This PDF file contains the front matter associated with SPIE Proceedings Volume 10330 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

Studying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g. Radiative Transfer Theory and Monte Carlo methods) but they do not treat coherence properties of light directly. Some variations of these methods allows to predict behavior of coherent light but only for an averaged realization of the scattering medium. This limits their application in studying many physical phenomena connected to a specific distribution of scattering particles (e.g. laser speckle). In general, numerical simulation of coherent light propagation in a specific realization of random medium is a time- and memory-consuming problem. The goal of the presented research was to develop new efficient method for solving this problem. The method, presented in our earlier works, is based on solving the Fredholm type integral equation, which describes multiple light scattering process. This equation can be discretized and solved numerically using various algorithms e.g. by direct solving the corresponding linear equations system, as well as by using iterative or Monte Carlo solvers. Here we present recent development of this method including its comparison with well-known analytical results and a finite-difference type simulations. We also present extension of the method for problems of multiple scattering of a polarized light on large spherical particles that joins presented mathematical formalism with Mie theory.

We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstruction result.

In non-rigid fringe projection 3D measurement systems, where either the camera or projector setup can change significantly between measurements or the object needs to be tracked, self-calibration has to be carried out frequently to keep the measurements accurate¹. In fringe projection systems, it is common to use methods developed initially for photogrammetry for the calibration of the camera(s) in the system in terms of extrinsic and intrinsic parameters. To calibrate the projector(s) an extra correspondence between a pre-calibrated camera and an image created by the projector is performed. These recalibration steps are usually time consuming and involve the measurement of calibrated patterns on planes, before the actual object can continue to be measured after a motion of a camera or projector has been introduced in the setup and hence do not facilitate fast 3D measurement of objects when frequent experimental setup changes are necessary. By employing and combining a priori information via inverse rendering, on-board sensors, deep learning and leveraging a graphics processor unit (GPU), we assess a fine camera pose estimation method which is based on optimising the rendering of a model of a scene and the object to match the view from the camera. We find that the success of this calibration pipeline can be greatly improved by using adequate a priori information from the aforementioned sources.

The European XFEL is a large-scale user 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 pulses (in the femtoseconds scale) and high average brilliance (1.6x10²⁵ photons / s / mm² / mrad²/ 0.1% bandwidth)1. Due to the short wavelength and high pulse energies, mirrors need to have a high-quality surface, have to be very long (1 m), and at the same time an effective cooling system has to be implemented. Matching these tight specifications and assessing them with high precision optical measurements is very challenging.

The mirrors go through a complicated and long process, starting from classical polishing to deterministic polishing, ending with a special coating and a final metrology assessment inside their mechanical mounts just before the installation. The installation itself is also difficult for such big mirrors and needs special care. In this contribution we will explain how we implemented the installation process, how we used the metrology information to optimize the installation procedure and we will show some preliminary results with the first mirrors installed in the European XFEL beam transport.

This article presents the result of the optical design of illuminating optical system for lightship using the freeform surface. It shows an algorithm of optical design of side-emitting lens for point source using Freeform Z function in Zemax non-sequential mode; optimization of calculation results and testing of optical system with real diode

We describe a setup for measuring the full angular Mueller matrix profile of a single mm- to μm-sized sample, and verify the experimental results against a theoretical model. The scatterometer has a fixed or levitating sample, illuminated with a laser beam whose full polarization state is controlled. The scattered light is detected with a combination of wave retarder, linear polarizer, and photomultiplier tube that is attached to a rotational stage. The first results are reported.

Johs and Hale developed the Kramers–Kronig consistent B-spline formulation for the dielectric function modeling in spectroscopic ellipsometry data analysis. In this article we use popular Akaike, corrected Akaike and Bayesian Information Criteria (AIC, AICc and BIC, respectively) to determine an optimal number of knots for B-spline model. These criteria allow finding a compromise between under- and overfitting of experimental data since they penalize for increasing number of knots and select representation which achieves the best fit with minimal number of knots. Proposed approach provides objective and practical guidance, as opposite to empirically driven or “gut feeling” decisions, for selecting the right number of knots for B-spline models in spectroscopic ellipsometry. AIC, AICc and BIC selection criteria work remarkably well as we demonstrated in several real-data applications. This approach formalizes selection of the optimal knot number and may be useful in practical perspective of spectroscopic ellipsometry data analysis.

We introduce the opto-mechanical architecture of a high precision, full Stokes vector, dual-channel polarimeter for the European Extremely Large Telescope’s High Resolution spectrograph (E-ELT HIRES). It is foreseen to feed two spectrograph modules simultaneously through the standard Front End subunit located on the Nasmyth platform via two fiber bundles; one optimized for the optical (BVRI), the other optimized for the infrared (zYJH) bands. The polarimeter is located below M4 in the f/4.4 intermediate focus, representing the only rotationally symmetric focus available, and is retractable. We illustrate the strategy of repositioning and aligning the instrument, provided that it has to withstand wind and earthquake loads and that the PSF is varying in width and position due to the active compensation by the co-phasing corrections. Preliminary results of its expected polarimetric sensitivity and accuracy are also analyzed for several configurations of M1 segments and suggest a stunning performance in the intermediate focus with cross talks of the order of 10^-7 but 10^-2 if it were located in the Nasmyth focus.

