This PDF file contains the front matter associated with SPIE Proceedings Volume 8789, including the Title Page, Copyright Information, Table of Contents, and the Conference Committee listing.

The aim of this paper is to present a new method of in-line determination of etching tool parameters deviation during the transistor fabrication. For that, we study the possibility to use an optical metrology technique, the scatterometry, and its capability to determine quickly and accurately the temporal evolution of geometric dimensions of a periodic pattern. In this case, this optical tool can be considered as an external monitoring probe. The experiments developed in this article are based on a DOE where 20 different experiments are made, followed both by scatterometric measurements and internal etching tool probes. Comparing the two outputs, we determine the correlations between the evolution of the geometrical parameters of the pattern and the fluctuation of the internal tool parameters. We conclude that the use of a scatterometer following the evolution of the geometrical parameters of a pattern during an etching process is also a good tool to in-line anticipate the drift of the etching parameters.

The fast evolution of microelectronics fabrication technology demands a concurrent development in metrology capabilities. In recent years, Mueller Matrix (MM) scatterometry has been asserted as a useful tool in characterizing critical dimensions (CD) in periodical arrays of nanometer-size structures. Specifically, some symmetry properties of the measured structure can be readily extracted from the MM, allowing effective isolation of abnormal features. One example is measuring deviations of grating structures from perfect mirror symmetry, characteristic of faults in the fabrication process. The most general form of the Muller matrix requires 16 independent measurements, and requires spectral ellipsometry. However, using some very general assumptions on the reflection properties of the measured sample, one can reduce this number considerably. Such realistic assumptions are time independence of the reflection properties, and homogeneity of the sample (i.e., constant reflectivity throughout the measurement spot), as is the common case in optical CD metrology targets. We show that under these assumptions the Mueller matrix can be completely measured using spectral reflectometry. The goal of characterizing asymmetry is then further analyzed, and a new approach for such measurement, based on spectral reflectometry, is presented. Specifically, using spectral differences metrology (SDM), this approach is shown to provide a simpler means to measure the same asymmetry-dependent quantity as targeted today using MM metrology, but requires only two distinct measurements leading to improved throughput.

At PTB we investigate the prospects of scatterometric methods for quantitative dimensional metrology of periodic micro- and nanostructures. Commonly applied approximations and simplifications may lead to contributions to the measurement uncertainty or even to systematic measurement errors. Here we present a short overview about the main effects connected with these simplifications. In particular we present numerical investigations of the influence of a finite beam size on the scatterometry results. The results indicate, that an impact of the finite beam size becomes significant only for tightly focused beams with a beam waist radius w_o smaller than 10 μm.

Extreme W scatterometry using radiation in the extreme ultraviolet photon energy range, with wavelengths around 13.5 nm, provides direct information on the performance of EUV optical components, e.g. EUV pho­ tomasks, in their working wavelength regime. Scatterometry with horizontal diffraction geometry, parallel to the grating lines (conical), and vertical scattering geometry, perpendicular to the lines (in-plane), was performed on EUV lithography mask test structures. Numerical FEM based simulations, using a rigorous Maxwell solver, compare both experimental set-ups with focus on the sensitivity of the diffraction intensities particularly with respect to the side wall angle.

A new methodology for 3D surface measurement based on phase shifted fringe pattern projection is presented which enables real-time measurement and high-speed performance of 3D measurements using stereo camera observation. The essence of the new technique is a drastic reduction of the fringe code which makes the process of pattern projection and image recording faster and real-time applicable. The new algorithm allows the complete omission of the typically used Gray code sequence or other additional code to the phase shifted sinusoidal fringe sequence. Its main concept is a special geometric design of the arrangement of the projection unit in relation to one of the involved cameras. The 3D point calculation is performed by triangulation between the two cameras with the help 3D point determination between the projection unit and one of the cameras. Whereas the second mode ensures the uniqueness, mode one realizes the accurate calculation. The realization of the uniqueness of the measurement is obtained by a corresponding arrangement of the parameters projected fringe width, the measurement volume size, the triangulation angle between the principal rays of first camera and the projection unit, and camera constants of second camera and projection unit. First experiments with a 3D measurement systems based on fringe projection technique show the robustness of the new method. Real time measurements can be performed which is the precondition of the supervision or quality check of several dynamic processes.

The tilted-wave interferometer (TWI) was recently developed by the University of Stuttgart for the high-accuracy measurement of aspheres and freeform surfaces. The system works in a non-null measurement fashion and si­ multaneously uses several test beams with different tilts. Reconstruction of the specimen under test from TWI measurements is challenging and in order to correctly separate the real surface topography from systematic aberrations, the employed interferometer needs to be characterized. This characterization, as well as the recon­ struction of the specimen from TWI measurements, requires sophisticated data analysis procedures including ray tracing and the solution of an inverse problem. A simulation environment was developed at the Physikalisch-Technische Bundesanstalt (PTB) in order to inves­ tigate the accuracy and stability of TWI systems, and to explore possibilities and limitations of this promising measurement technique. Virtual experiments were carried out to quantify the sensitivity of the results with respect to the assumed linearity in the reconstruction procedure, positioning errors, and measurement noise. Our first results suggest that the mathematical TWI reconstruction technique basically allows highly accurate measurements with uncertainties down to a few nanometers, provided that calibration errors of the optical sys­ tems are kept small. The stability of the results and their accuracy can, however, depend significantly on the particular surface of the specimen and on the choice of experimental settings.

