able to monitor the system during operation. This could enable real time tracking of errors up to the sampling rate of the detector making the method suitable for measurements of system dynamics. The method can potentially be enhanced to detect some lens deformations in combination with mechanical finite element simulation.

The Bidirectional Scattering Distribution Function (BSDF) of a surface depicts how it scatters the optical radiation, being therefore fundamental in order to explain the visual appearance of the objects. This work assesses the effect that the use of non-zero solid angles of illumination and detection has in the BSDF measurement, and it proposes a matrix-based formalism to allow this effect to be compensated from the measured BSDF and from the previous knowledge of the solid angles involved in the measurements. This deconvolution is important to obtain a better insight of the surface gloss, since it provides a more accurate absolute peak measurement and a better angular resolution in the directional scattering determination.

We present an approach to an analysis of the third order monochromatic and chromatic aberrations of refractive fluid lenses with a variable focal length. A detailed theoretical analysis is performed for a simple variable-focus lens and formulas are derived for an optical design of such lenses. The advantage of these active lenses is their capability to change continuously the focal length within a certain range. These lenses give a possibility to design non-conventional optical systems which change their parameters (focal length, magnification, etc.) in a continuous way without a need for mechanical movements of lenses. Such lenses with a variable focal length make possible to design optical systems with functions that are difficult or even impossible to combine using conventional approaches. We perform an analysis of optical design of such lenses. The experimental analysis and calculations are provided for Varioptic lens Arctic-416. Potential applications of variable-focus liquid lenses in optical microscopy are analyzed and simulated. We also investigate a possibility of increasing the depth of focus using such lenses and the influence of a variable-focus lens on the image quality.

A method for simulating the transient optical response of a multilayered sample subject to a spatially and temporally varying field distribution is presented. The transient optical response of a sample probed in the reflection configuration, is characterized by the 2x2 Jones transient reflection matrix: ▵R(t)-R^-1 (TRM). Signals in transient reflectometry, interferometry, and polarimetry measurements can be readily extracted from the TRM. A matrix formalism based on 4x4 transfer matrix is used for calculating the TRM. The formalism facilitates the simulation of transient phenomena in anisotropic stratified samples in the presence of non-homogeneous perturbing fields like electric, magnetic, and strain fields. Various areas of experimental research may benefit of this matrix formalism: picosecond acoustics, electro-optic sampling, magneto-optic sampling, and others area of research involving fast/ultrafast phenomena in multilayered samples studied with the pump-probe technique.

We discuss and demonstrate the optimal scanning functions of a galvanometer-based scanner (GS) from an optomechanical point of view. Triangular versus sawtooth and sinusoidal scanning functions are reviewed briefly. From this discussion, we focus on triangular functions with linear active portions and as fast as possible non-linear stop-and-turn portions, necessary to obtain an as high as possible duty cycle. We have studied analytically the performances of these return portions for various sinusoidal, parabolic and higher order polynomial equations. Contrary to what is pointed out in the literature, where linear + sinusoidal scanning function was considered best, we demonstrated that actually the linear + parabolic function provides the highest duty cycle (i.e. time efficiency of the scanning process). The second part of the study approaches the command function, given by the input voltage of the GS that has to provide the optimal scanning function discussed above. This command function is considered in relationship with the active torque that drives the device. This torque is studied with regard to the constructive parameters of the device (moment of inertia, damping coefficient and elastic coefficient of the torsion springs), and to the imposed parameters of the scanning regime (scan frequency, amplitude, velocity and duty cycle). Especially the trade-off that can be done between the various - and contradictory - requirements one has for the device is of interest. The main one is between the duty cycle and the maximum value of the command voltage, in order to minimize the maximum input electrical signal for the device with a minimum loss in what concerns the scan efficiency. Thus, this modeling of the active torque can show the practical limits of the duty cycle, after the study concerning the scanning function has demonstrated its theoretical limitations.

Characterization of acoustic modes is important in the study of Brillouin gain spectrum. In this paper, acoustic modes of a suspended core fiber are numerically calculated by finite element method. Due to high contrast between mechanical coefficient of silica and air, full vectorial finite element method is used. Since core of SCF is surrounded by large air holes, the solutions are compared with those for a bare cylindrical silica rod in air.

Simulations of light scattering off an extreme ultraviolet lithography mask with a 2D-periodic absorber pattern are presented. In a detailed convergence study it is shown that accurate results can be attained for relatively large 3D computational domains and in the presence of sidewall-angles and corner-roundings.

This paper is concerned with the modelling of the complete opto-mechanical measurement system, including shearography instrument, loading technique and the response of the object under test and the comparison of the simulation results with experimental results. To show the applicability of this technique, the response of an aluminium flat plate sample under thermal load was analysed. First a finite element model of the plate was generated, using an experimentally measured temperature profile. The strain and displacement values obtained from the finite element model were used to simulate the phase-map in the optical part of the model. The simulated phase maps were then compared qualitatively with experimental phase maps measured using shearography. This approach is suitable to understand the response of components under load and to predict anomalies such as defects, thereby making the analysis of measured phase maps easier and less empirical.