Recovering phase information with Deterministic approaches as the Transport of Intensity Equation (TIE) has recently emerged as an alternative tool to the interferometric techniques because it is experimentally easy to implement and provides fast and accurate results. Moreover, the potential of employing partially coherent illumination (PCI) in such techniques allow obtaining high quality phase reconstructions providing that the estimation of the corresponding Phase Transfer Function (PTF) is carried out correctly. Hence, accurate estimation of the PTF requires that the physical properties of the optical system are well known. Typically, these parameters are assumed constant in all the set of measurements, which might not be optimal. In this work, we proposed the use of an amplitude Spatial Light Modulator (aSLM) for tuning the degree of coherence of the optical system. The aSLM will be placed at the Fourier plane of the optical system, and then, band pass filters will be displayed. This methodology will perform amplitude modulation of the propagated field and as a result, the state of coherence of the optical system can be modified. Theoretical and experimental results that validate our proposed technique will be shown.

The optical properties of the guided modes in the core of photonic crystal fibers (PCFs) can be easily manipulated by changing the air-hole structure in the cladding. Special properties can be achieved in this case such as endless singlemode operation. Endlessly single-mode fibers, which enable single-mode guidance over a wide spectral range, are indispensable in the field of fiber technology. A two-dimensional photonic crystal with a silica central core and a micrometer-spaced hexagonal array of air holes is an established method to achieve endless single-mode properties. In addition to the guidance of light in the core, different cladding modes occur. The coupling between the core and the cladding modes can affect the endlessly single-mode guides. There are two possible ways to determine the dispersion: measurement and calculation.

We calculate the group velocity dispersion (GVD) of different cladding modes based on the measurement of the fiber structure parameters, the hole diameter and the pitch of a presumed homogeneous hexagonal array. Based on the scanning electron image, a calculation was made of the optical guiding properties of the microstructured cladding. We compare the calculation with a method to measure the wavelength-dependent time delay. We measure the time delay of defined cladding modes with a homemade supercontinuum light source in a white light interferometric setup. To measure the dispersion of cladding modes of optical fibers with high accuracy, a time-domain white-light interferometer based on a Mach-Zehnder interferometer is used. The experimental setup allows the determination of the wavelengthdependent differential group delay of light travelling through a thirty centimeter piece of test fiber in the wavelength range from VIS to NIR. The determination of the GVD using different methods enables the evaluation of the individual methods for characterizing the cladding modes of an endlessly single-mode fiber.

One main focus of high precision heterodyne displacement interferometers are the means of splitting and merging for the reference (R) and measurement (M) beams when a cancelable circuit is implemented. Optical mixing of R and M gives birth to a systematc error called cyclic error, which appears as a periodic offset between the detected displacement and the actual one.

A simple derivation of the cyclic error due to optical mixing is proposed for the cancelable circuit design. R and M beatings are collected by two photodiodes and conveniently converted by transimpedance amplifiers, such that the output signals are turned into ac-coupled voltages. The detected phase can be calculated as a function of the real phase (a change in optical path difference) in the case of zero-crossing detection. What turns out is a cyclic non-linearity which depends on the actual phase and on the amount of optical power leakage from the R channel into the M channel and vice versa. We then applied this result to the prototype of displacement gauge we are developing, which implements the cancelable circuit design with wavefront division. The splitting between R and M is done with a double coated mirror with a central hole, tilted by 45° with respect to the surface normal. The interferometer features two removable diffraction masks, respectively located before the merging point (a circular obscuration) and before the recombination point (a ring obscuration). In order to predict the extent of optical mixing between R and M, the whole layout was simulated by means of the Zemax ® Physical Optics Propagation (POP) tool. After the model of our setup was built and qualitatively verified, we proceeded by calculating the amount of optical leakages in various configurations: with and without the diffraction masks as well as for different sizes of both the holey mirror and the diffraction masks. The corrisponding maximum displacement error was then calculated for every configuration thanks to the previously derived formula. The insertion and optimization of the diffraction masks greatly improved the expected optical isolation inside the system.

Data acquisition from our displacement gauge has just started. We plan to experimentally verify such results as soon as our prototype gauge will reach the desired sub-nanometer sensitivity.

Previous implementations of the phase diffuser used in the multiple-plane phase retrieval method included a diffuser glass plate with fixed optical properties or a programmable yet expensive spatial light modulator. Here a model for phase retrieval based on a digital micromirror device as amplitude diffuser is presented. The technique offers programmable, convenient and low-cost amplitude diffuser for a non-stagnating iterative phase retrieval. The technique is demonstrated in the reconstructions of smooth object wavefronts.

Calibration which defines the relationship between the phase and depth data is the important part of the fringe projection profilometry. In practice, the inherently nonlinear and spatially variable relationship between the absolute phase of the projected fringe and the object surface depth without using telecentric lens make calibration problematic in the measurement of small object. In order to obtain this problem, a flexible, simple telecentric three dimensional measurement system is proposed. Because of the characteristic that the size of object will not change with depth in telecentric imaging, the absolute phase is linear with the depth and the process of calibration become simpler. The experiment result indicate that the standard deviation of calibration result at z coordinate is within 5 μm, while that at x and y coordinate is within 3 μm. Three-dimensional shape reconstruction of a coin value ¥1 and measurement of central circle points of the calibration target further verify the validity of the proposed calibration method.

In this paper, we have employed the L² waveguides in order to guide the light into two different arms constructed by the inclusion of an engineered obstacle in front of the input optical port. The light which travels inside the core liquid is coupled into these two arms experiencing different optical paths due to the asymmetric geometry of the obstacle and also the different used cladding liquids. We have used several sets of coupled hydrodynamic-electromagnetic simulations to characterize the interferometer based on the output intensity of the waveguide. The simulation results indicate that this technique has a maximum sensitivity of 595%/RIU and a maximum resolution of 3.3×10^-6 RIU which depends on the range of flow rate.