Optical feedback interferometry is a well known technique that can be used to build non-contact, cost effective, high resolution sensors. In the case of displacement measurement, different research groups have shown interest in increasing the resolution of the sensors based on this type of interferometry. Such efforts have shown that it is possible to reach better resolutions by introducing external elements such as electro-optic modulators, or by using complex signal processing algorithms. Even though the resolution of the technique has been increased, it is still not possible to characterize displacements with total amplitudes under λ/2. In this work, we propose a technique capable of measuring true nanometre amplitude displacements based on optical feedback interferometry. The system is composed by two laser diodes which are calibrated within the moderate feedback regime. Both lasers are subjected to a vibration reference and only one of them is aimed to the measurement target. The optical output power signals obtained from the lasers are spatially compared and the displacement information is retrieved. The theory and simulations described further on show that sub-nanometre resolution may be reached for displacements with amplitudes lower than λ/2. Expected limitations due to the measurement environment will also be discussed in this paper.

In speckle interferometry (SI), there are different techniques for acquiring information about a surface under test. The surface roughness is one parameter of interest. In the past, there have been different attempts to create models for relating the surface roughness to SI. By using, e.g., angular or spectral speckle correlation techniques, it is possible to estimate the roughness of a test sample qualitatively and to classify different magnitudes of roughness. Yet, there is no method to measure roughness quantitatively by using speckle interferometry. In this work, one possible reason for this restriction is investigated. By using a numerical simulation, it is shown that SI is not only sensitive with respect to a statistical distribution of a test sample but also to the kind of structure and inner dependency of the surface. Finally, a conclusion for roughness measurement using SI in general is drawn and an outlook is given.

A tilt mirror’s deflection angle tracking setup is examined from a theoretical point of view. The proposed setup is based on a simple optical approach and easily scalable. Thus, the principle is especially of interest for small and fast oscillating MEMS/MOEMS based tilt mirrors. An experimentally established optical scheme is used as a starting point for accurate and fast mirror angle-position detection. This approach uses an additional layer, positioned under the MOEMS mirror's backside, consisting of a light source in the center and two photodetectors positioned symmetrical around the center. The mirror’s back surface is illuminated by the light source and the intensity change due to mirror tilting is tracked via the photodiodes. The challenge of this method is to get a linear relation between the measured intensity and the current mirror tilt angle even for larger angles. State-of-the-art MOEMS mirrors achieve angles up to ±30°, which exceeds the linear angle approximations. The use of an LED, small laser diode or VCSEL as a lightsource is appropriate due to their small size and inexpensive price. Those light sources typically emit light with a Gaussian intensity distribution. This makes an analytical prediction of the expected detector signal quite complicated. In this publication an analytical simulation model is developed to evaluate the influence of the main parameters for this optical mirror tilt-sensor design. An easy and fast to calculate value directly linked to the mirror’s tilt-angle is the “relative differential intensity” (RDI = (I₁ − I₂) / (I₁ + I₂)). Evaluation of its slope and nonlinear error highlights dependencies between the identified parameters for best SNR and linearity. Also the energy amount covering the detector area is taken into account. Design optimizing rules are proposed and discussed based on theoretical considerations.

To gather information about physical parameters from electric or electronic methods, the signal to noise ratio (SNR) plays a decisive role. It can be used as a measure of goodness for the current data acquisition. With a laser Doppler vibrometer a contactless measurement of oscillating surfaces is available. It uses the Doppler Effect caused by the local deviation of an oscillating surface, which can be analyzed interferometrically. Depending on the roughness of the surface, interference phenomena can occur and are usually known as speckle effects. The coherence behavior of the light in a laser Doppler vibrometer can lead to destructive interference, with the result that the signal to noise ratio is too low to perform a sufficient measurement. This interference related phenomenon is also called speckle-dropout. To counteract this effect, the vibrometer was equipped with an adaptive optics, which can modify specifically the phase front of the coherent wave. In a first approach, the potential of signal optimization was investigated. Based on superposed Zernike polynomials, special phase pattern were calculated and written into that adaptive optics. Such polynomials are the common method to describe wave fronts in optical systems and, accordingly, are sufficiently precise analyzed. Each Zernike polynomial has a related coefficient to weight it individually in a superposition. These coefficients are the decision variables in an optimization algorithm. Correlated with a loop- back control, the coefficients can be interpreted as regulating variables. With the assumption that the system states are close enough to the optimal states, an extremum seeking control was developed to track and hold the system at that optimum. The algorithm depends on the successive parabolic interpolation, which was developed by Heath for one-dimensional problems. It was extended for solving a multi-dimensional problem definition and, furthermore, embedded into a loop- back control. This paper presents the current design of the extremum seeking control and discusses the benefits with some results of the improved measurements and is structured as follows. The investigated system will be introduced in section 1. Also, the measurement concept will be shown in this section. It is followed by the mathmatical framework in section 2. It gives an overview over the developed concepts based on the successive parabolic interpolation. In addition, the Newton method, an approach to solve a non-linear optimization problem, is described. The next section 3 contains the nucleus of the work. It deals with the derivation of the developed control law of the extremum seeking control. The paper is completed with a results section and the conclusion of this work.

A physical model eye was constructed to test the quality of ophthalmic instruments. The accuracy and precision of two commercially available instruments were analysed. For these instruments, a particular model eye was obtained which mimicked the physical properties that would be usually measured e.g. corneal topography or optical path within the human eye. The model eye was designed using relatively simple optical components (e.g. plano-convex lenses) separated by appropriate intraocular distances taken from the literature. The dimensions of the model eye were known a priori: The lenses used in the construction of the model eye were characterised ac­ cording to values given in the manufacturers' data sheets and also through measurement using an interferometer. The distances between the lens surfaces were calculated using the interferometric data with reverse ray-tracing. Optical paths were calculated as the product of refractive index and axial distance. The errors inherent in mea­ suring these ocular parameters by different ophthalmic instruments can be considered as producing an erroneous value for the overall refractive power of the eye. The latter is a useful metric for comparing various ophthalmic devices where the direct comparison of quality is not possible or is not practical. For example, a 1% error in anterior corneal radius of curvature will have a more detrimental effect than the same error in posterior corneal radius, due to the relative differences in refractive indices at those surface boundaries. To quantify the error in ocular refractive power, a generic eye model was created in ZEMAX optical design software. The parametric errors were then used to compute the overall error in predicting ocular refractive power, thus highlighting the relative importance of individual errors. This work will help in future determination of acceptable levels of metrological errors in ocular instrumentation.

The accurate and traceable form measurement of optical surfaces has been greatly advanced by a new generation of surface profilometers which are based on the reflection of light at the surface and the measurement of the reflection angle. For this application, high-resolution electronic autocollimators provide accurate and traceable angle metrology. In recent years, great progress has been made at the Physikalisch-Technische Bundesanstalt (PTB) in autocollimator calibration. For an advanced autocollimator characterisation, a novel calibration device has been built up at PTB: the Spatial Angle Autocollimator Calibrator (SAAC). The system makes use of an innovative Cartesian arrangement of three autocollimators (two reference autocollimators and the autocollimator to be calibrated), which allows a precise measurement of the angular orientation of a reflector cube. Each reference autocollimator is sensitive primarily to changes in one of the two relevant tilt angles, whereas the autocollimator to be calibrated is sensitive to both. The distance between the reflector cube and the autocollimator to be calibrated can be varied flexibly. In this contribution, we present the SAAC and aspects of the mathematical modelling of the system for deriving analytical expressions for the autocollimators’ angle responses. These efforts will allow advancing the form measurement substantially with autocollimator-based profilometers and approaching fundamental measurement limits. Additionally, they will help manufacturers of autocollimators to improve their instruments and will provide improved angle measurement methods for precision engineering.

The paper presents a mathematical modeling of the transmission / modulation functions of the classical optical chopper wheels - with windows with linear edges. Based on our previous analytical analysis on constant intensity distributions (top-hat) laser beams, in the present paper the complete modeling and simulation of the chopping process of the light beam sections with Gaussian distributions is proposed. The different possible cases of the relationships between the geometry of the chopper blades and of the beam section in the plane of the wheel are considered. The three relevant situations that can be met are approached: (i) large blades in front of the beam section (that can be thus completely covered by each blade): (ii) narrow single blade in front of the (larger) beam section; (iii) multiple narrow blades placed simultaneously in front of the beam section. The experimental chopper module we have built with different chopper wheels that we have designed and fabricated as prototypes is also reviewed. Perspectives and future work on other types of optical chopper configurations conclude the study.

The goal of deconvolution microscopy for phase-contrast imaging is to reassign the optical blur to its original position and to reduce statistical noise, thus visualizing the cellular structures of living cells in three dimensions and at subresolution scale. The major features of this technology for a phase-contrast microscopy are discussed through a series of theoretical analyses. A few of possible sources of aberrations and image degradation processes are presented. The theoretical and experimental results have shown that deconvolution microscopy can enhance resolution and contrast by either subtracting or reassigning out-of-focus blur.

Image stitching is a technique used to measure large surface areas with high resolution while maintaining a large field of view. We work on improving data fusion by stitching in the field of microscopic analysis of technical surfaces for structures and roughness. Guidance errors and imaging errors such as noise cause problems for seamless image fusion of technical surfaces. The optical imaging errors of 3D Microscopes, such as confocal microscopes and white light interferometers, as well as the guidance errors of their automated positioning systems have been measured to create a software to simulate automated measurements of known surfaces with specific deviations to test new stitching algorithms. We measured and incorporated radial image distortion, interferometer reference mirror shape deviations, statistical noise, drift of the positional axis, on-axis-accuracy and repeatability of the used positioning stages and misalignment of the CCD-Chip with respect to the axes of motion. We used the resulting simulation of the measurement process to test a new image registration technique that allows for the use of correlation of images by fast fourier transform for small overlaps between single measurements.