Accurate scatterometry and ellipsometry characterization of non-perfect thin films and nanostructured surfaces are challenging. Imperfections like surface roughness make the associated modelling and inverse problem solution difficult due to the lack of knowledge about the imperfection on the surface. Combining measurement data from several instruments increases the knowledge of non-perfect surfaces. In this paper we investigate how to incorporate this knowledge of surface imperfection into inverse methods used in scatterometry and ellipsometry using the Rigorous Coupled Wave Analysis. Three classes of imperfections are examined. The imperfections are introduced as periodic structures with a super cell periods ten times larger than the simple grating period. Two classes of imperfections concern the grating and one class concern the substrate. It is shown that imperfections of a few nanometers can severely change the reflective response on silicon gratings. Inverse scatterometry analyses of gratings with imperfection using simulated data with white noise have been performed. The results show that scatterometry is a robust technology that is able to characterize grating imperfections provided that the imperfection class is known.

The goal of this work is to describe a simulatively designed scatterometry approach for the in-line characterization of sub-wavelength sinusoidal gratings, which are formed on a transparent foil in a roll-to-roll procedure. The challenge is to acquire the 3D information of the workpiece, i.e., to measure the grating height in addition to the grating period with nm precision. The grating period is obtained straightforward from the position of the first order diffraction maxima in the reflection and the transmission region. For determining the grating height, the inverse problem is solved, i.e., the relation between the scattered intensities of the diffraction maxima and the grating height is extracted from light scattering simulations. The measurement uncertainty is evaluated for different instrumentation and simulation parameters, such as the detection and incidence angle, the laser wavelength as well as the input parameters of the simulation. As a result, the measurement uncertainty for the grating period and the height is estimated to 0.3 nm and ≤8 nm, respectively, when using laser light in the visible wavelength range. Large area scanning measurements performed offline using the setup parameters derived from simulations verify the sensitivity of the presented measurement approach for identifying local variations of the spatial surface properties. Depending on the chosen detection system, sampling rates up to the MHz range are feasible meeting the requirements of in-line process control of the roll-to-roll production procedure.

Laser focus sensors (LFS)¹ attached to a scanning nano-positioning and measuring machine (NPMM) enable near diffraction limit resolution with very large measuring areas up to 200 x 200 mm¹. Further extensions are planned to address wafer sizes of 8 inch and beyond. Thus, they are preferably suited for micro-metrology on large wafers. On the other hand, the minimum lateral features in state-of-the-art semiconductor industry are as small as a few nanometer and therefore far beyond the resolution limits of classical optics. New techniques such as OCD or ODP^3,4 a.k.a. as scatterometry have helped to overcome these constraints considerably. However, scatterometry relies on regular patterns and therefore, the measurements have to be performed on special reference gratings or boxes rather than in-die. Consequently, there is a gap between measurement and the actual structure of interest which becomes more and more an issues with shrinking feature sizes. On the other hand, near-field approaches would also allow to extent the resolution limit greatly⁵ but they require very challenging controls to keep the working distance small enough to stay within the near field zone.

Therefore, the feasibility and the limits of a LFS scanner system have been investigated theoretically. Based on simulations of laser focus sensor scanning across simple topographies, it was found that there is potential to overcome the diffraction limitations to some extent by means of vicinity interference effects caused by the optical interaction of adjacent topography features. We think that it might be well possible to reconstruct the diffracting profile by means of rigorous diffraction simulation based on a thorough model of the laser focus sensor optics in combination with topography diffraction ⁶ in a similar way as applied in OCD. The difference lies in the kind of signal itself which has to be modeled. While standard OCD is based on spectra, LFS utilizes height scan signals. Simulation results are presented for different types of topographies (dense vs. sparse, regular vs. single) with lateral features near and beyond the classical resolution limit. Moreover, the influence of topography height on the detectability is investigated. To this end, several sensor principles and polarization setups are considered such as a dual color pin hole sensor and a Foucault knife sensor. It is shown that resolution beyond the Abbe or Rayleigh limit is possible even with “classical” optical setups when combining measurements with sophisticated profile retrieval techniques and some a-priori knowledge. Finally, measurement uncertainties are derived based on perturbation simulations according to the method presented in ⁷.

If a moving camera observes a specular surface that reflects some distant environment, the recorded pixel values do not directly characterise the surface. However, the associated optical flow (OF), or specular flow (SF), as it is known in this case, is an (almost) environment-agnostic observable that depends on the camera position and the mirror shape. We present a derivation of the SF expected for a given view ray and mirror form, and establish a simple relation between the SF and the Gaussian curvature of the surface. The quality of the simulated SF is studied using physically-accurate rendering and state-of-the-art OF estimation software. Finally, we suggest and numerically verify a method to reconstruct the surface shapes from the SF, and discuss the possible ambiguities of the reconstruction.

In this work, we design a conical null-screen for testing non-symmetric corneas. We proposed a custom evaluation algorithm in order to calculate the shape of the corneal surface. This data is fitting to a custom non-symmetrical shape surface, taking into account orthogonal polynomials, in order to obtain the geometrical parameters such as the radius of curvature and conical constant. In order to proof our proposal, we perform some corneal topography measurements.

We present a method for testing the shape quality of the reflecting surface of a parabolic trough solar collector (PTSC) with flat null-screens. We develop a custom algorithm to reconstruct the surface taking into account the differences between the normal vector of the true surface and the reference one. Also, we perform a numerical simulation to analyze the accuracy of the method by introducing controlled systematic errors such as misalignments of the null-screen or the CCD plane.