Scanning near-field optical microscopy (SNOM) is a powerful tool providing measurement of the near-field intensity of nano-structured surface layers. These measurements can be combined with rigorous solving of Maxwell's equations to gain insight into light propagation inside the layer. However, there are often major differences between the simulated near-field intensity directly above the surface and SNOM measurements. The SNOM measurements are being performed in a way that sample and probe have a distance of about 20 nm at their closest point, therefore the finite size of the probe has a severe impact on the measurement, e.g. for textured surfaces. Any steep flank present in the topography leads to an increased distance between the aperture of the probe and the sample surface, since the shortest distance between sample and probe occurs at the side of the tip. This behavior modifies the measurement at all points where the geometry does not allow for the aperture to be placed 20 nm over the topography, since another part of the probe would get in contact with the surface. To account for these topography artifacts in our simulations, we developed an algorithm to calculate the height of the probe above each point of the surface. Taking this position into account for each point of the topography measurement, we are able to obtain an intensity distribution at the same positions as the SNOM measurement. This intensity distribution shows a much better agreement to experiment than assuming a constant distance of 20 nm from the surface. We illustrate this algorithm and its consequences for comparisons between SNOM measurements and simulation using the textured transparent front contact of a silicon-based thin-film solar cell as an example. In such devices, the absorber layer of the cell is typically thinner than the absorption length of the incident light, especially in the long wavelength region. Due to the texture, the effective light path can be prolonged, and near-field measurements allow for an insight into light intensity close to the interface as well as guided modes.

Defect parameters retrieval from diffraction-limited images is demonstrated. The parameters of defects in nanostructures are retrieved from measured aerial images of high NA-projection systems. The difference between images of masks with and without defects is used as a reference to reconstruct the parameters of the defect. An error function is defined, and the whole retrieval procedure can be expressed as an optimization problem. The performance of the technique was simulated by the lithography and imaging simulator Dr.LiTHO. The dependencies of the retrieval results on optimizers, illumination settings, defect sizes, and reference images are presented. The evaluation of the performance of the technique is performed by comparison of the retrieval errors for defect shapes, mask patterns, and types of noise. Moreover, the sensitivity of the defect detection to Zernike aberrations of the optical image projection lens and the retrieval accuracy for different mask models and types of defects are investigated.

The Fourier modal method (FMM), also referred to as Rigorous Coupled-Wave Analysis (RCWA), is based on Fourier-mode expansions and is inherently built for periodic structures such as diffraction gratings. When the infinite periodicity assumption is not realistic, the finiteness of the structure has to be incorporated into the model. In this paper we discuss the recent extensions of the FMM for finite structures. First, we explain how an efficient FMM-based method for finite structures is obtained by a reformulation of the governing equations and incorporation of perfectly matched layers (PMLs). Then we show that the computational cost of the method can be further reduced by employing an alternative discretization instead of the classical one. Numerical results demonstrate the characteristics of the discussed FMM-based methods and include a discussion of computational complexities.

High-contrast gratings (HCG) are the ultra-thin elements set to operate in near-wavelength regime with the period of the grating smaller then wavelength and with the high-index grating fully surrounded by low-index material. We concentrate on topics scarcely explored in the literature such as the spectral response phenomenology of HCGs with the complex unit cells. We show that the spectral response is robust under the symmetric unit cell perturbations, while asymmetric unit cell perturbations may introduce completely new spectral response. Further, we show examples of highly fragmented spectra present in the case of HCGs with the aperiodic topology in the unit cell. Our results can serve as guidance for the design of the complex HCGs and help with the choice of the efficient initial grating topology prior to global optimization procedure.

The transport of intensity equation (TIE) describes the relation between the object phase and the intensity distribution in the Fresnel region and can be used as a non-interferometric technique to estimate the phase distribution of an object. A number of techniques have been developed to solve the TIE. In this work we focus on one popular class of Poisson solvers that are based on Fourier and the Multigrid techniques. The aim of this paper is to present an analysis of these types of TIE solvers taking into account the effect of the boundary condition, i.e. the Neumann Boundary Condition (NBC), the Dirichlet Boundary Condition (DBC), and the Periodic Boundary Condition (PBC). This analysis, which depends on the location of an object wave-front in the detector plane, aims to identify the advantages and disadvantage of these kinds of solvers and to provide the rules for choice of the best fitted boundary condition.