Controlling the polarization of light is crucial in numerous applications such as spectroscopy, ellipsometry, photo lithography or industrial vision. Polarization control can be realized by wire grid polarizers (WGPs), which are large aspect ratio, zero order gratings. These elements provide an anisotropic transmittance depending on the polarization direction of the incident light. WGPs’ high attractiveness originates from their large free aperture, while simultaneously being extremely thin. Furthermore, these elements can be easily integrated into other nano-optical devices. Recently, such elements were successfully developed for applications down to the deep ultra violet spectral range. However, at shorter wavelengths the influence of roughness of the structures poses a severe limitation on the feasible optical performance. To tackle this problem, we numerically simulated the impact of line edge roughness on the polarization properties of WPGs. Therefore, we generated edge position data of rough grating lines by means of the Thorsos method and calculated the resulting optical response by finite difference time domain method. With this procedure the influence of standard deviation, correlation length, Hurst exponents and wavelength was investigated. We find that for standard deviations of 2.5 nm and 5.0 nm the polarization contrast is reduced by a factor of 3 and 7, respectively. The polarization contrast shows a minimum for intermediate correlation lengths, while virtually no impact of the Hurst exponent is observed. This is explained by several mechanisms occurring for different ratios between the spatial frequency of the roughness and the frequency of incident light. Our theoretical findings correlate well with experimental results we retrieved with measured roughness parameters of fabricated elements.

Lamellar gratings are widely used diffractive optical elements and are prototypes of structural elements in integrated electronic circuits. EUV scatterometry is very sensitive to structure details and imperfections, which makes it suitable for the characterization of nanostructured surfaces. As compared to X-ray methods, EUV scattering allows for steeper angles of incidence, which is highly preferable for the investigation of small measurement fields on semiconductor wafers. For the control of the lithographic manufacturing process, a rapid in-line characterization of nanostructures is indispensable. Numerous studies on the determination of regular geometry parameters of lamellar gratings from optical and Extreme Ultraviolet (EUV) scattering also investigated the impact of roughness on the respective results. The challenge is to appropriately model the influence of structure roughness on the diffraction intensities used for the reconstruction of the surface profile. The impact of roughness was already studied analytically but for gratings with a periodic pseudoroughness, because of practical restrictions of the computational domain. Our investigation aims at a better understanding of the scattering caused by line roughness. We designed a set of nine lamellar Si-gratings to be studied by EUV scatterometry. It includes one reference grating with no artificial roughness added, four gratings with a periodic roughness distribution, two with a prevailing line edge roughness (LER) and another two with line width roughness (LWR), and four gratings with a stochastic roughness distribution (two with LER and two with LWR). We show that the type of line roughness has a strong impact on the diffuse scatter angular distribution. Our experimental results are not described well by the present modelling approach based on small, periodically repeated domains.

The loss of the information, due to the diffraction and the evanescent waves, limits the resolving power of classical optical microscopy. In air, the lateral resolution of an optical microscope can approximated at half of the wavelength using a low-coherence illumination. Recently, several methods have been developed in order to overcome this limitation and, in 2011, a new far-field and full-field imaging technique was proposed where a sub-diffraction-limit resolution has been achieved using a transparent microsphere. In this article, the phenomenon of super-resolution using microsphere-assisted microscopy is analysed through rigorous electro-magnetic simulations. The performances of the imaging technique are estimated as function of optical and geometrical parameters. Furthermore, the role of coherence is introduced through the temporal coherence of the light source and the phase response of the object.

The sizes of non-negligible defects in the patterning of a semiconductor device continue to decrease as the dimensions for these devices are reduced. These “killer defects” disrupt the performance of the device and must be adequately controlled during manufacturing, and new solutions are required to improve optics-based defect inspection. To this end, our group has reported [Barnes et al., Proc. SPIE 1014516 (2017)] our initial five-wavelength simulation study, evaluating the extensibility of defect inspection by reducing the inspection wavelength from a deep-ultraviolet wavelength to wavelengths in the vacuum ultraviolet and the extreme ultraviolet. In that study, a 47 nm wavelength yielded enhancements in the signal to noise (SNR) by a factor of five compared to longer wavelengths and in the differential intensities by as much as three orders-of-magnitude compared to 13 nm. This paper briefly reviews these recent findings and investigates the possible sources for these disparities between results at 13 nm and 47 nm wavelengths. Our in-house finite-difference time-domain code (FDTD) is tested in both two and three dimensions to determine how computational conditions contributed to the results. A modified geometry and materials stack is presented that offers a second viewpoint of defect detectability as functions of wavelength, polarization, and defect type. Reapplication of the initial SNR-based defect metric again yields no detection of a defect at λ = 13 nm, but additional image preprocessing now enables the computation of the SNR for λ = 13 nm simulated images and has led to a revised defect metric that allows comparisons at all five wavelengths.

In this work we consider a microscopic optical system in which the beam with an optical vortex illuminates the sample. The sample modifies the geometry of the vortex beam wavefront and the information about it is transferred into the detection plane. It is shown that the beam at the detection plane can be represented by two parts: non-disturbed vortex part and sample part. We propose and test a scheme for recovering the phase changes caused by sample inserted into the vortex beam. The numerical simulations are supported by the experimental work.

To learn about the challenges, difficulties and technological steps in fabrication of a metal lens, a cascaded plasmonic superlens was fabricated in this paper and then its subwavelength imaging capability is demonstrated. First, we developed separately the fabrication and characterization procedures for each part in the cascaded superlens structure (composed of a planar plasmonic lens and a double layer meander structure) to show the precise fabricating process and results. Then the two parts of the cascaded structure were stacked together on the top of a double-slit object. First a larger slit width of 400 nm and a slit distance of 800 nm were used for easily obtaining a larger transmittance intensity distribution. The results show a good agreement between the experiment and simulation. Then a double-slit with width of 100 nm and distance of 180 nm were used to further test the resolving power of the superlens. The captured images show that the desired subwavelength resolution in the far field can be realized with the fabricated superlens.

In this paper we show, how different optical elements affect the polarization state. We show it on the examples of elementary optical elements, such as refracting and reflecting surfaces and an anisotropic waveplate, and more complex elements: a plane-parallel plate, a Dove prism, a spherical lens, an image sensor. The method of considering the calculated influence on the example of Stokes polarimetry is also shown.

Most laser scanners applications require a linear scanning function, i.e., a constant scanning speed. One of the possible and simplest methods to achieve this – for both scanners with rotational (i.e., polygonal) or oscillatory (i.e., galvanometer) mirrors – is to increase the distance between the mirror and the scanned plane. In order to achieve this, we propose and study a simple and low-cost optical configuration with two plane mirrors set at a certain adjustable angle. The multiple reflections of a laser beam on the two mirrors are considered, the number of images produced is deduced, and the total optical path is obtained. The device is considered for a dimensional measurement application, usually called an optical micrometer - in a set-up which includes the two angular mirrors between a laser scanner with oscillatory or rotational mirrors and its objective lens. This simple device increases the path of the laser beam between the scanning mirror and the lens in a compact construct. The linearity of the scanning function is thus increased, while the total size of the system is reduced – with regard to other possible set-ups. A multi-parameter analysis is proposed and briefly pointed out with regard to the characteristics of the system.

In this work we have measured the group-delay dispersion of an empty Michelson interferometer for s- and p-polarized light beams applying two different non-polarizing beam splitter cubes. The interference pattern appearing at the output of the interferometer was resolved with two different spectrometers. It was found that the group-delay dispersion of the empty interferometer depended on the polarization directions in case of both beam splitter cubes. The results were checked by inserting a glass plate in the sample arm of the interferometer and similar difference was obtained for the two polarization directions. These results show that to reach high precision, linearly polarized white light beam should be used and the residual dispersion of the empty interferometer should be measured at both polarization directions.

This paper is focused on a theoretical general description of membrane deformation in membrane liquid lenses, which is based on the theory of large deformations of thin plates under uniform hydrostatic loading. The general formulas are derived, leading to a system of differential equations that describe the shape of a deformed membrane. Since an analytical solution cannot be found, numerical methods are applied and the membrane shape is calculated for given practical examples. Further, the dependency of maximal deflection of the membrane on the applied hydrostatic pressure is analysed. For a better understanding and possibility of modelling the membrane shape in an optical design software, the shape is depicted as aspherical. Finally, the theoretical simulations are compared with experimental results for a given membrane and applied loadings. It is clearly seen that the shape of the membrane does not correspond to a sphere even under low applied pressures. Therefore, the presented analysis could have a significant impact in optical design. Using the results of the paper and numerical examples, one can easily model many cases of membrane liquid lenses and exploit the results of the simulation for precise description of optical systems with active components.

The successful integration of graphene into microelectronic devices depends strongly on the availability of fast and nondestructive characterization methods of graphene grown by CVD on large diameter production wafers [1-3] which are in the interest of the semiconductor industry. Here, a high-throughput optical metrology method for measuring the thickness and uniformity of large-area graphene sheets is demonstrated. The method is based on the combination of spectroscopic ellipsometry and normal incidence reflectometry in UV-Vis wavelength range (200-800 nm) with small light spots (~ 30 μm²) realized in wafer optical metrology tool. In the first step graphene layers were transferred on a SiO₂/Si substrate in order to determine the optical constants of graphene by the combination of multi-angle ellipsometry and reflectometry. Then these data were used for the development of a process control recipe of CVD graphene on 200 mm Ge(100)/Si(100) wafers. The graphene layer quality was additionally monitored by Raman spectroscopy. Atomic force microscopy measurements were performed for micro topography evaluation. In consequence, a robust recipe for unambiguous thickness monitoring of all components of a multilayer film stack, including graphene, surface residuals or interface layer underneath graphene and surface roughness is developed. Optical monitoring of graphene thickness uniformity over a wafer has shown an excellent long term stability (s=0.004 nm) regardless of the growth of interfacial GeO₂ and surface roughness. The sensitivity of the optical identification of graphene during microelectronic processing was evaluated.

This optical metrology technique with combined data collection exhibit a fast and highly precise method allowing one an unambiguous detection of graphene after transferring as well as after the CVD deposition process on a Ge(100)/Si(100) wafer. This approach is well suited for industrial applications due to its repeatability and flexibility.

This work presents the first results obtained in the validation study of an innovative technique to calculate the contact angle of a solid surface by means of a confocal device, which confirms the reliability and the accuracy of the presented method.

A measurement technique has been developed to measure the contact angle with of a confocal device. This technique has the unique advantage of allowing to perform both topography and contact angle measurements in the same location, therefore avoiding any shift in the sample positioning between the two measurements and ensuring the proper location of both measurements in the same area of the sample, thus enhancing the evaluation of the surface energy of the surface.