An exact Dyson equation for averaged over electromagnetic crystal unit cell propagating total wave electric field is derived, with supposing the incident wave electric field to have the Floquet property. The mass operator related to periodic structure effective tensor dielectric permittivity is written as double Fourier transform from electric field Tscattering operator of the structure unit cell. The Lippmann-Swinger equation for the unit cell T-scattering operator, written in terms of the unit cell T-scattering operator in free space and the electric field lattice tensor Green function interaction part, is resolved by quasi-separable method. This recently presented quasi-separable approach to unit cell Tscattering operator enables one to consider unit cell containing several particles, with coupling between them directly inside the cell as well as through the structure via above lattice Green function interaction part. The obtained quasiseparable unit cell T-scattering operator is applied to study double diamagnetic-paramagnetic narrow peak in artificial periodical material with unit cell including the coupled plasmonic particles. Actually this magnetic phenomenon is appeared as combination result of space-group resonance between two small dielectric spheres and plasmonic resonance inside a single sphere. Studying the magnetic response of disordered media, we use Dyson self-consistent exact equation for ensemble averaged wave electric field inside dense discrete random media, with a random mass operator having been put under averaging sign. The random mass operator was written in terms of particles’ correlations functions of all orders and particles’ clusters’ T-scattering operators. We discuss comparison between the unit cell T-scattering operator of periodic discrete structure and a cluster T-scattering operator of random discrete structure and consider the above double diamagnetic–paramagnetic peak also in random discrete structure of coupled small plasmonic dielectric spherical particles.

This study investigates a method to access the power splitting performances of multimode interference waveguides based on analytical nonlinear modal propagation analysis method in the presence of the Kerr nonlinear effect for device miniaturization. Nonlinear multimode interference waveguide has been already reported in a few work based on beam propagation analysis (BPM) for make a special path with intense input for switching purposes. BPM method does not seem a capable method for study the multimode waveguide performance in small lengths. Therefore, we established the nonlinear modal propagation analysis on the way that is determined based on the propagation of all nonlinear guided modes throughout the medium whereas this shows the amplitude and phase changes of the guided modes. In fact mentioned change lead to induction of nonlinearity on original guided modes and make them nonlinear. In this paper, the nonlinear guided modes which are excitedfrom input beam are measured with solve the nonlinear differential equation. Intensity distribution among the multimode waveguide as a simulation tool assist us to show the possibility to access to 1×N power splitters whereas they operate on small lengths in comparison with past reports in linear regimes. In fact the formation of parallel self- images determined the outputs for splitter and the resolution and contrast of image show the uniformity and insertion loss that result demonstrate desirable uniformity and insertion loss so that miniaturization does not decrease the performance. Also the simulation result shows proposed active device is more sensitive to the input intensity. This sensitive can be a foundation for propose an arbitrary power splitter ratio devices.

In this contribution optical properties of new metallic nanoparticles for biomedical applications are investigated. These particles consist of a pair of opposing gold prisms with asymmetric dielectric holes. In this configuration the structure exhibits multi-resonant behavior in the Visible and Near Infrared Region, useful tool for multi-sensing platform based on local refractive index measurements. The electromagnetic properties of the structure are evaluated in terms of extinction cross-section through proper full-wave simulations. The sensitivity performances for the local refractive index variation are discussed. The obtained results show that the proposed particles could be efficiently applied for sensing applications.

Hollow-core photonic bandgap fibers guide light using diffraction rather than total internal reflection as is the case with normal single- mode communications fibers. The fibers consist of a hollow capillary (~19 micrometers in diameter) surrounded by capillary (~4 micrometers in diameter) arranged in a honey-comb like structure. The honey-comb structure scatters light in the core such that light within the bandgap wavelengths cannot escape from the core. However, the bandgap properties greatly depend on the accuracy with which the microstructures can be controlled during the fabrication process. For measuring the geometrical properties of hollow core photonic crystal fibers with a honeycomb cladding structure we use an angular scatterometric setup. For analyzing the experimentally obtained data we rigorously compute the scattering signal by solving Maxwell's equations with finite-element methods. This contribution focuses on the numerical analysis of the problem. A convergence analysis demonstrates that we reach highly accurate solutions. Our results show very good qualitative agreement between experimental and numerical results. We furthermore demonstrate concepts for accurately monitoring dimensional parameters in the fiber manufacturing process.

Scatterometry is a well-established optical metrology method used in research as well as in industrial applications to precisely characterize small structures. The method is based on a comparison of the measured scattered light field to the rigorously simulated scattered light field based on a model of the real structure. Although in recent time this method has been steadily improved and extended to characterize structures down to sub-lambda size, the sensitivity towards the parameters of interest is generally decreasing for smaller structures, which makes the characterization more and more difficult. Opposed to other efforts based on changing the measurement configuration or combining different measurement methods, we have chosen to address the fundamental cause of this loose of information: As known from theory the electromagnetic near field is directly dominated by currents and charge-separations in the illuminated structure, while the far field is produced by its corresponding near field and is not directly linked to the charges and currents induced in the structure. For that reason the transition from the near field to the far field, which is accessible in a scatterometric measurement, causes information loss about the structure. In our approach we directly influence the near field with the introduction of additional structures in the direct vicinity of the sub-lambda grating to be characterized. With rigorous electromagnetic simulations we optimize the design of these near field structures to increase the information content of the scatterometric signatures which can be detected in the far field region. We show the optimization of scatterometric signatures for a silicon line grating and compare the gain of information obtained by the near field design. Understanding the influence of the near field on the scatterometric signatures can help to address the increasing demand on quality management caused by the constant miniaturization in industrial applications.

The precise and accurate determination of critical dimensions of photo masks and their uncertainties is important in the lithographic process to ensure operational reliability of electronic compounds. Scatterometry is known as a fast, non-destructive optical method for the indirect determination of geometry parameters. In recent years novel methods for solving the inverse problem of scatterometry have enabled a more reliable determination of grating parameters. In this article we present results from maximum likelihood parameter estimations based on numerically simulated EUV scatterometry data. We approximately determine uncertainties of these parameters by a Monte Carlo method with a limited amount of samplings and by employing the Fisher information matrix. Furthermore, we demonstrate that the use of incomplete mathematical models may lead to severe distortions in the calculations of the uncertainties by the approximate Fisher matrix approach as well as to substantially larger uncertainties for the Monte Carlo method.

The impact of line-edge (LER) and line-width roughness (LWR) on the measured diffraction patters in extreme ultraviolet (EUV) scatterometry has been investigated in recent publications. Two-dimensional rigorous numerical simulations were carried out to model roughness. Simple analytical expressions for the bias in the mean efficiencies stemming from LER and LWR were obtained. Applying a similar approach for DUV scatterometry to investigate the impact of line roughness we obtain comparable results.

In order to assist a system design of laser coherent Doppler wind sensor for active pitch control of wind turbine systems (WTS), we developed a numerical simulation environment for modeling and simulation of the sensor system. In this paper we present this simulation concept. In previous works, we have shown the general idea and the possibility of using a low cost coherent laser Doppler wind sensing system for an active pitch control of WTS in order to achieve a reduced mechanical stress, increase the WTS lifetime and therefore reduce the electricity price from wind energy. Such a system is based on a 1.55μm Continuous-Wave (CW) laser plus an erbium-doped fiber amplifier (EDFA) with an output power of 1W. Within this system, an optical coherent detection method is chosen for the Doppler frequency measurement in megahertz range. A comparatively low cost short coherent length laser with a fiber delay line is used for achieving a multiple range measurement. In this paper, we show the current results on the improvement of our simulation by applying a Monte Carlo random generation method for positioning the random particles in atmosphere and extend the simulation to the entire beam penetrated space by introducing a cylindrical co-ordinate concept and meshing the entire volume into small elements in order to achieve a faster calculation and gain more realistic simulation result. In addition, by applying different atmospheric parameters, such as particle sizes and distributions, we can simulate different weather and wind situations.

In dimensional measurements by laser interferometry, when the accuracy approaches 10^-9 λ, wavefront aberra­ tions cause systematic variations of the fringe period. This paper illustrates how these effects are modeled and experimentally studied in the measurements of the lattice parameter and the topographical survey of 1 kg Si spheres, which measurements are necessary to "count" atoms and to make it possible to realize the kilogram from the Planck constant value.

The LISA Pathfinder mission to space employs an optical metrology system (OMS) at its core to measure the distance and attitude between two freely floating test-masses to picometer and nanorad accuracy, respectively, within the measurement band of [1 mHz, 30 mHz]. The OMS is based upon an ultra-stable optical bench with 4 heterodyne interferometers from which interference signals are read-out and processed by a digital phase-meter. Laser frequency noise, power fluctuations and optical path-length variations are suppressed to uncritical levels by dedicated control loops so that the measurement performance approaches the sensor limit imposed by the phasemeter. The system design is such that low frequency common mode noise which affects the read-out phase of all four interferometers is generally well suppressed by subtraction of a reference phase from the other interferometer signals. However, high frequency noise directly affects measurement performance and its common mode rejection depends strongly on the relative signal phases. We discuss how the data from recent test campaigns point towards high frequency phase noise as a likely performance limiting factor which explains some important performance features.

In the current article an advanced method of EFPI baseline measurement by use of spectral function approximation is proposed. The method provides an increase in EFPI baseline measurement precision and computational acceleration. The method bases on two foundations provided by analysis of low-finesse Fabry-Perot interferometer model: reduction of search domain and taking into account the most informative spectral intervals, providing a greater impact on the residual of measured and theoretical EFPI spectral functions. Proposed signal processing method resulted in the EFPI baseline measurement resolution less than 50 pm for the cavity length values between 20 and 700 μm.

We have provided a comparative analysis of methods that involves multi-angle averaging, pseudo multi-angle averaging, single-rotation and variants based on the combinations. All these methods require measurement results being determined at rotational positions, serving for the interferometric measurement of rotationally asymmetric surface deviation of a specimen. Zernike coefficients and power spectral density (PSD) are computed and used for detailed comparison. The experimental results show that single-rotation method gives noticeably smoother result, thus it is limited to applications of measuring low spatial frequency deviations, taking the advantage of quick measurement time with fairly accurate rms results and potentially less influence of environment; in contrast, the result with multi-angle averaging contains more information of mid and high spatial frequency but it’s time-consuming. The pseudo multi-averaging method is the concise variant with fewer measurements. Its result contains more noise errors depending on the number of rotational measurements of multi-averaging method.