Specifically, this technique uses the confocal device to measure some parameters of the drop, such as the height (ℎ) and the apparent diameter (􀜮), in a top-view configuration. The drop volume is already known and small enough to discard gravity effects, so the shape of the drop can be approximated by a truncated sphere. Several purely geometric calculations are available to calculate the radius de of the drop and subsequently, the contact angle.

This work reports the first results of the ongoing validation study of this technique and the several mathematical calculations employed to extract the contact angle value. These initial measurements were performed for a hydrophobic surface with water as a measurement liquid. The contact angles for different set of drops for this sample were also measured by a commercial contact angle meter in side-view configuration, with the same liquid and drop dimensions, in order to verify the validity and the accuracy of the presented technique. This validation of the calculation of the contact angle is the first step for the further validation of the developed measurement method for the surface energy determination.

This study reports an application of a fiber-optic LED-based illumination system to solve an inverse problem in optical measurements of characteristics of a single-mode fiber. The illumination system has the advantages of low temporal coherence, high intensity, collimation, and thermal stability of the emission spectrum. The inverse analysis is investigated to predict the values of the diameter and refractive index of a single-mode fiber and applies to the far field scattering pattern in the vicinity of a polychromatic rainbow. As the inversion possibility depends considerably on the properties of the incident radiation, a detailed discussion is provided on both the specification of the illumination system as well as preliminary characteristics of the produced radiation. The illumination system uses a direct coupling between a thermally-stabilized LED junction and a plastic optical fiber, which transmits light to an optical collimator. A numerical study of fiber-to-LED coupling efficiency helps to understand the influence of lateral and longitudinal misalignments on the output power.

The paper presents a new comprehensive approach to modeling and analysis of processes occurring during the blood flow in the arm‟s small vessels as well as non-invasive measurement method of mixed venous oxygen saturation. During the work, a meta-analysis of available physiological data was performed and based on its result a hybrid model of forearm vascular tree was proposed. The model, in its structure, takes into account a classical nonlinear hydro-electric analogy in conjunction with light-tissue interaction. Several geometries of arm vascular tree obtained from magnetic resonance angiography (MRA) image were analyzed which allowed to proposed the structure of electrical analog network. Proposed model allows to simulate the behavior of forearm blood flow from the vascular tree mechanics point of view, as well as effects of the impact of cuff and vessel wall mechanics on the recorded photoplethysmographic signals. In particular, it allows to analyze the reaction and anatomical effects in small vessels and microcirculation caused by occlusive maneuver in selected techniques, what was of particular interest to authors and motivation to undertake research in this area. Preliminary studies using proposed model showed that inappropriate selection of occlusion maneuver parameters (e.g. occlusion time, cuff pressure etc.), cause dangerous turbulence of blood flow in the venous section of the vascular tree.

This contribution describes how to model the influence of spherical aberration coefficients on the depth of focus of optical systems. Analytical formulas for the calculation of beam's caustics are presented. The conditions for aberration coefficients are derived for two cases when we require that either the Strehl definition or the gyration radius should be the identical in two symmetrically placed planes with respect to the paraxial image plane. One can calculate the maximum depth of focus and the minimum diameter of the circle of confusion of the optical system corresponding to chosen conditions. This contribution helps to understand how spherical aberration may affect the depth of focus and how to design such an optical system with the required depth of focus. One can perform computer modelling and design of the optical system and its spherical aberration in order to achieve the required depth of focus.

We present a phase-field model for predicting elastic effects on microstructure evolution at the process of laser sintering with powder injection. We derive a system of governing equations describing coupling effects among phase variable, concentration, thermal and elastic displacement fields based on the principle of entropy production positiveness, in which thermal and concentration expansions, mechanical anisotropy effects, transformation dilatation, and strain dependency on phase transformation are considered. The microstructure model is coupled with a macroscopic thermodynamic model. Effects of thermo-capillary and thermo-gravitation convections are included. The possibility to describe the process of structure formation at the phase interface during the melt crystallization is discussed. This model enables prediction and visualization of grain structures during and after the laser sintering process.

The report presents the results of computer simulation of a polarimetric unit of a high spectral resolution spectrograph with fiber optic input for the 6-m telescope of SAO RAS. The module permits evaluating the polarization state of the incoming radiation. The algorithm of calculation of the instrumental polarization introduced by the BTA main mirror and matching optics of polarimetric unit is based on the Mueller matrices method. The ways of evaluation methods of the degree of polarization, azimuth angle and ellipticity of radiation transmitted through the BTA main mirror and matching optics of polarimetric unit are shown. The obtained results of computer simulation, after comparison with practical data and inevitable insignificant refinements can be taken as a basis for creation of an accurate model of the map of polarization errors introduced by the BTA main mirror and its tools.

In this work, we perform the characterization of a conical null-screen corneal topographer. For this, we design a custom null-screens for testing a reference spherical surfaces with a radius of curvature of 7.8 mm. We also test a 1/2-inch (12.7 mm) diameter stainless steel sphere and an aspherical surface with a radius of curvature of 7.77 mm. We designed some different target distributions with the same target size to evaluate the shape of the reference surfaces. The shape of each surface was recovered by fitting the experimental data to a custom shape using the least square methods with an iterative algorithm. The target distributions were modified to improve the accuracy of the measurements. We selected a distribution and evaluate the accuracy of the algorithms to measure spherical surfaces with a radius of curvature from 6 mm to 8.2 mm by simulating the reflected pattern. We also simulate the reflected patter by changing the position of the surface along the optical axis and then we measure the resulting radius of curvature.