A new method for adjusting the lateral transfer hollow retroreflector is presented. It allows in a simple way to adjust the hollow retroreflectors with a lateral shifting. It enables to make the manufacturing process of adjustable lateral hollow retroreflectors easier and cheaper. The testing optical bed of this method is displayed. The evaluation of uncertainties and a limit value for this method are given.

In Cartesian coordinate system, a flat can be expressed as the sum of even-odd, odd-even, even-even and oddodd functions. In the traditional three-flat even and odd function method, odd-odd function is difficult to obtain. In our paper the odd-odd function can be solved by use the Dove prism which can rotate the optical axis. The odd-odd function can calculate exactly. The even-odd, odd-even, even-even can be solved by rotating the flat 180°like the traditional method. Only five configurations are used to test the flats. The theoretical derivation and analysis are presented.

We investigate the scan patterns produced using different pairs of Risley prisms. Combinations of optical wedges with different prism angles (corresponding to different deviations angles of the prisms) are considered to complete the exact modeling of the scanning process using specialized mechanical design programs. While this procedure is somehow elaborate with regard to approximate methods, it has the advantage of providing the exact movement laws of the laser spot on various types of surfaces scanned with this type of refractive device. The study is made with regard to the characteristic parameters of the device, such as θ₁ and θ₂ - the prism angles of the two wedges, ω₁ and ω₂ - the rotating speeds of the two wedges, and the geometry of the scanner (which includes the distance between the two prisms, their orientation, and the distance to the scanned plane). The scanner is approached for a row of values of the characteristic parameters k=θ₂/θ₁ and M=ω₂/ω₁ introduced in Marshall’s classical work. The results allow for choosing the most appropriate patterns for specific scanning applications.

Our work is focused on a problem of numerical evaluation of Zernike polynomials and their Cartesian partial derivatives. Since the direct calculation using explicit definition relations is relatively slow and it is numerically instable for higher orders of evaluated polynomials there is a need for a more effective and stable method. In recent years several recurrent methods were developed for numerical evaluation of Zernike polynomials. These methods are numerically stable up to very high orders and they are much faster than direct calculation. In our work a brief review of the existing methods for calculation of Zernike polynomials is given and then an analogous recurrence method for evaluation of x and y partial derivatives of Zernike polynomials is proposed. The numerical stability of this method and the comparison of computation time with respect to the direct method is presented using computer simulations. The proposed method can be used e.g. in optical modeling for expressing the shape of optical surfaces or in optical measurement methods based on the wavefront gradient measurements (Shack-Hartmann wavefront sensor, pyramidal sensor or shearing interferometry), where modal wavefront reconstruction using Zernike polynomials is often used.

The paper presents an insight into our current researches on galvanometer-based scanners (GSs). A brief overview is first performed on the state-of-the-art, as well as on some of our contributions to optimize the scanning and the command functions of this most used scanning device. Considerations on the use of GSs in high-end biomedical imaging applications such as Optical Coherence Tomography (OCT) are made, with a focus towards obtaining the best possible duty cycles and artifact-free OCT images when using GSs for lateral scanning, as studied in our previous works. The scope of our present study is to obtain the mathematical model of a GS system (motor and controller included) in order to optimize the command functions of the device and to support the development of some more advanced control structures. The study is centered on the mathematical and experimental modeling of GSs. Thus, the results of an experimental identification made on a classical multi-parameter mathematical model proposed for such a system are presented. The experiments are carried out in different operating regimes, and the specific characteristic parameters of the GS are determined. Using these parameters obtained experimentally, we carry out simulations in Mathlab Simulink to validate the theoretical model. With the indentified model, an extended control solution is proposed. We point out the match between the theory and the results of the simulations and of the testing for different types of input signals, such as triangular, sinusoidal, and sawtooth with different duty cycles.

The European XFEL is a large facility under construction in Hamburg, Germany. It will provide a transversally fully coherent X-ray radiation with outstanding characteristics: high repetition rate (up to 2700 pulses with a 0.6 milliseconds long pulse train at 10Hz), short wavelength (down to 0.05 nm), short pulse (in the femtoseconds scale) and high average brilliance (1.6•10²⁵ photons / s / mm² / mrad²/ 0.1% bandwidth). Due to the very short wavelength and very high pulse energy, mirrors have to present high quality surface, to be very long, and at the same time to implement an effective cooling system. Matching these tight specifications and assessing them with high precision optical measurements is very challenging. One of the three foreseen beamlines operates in the soft X-ray range and it is equipped with a diffractive monochromator. The monochromator is using a variable line spacing grating that covers the wavelength range from 4.6nm to 0.41 nm (energies from 270eV to 3000eV). The grating profile is blazed, and due to the small angle and relatively few lines/mm, it is also very challenging to realize and to be characterized. In this contribution we discuss about the requirements of the optics involved in the soft X-ray monochromator. We describe mirror and grating specifications, and the tests that could be carried out during and after the manufacturing in order to ensure the specifications match.