Lidar ratio (LR) is an important parameter to invert the lidar equation to subsequently get information from the lidar signals. Therefore, it is the objective of this study to assess the LR values for each day to implement into the inversion method. An algorithm has been generated to estimate the lidar ratios in Penang for the Raymetrics ground-based lidar. Daily average humidity and visibility parameters was obtained and the lidar ratios for each day in year 2014 and year 2015 were assessed. It is found that the LR values in the year 2014 and 2015 generally lie in the range from 55 sr to 85 sr. Maximum LR values in the year 2014 and 2015 is 141 sr and 177 sr respectively. Both years has the same minimum LR value of 46 sr. Extreme values are found in both years during the haze events that occurred in Penang. The LR values estimated are valuable as they represent the atmospheric conditions in Penang and plays an utmost important role in the lidar inversion method.

Traditional methods of measuring out-of-squareness of ultra-precision motion stage have many limitations, especially the errors caused by inaccuracy of standard specimens, such as bare L-square and optical pentaprism. And generally, the accurate of out-of-squareness measurement is lower than the accurate of interior angles of standard specimens. Based on the error separation, this paper presents a novel method of out-of-squareness measurement with a polygon artifact. The angles bounded with the guideways and the edges of polygon artifact are measured, and the out-of-squareness distraction is achieved by the principle that the sum of internal the angles of a convex polygon artifact is (n-2)π. A out-of-squareness metrical experiment is carried out on the profilometer by using an optical square brick with the out-of-squareness of interior angles at about 1140.2 arcsec. The results show that the measurement accuracy of three out-of-squareness of the profilometer is not affected by the internal angles. The measurementwith the method can be applied to measure the machine error more accurate and calibrate the out-of-squareness of machine.

The article is devoted to the optimization of optoelectronic systems of the spatial position of objects. Probabilistic characteristics of the detection of an active structured mark on a random noisy background are investigated.

The developed computer model and the results of the study allow us to estimate the probabilistic characteristics of detection of a complex structured mark on a random gradient background, and estimate the error of spatial coordinates. The results of the study make it possible to improve the accuracy of measuring the coordinates of the object. Based on the research recommendations are given on the choice of parameters of the optimal mark structure for use in opticalelectronic systems for monitoring the spatial position of large-sized structures.

In this article, we investigate the penalized spline (P-spline) approach to restrict flexibility of dielectric function parameterization by B-splines and prevent overfitting of the ellipsometric data. The penalty degree is easily controlled by a certain smoothing parameter. The P-spline approach offers a number of advantages over well-established B-spline parameterization. First of all, it typically uses an equidistant knot arrangement which simplifies the construction of the roughness penalties and makes it computationally efficient. Since P-splines possess the “power of the penalty” property, a selection of the number of knots is no longer crucial, as long as there is a minimum knot number to capture all significant spatial variability of the data curves. We demonstrate the proposed approach by real-data application with ellipsometric spectra from aluminum-coated sample.

3D mathematical model of non-stationary processes of heat and mass transfer was developed for additive manufacturing of materials by direct laser metal deposition. The model takes into account self-consistent dynamics of free surface, temperature fields, and melt flow speeds. Evolution of free surface is modelled using combined Volume of Fluid and Level-Set method. Article presents experimental results of the measurement of temperature distribution in the area of bead formation by direct laser metal deposition, using multi-channel pyrometer, that is based on two-color sensors line. A comparison of experimental data with the results of numerical modeling was carried out. Features of thermal dynamics on the surface of melt pool have been detected, which were caused by thermo-capillary convection.

In this work, a simple method is introduced for estimating the number of the nanoparticles in an active sample based on random laser theory. The sample includes nanoparticles which are distributed randomly. Because of multiple scattering random laser action can occurs when the sample is pumped optically. Here, one-dimensional random laser system is considered and the sample changes are added to the system by changing the number or size of layer. The spectral emission of the sample is calculated by transfer matrix method. The statistical behavior of output emission spectrum is achieved by calculating the averaged spectrum from many random realizations. The results of simulation shows that changes in the number of nanoparticles (or in the averaged size) can be estimated from the statistical random laser output emission and averaged lasing wavelength. This proposed method is fast, non-contact, and needs to a simple setup. Also, it can be used for biological and chemical medium for analysis of different parameters which effect on the spectral random emission.

The goal of the work is modeling and development of nondestructive method for the doped semiconductor layer diagnostics and measurement of the impurity levels depth relatively to the conduction band. To carry out diagnostics for materials with a high linear absorption there is required a method allows to measure material characteristics on the surface layer. To solve this problem was chosen reflected degenerate four-wave mixing technique. Nonlinear response increases dramatically in the case of the resonant excitation of electron-hole transition. Reflected degenerate four-wave mixing has been discovered in the case of one-photon resonant excitation of the excitons (electron – hole) transition for the atomic-like model structure (highly absorbing colloidal solution of CdSe/ZnS quantum dots (QDs)) by powerful beams of mode-locked laser with picosecond pulse duration. Formation of the beams in forward direction can be explained both self-diffraction of the input beams at the induced one-dimensional photonic crystal (induced diffraction grating) and by forward degenerate four-wave mixing. Backward direction beams formation can be explained only by reflected degenerate four-wave mixing.

In this work, a multilayer nanocomposite based fiber optic SPR sensor is considered and especially designed for CO2 gas detection. This proposed fiber sensor consists of fiber core, gold-silver alloy and the absorber layers. The investigation is based on the evaluation of the transmitted-power derived under the transfer matrix method and the multiple-reflection in the sensing area. In terms of sensitivity, the sensor performance is studied theoretically under various conditions related to the metal layer and its gold and silver nanoparticles to form a single alloy film. Effect of additional parameters such as the ratio of the alloy composition and the thickness of the alloy film on the performance of the SPR sensor is studied, as well. Finally, a four-layer structure is introduced to detect carbon dioxide gas. It contains core fiber, gold-silver alloy layer, an absorbent layer of carbon dioxide gas (KOH) and measurement environment. Lower price and size are the main advantages of using such a sensor in compare with commercial (NDIR) gas sensor. Theoretical results show by increasing the metal layer thickness the sensitivity of sensor is increased, and by increasing the ratio of the gold in alloy the sensitivity is decreased.

For many years, computer modeling program used for lecture demonstrations. Most of the existing commercial software, such as Virtual Lab, LightTrans GmbH company are quite expensive and have a surplus capabilities for educational tasks. The complexity of the diffraction demonstrations in the near zone, due to the large amount of calculations required to obtain the two-dimensional distribution of the amplitude and phase. At this day, there are no demonstrations, allowing to show the resulting distribution of amplitude and phase without much time delay. Even when using Fast Fourier Transform (FFT) algorithms diffraction calculation speed in the near zone for the input complex amplitude distributions with size more than 2000 × 2000 pixels is tens of seconds. Our program selects the appropriate propagation operator from a prescribed set of operators including Spectrum of Plane Waves propagation and Rayleigh-Sommerfeld propagation (using convolution). After implementation, we make a comparison between the calculation time for the near field diffraction: calculations made on GPU and CPU, showing that using GPU for calculations diffraction pattern in near zone does increase the overall speed of algorithm for an image of size 2048×2048 sampling points and more. The modules are implemented as separate dynamic-link libraries and can be used for lecture demonstrations, workshops, selfstudy and students in solving various problems such as the phase retrieval task.

Interpolation and approximation methods for freeform surface synthesis are analyzed using the developed software tool. Special computer tool is developed and results of freeform surface modeling with piecewise linear interpolation, piecewise quadratic interpolation, cubic spline interpolation, Lagrange polynomial interpolation are considered. The most accurate interpolation method is recommended. Surface profiles are approximated with the square least method. The freeform systems are generated in optical design software.

The objective of this study is to propose and introduce nonlinear modal propagation analysis (NMPA) method being a viable way to study the application of graphene based multimode interference (MMI) coupler as an optical refractive index sensor. The purpose of using graphene in this study is because of its high optical nonlinearity as well as having a small bandgap due to its thin layer. The graphene based sensor can be tuned for highest sensitivity in wavelength and refractive index to detect the clad material. Graphene will act as the core of the sensor which will be placed on top of the sample. The clad refractive index value can be obtained by observing and analyzing the change in the output facet intensity of the sensor. The result also shows that the sensor has high sensitivity due to the usage of graphene and nonlinear region.

Bessel beam has the advantages of reducing scattering artefacts and increasing the quality of the image and penetration. This paper proposed to generate a guide star by Bessel beam with vortex phase, and to use the beacon with special spot structure to measure the atmosphere turbulence aberrations. With the matching algorithm of measured characteristic spot in each subaperture, the detection accuracy of Hartmann wavefront sensor can be improved. Based on wave optics theory, the modeling of Bessel beam guide star and wavefront sensing system was built. The laser guide star beacon generated by Bessel beam with vortex phase and beacon echo wave measured by Hartmann sensor were both simulated. Compared with the results measured by echo wave from Gauss beam generated guide star beacon, this novel method can reduce the error of wavefront detection and increase the detection accuracy of Hartmann sensor.

Full-aperture noninterferometric phase retrieval system, namely one single shot, can overcome the impact of low Signal-to-Noise ratio in the condition of weak illumination by extended beacon. Contributing to its robustness and practicability, the technology has been widely applied in industrial inspections. However, the technology is limited by the operational speed and the accuracy of the phase retrieval algorithm in most situations. Based on phase space optics, an analytical relationship can be set up between the phase of the quasi-coherent light field from the extended beacon of small field of view and 3 adjacent intensity distributions, which may be resolved fast. That is, the unknown phase is equal to the convolution of the partial differential of the difference value of the three intensities with respect to the rotation angle of the phase space and the sign function. This paper introduces a design and realization which accomplishes this goal using a specially designed chromatic aberration lens and a 3CCD camera. By this way, three high resolution images of the beacon can be captured within a single shot. The numerical simulation results show that the method can accurately recover aberrations of more than 10 orders.

We extend the principles of the null-screen method for testing fast aspheric surfaces with polynomial expansion. We present the formulae to design the null-screen in such a way that the image on the CCD is a perfect array circular points; the departures of the surface from a perfect shape are observed as deformations of the array in the image. For the testing of fast aspherics with polynomial expansion, we propose some geometrical configurations. In addition, we perform an analysis of the deformations of the image of the null-screen reflected by the testing surface due to the slop defects of the surface. Experimental results for the testing fast aspherics are shown. The main advantages and the limitations of the method will be discussed.

We present the numerical simulation of a ray selector with a uniform distribution. This selector shall be used in a deflectometry arrangement and the detection plane of spots necessary in the deflectometry shall be placed at an arbitrary distance from the lens under test. To perform this task, the vector form of the exact ray tracing is used through a lens and from these positions determine the shape of the convex surface of the lens. This program is flexible and can be used on other types of optical surfaces, and different ray distribution, including null distribution. The first preliminary results are shown below.