Two different techniques, based on Liquid Crystal on Silicon technology, are proposed in this work to obtain superresolved images of an object. Whereas one of the methods is based on a structured illumination of the object, the second one achieves super-resolution by generating different sub-pixel displacements of the object image. In the first approach, object is simultaneously illuminated with different tilted beams, coding different information of the object. Different tilted beams, generated by means of the LCoS display, produce an on-axis interferometry scheme. By adding different combinations of constant phases at the generated beams, different interferograms are acquired. Using proper selection of constant phases for each of the interferograms, the synthetic aperture can be calculated. To this aim, a post processing is applied, where Fourier transforms of each interferogram is calculated, and where each portion of the object spectrum is spatially shifted at its correct position. Finally, by combining all the portions of the object spectrum, and by applying inverse Fourier transform of the synthesized spectrum, a super-resolved image of the object is achieved. In the second approach, Liquid Crystal on Silicon display is used to generate different linear phases at the object spectral plane, leading to different sub-pixel displacements of the object image at the image plane. In this way, images of the same object with different shifts are sampled by Charge-Coupled Device camera. Finally, by properly combining the different images obtained, an image with larger resolution than the original one is achieved. Experimental results obtained for the two proposed techniques are also provided in this work, confirming their usefulness to obtain super-resolved images.

S-Genius is a new universal scatterometry platform, which gathers all the LTM-CNRS know-how regarding the rigorous electromagnetic computation and several inverse problem solver solutions. This software platform is built to be a userfriendly, light, swift, accurate, user-oriented scatterometry tool, compatible with any ellipsometric measurements to fit and any types of pattern. It aims to combine a set of inverse problem solver capabilities — via adapted Levenberg- Marquard optimization, Kriging, Neural Network solutions — that greatly improve the reliability and the velocity of the solution determination. Furthermore, as the model solution is mainly vulnerable to materials optical properties, S-Genius may be coupled with an innovative material refractive indices determination. This paper will a little bit more focuses on the modified Levenberg-Marquardt optimization, one of the indirect method solver built up in parallel with the total SGenius software coding by yours truly. This modified Levenberg-Marquardt optimization corresponds to a Newton algorithm with an adapted damping parameter regarding the definition domains of the optimized parameters. Currently, S-Genius is technically ready for scientific collaboration, python-powered, multi-platform (windows/linux/macOS), multi-core, ready for 2D- (infinite features along the direction perpendicular to the incident plane), conical, and 3D-features computation, compatible with all kinds of input data from any possible ellipsometers (angle or wavelength resolved) or reflectometers, and widely used in our laboratory for resist trimming studies, etching features characterization (such as complex stack) or nano-imprint lithography measurements for instance. The work about kriging solver, neural network solver and material refractive indices determination is done (or about to) by other LTM members and about to be integrated on S-Genius platform.

A phase recovery procedure from several interferograms acquired in highly noisy environments as severe vibrations is described. This procedure may be implemented when phase shifting techniques may not be applicable due to the high error in the phase shift due to the vibrations. The phase differences among successive interferograms may contain nonlinear terms that could lead a sign changes in the supposed constants shift terms among acquired images. This can not be handled correctly with algorithms that corrects small nonlinearities in the phase shifts due to moderate disturbances during the phase shifting process. In most interferometric configurations for phase measurements the main effect of vibrations is to introduce a misalignment in the interferometric setup. Then, the phase differences between each interferogram may contain piston, tilt, and defocus errors. We observed that the tilt term is often the most dominant of the phase differences terms. In such cases, cosine of the phase differences among interferograms may be recovered. This cosine may be processed with Fourier methods in order to recover the phase differences. Once the phase differences are available the phase encoded in the interferograms may be determined. The proposed algorithm is tested in real interferograms.

The diffractive optical element (DOE) has the transformation function of wavefront, and its applications are forming or homogenization of beam, and aberration correction, and so on. In this study, we evaluate possibility as storage application of the DOE. The optical data storage using the DOE is thought of as a kind of holographic data storage (HDS). In the HDS, digital data is recorded and read out as modulated 2-dimensional page data, instead of bit-by-bit recording in conventional optical storages. Therefore, HDS actualize high data transfer rate. We design and optimize phase distribution of the DOE using the iterative method with regularization. In the optimization process, we use iterative Fourier transform algorithm (IFTA) that is known as Gerchberg–Saxton (GS) algorithm. At this time, the regularization method is adopted to suppress minute oscillation of the diffraction pattern. Designed and optimized DOE is fabricated by ultraviolet (UV) nanoimprinting technology. High productivity can be expected by adopting nanoimprinting technology. DOEs are duplicated on the silicon (Si) substrate as reflection-type elements. Fabricated DOE is evaluated in the experiment. We verify that DOE for optical data storage can be actualized through our approach.