This PDF file contains the front matter associated with SPIE Proceedings Volume 11057 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

This Conference Presentation, “Numerical optimization of resonant photonic devices,” was recorded at SPIE Optical Metrology 2019, held in Munich, Germany.

The production of modern semiconductor devices is based on photolithography, a process through which a pattern engraved on a mask is projected on a silicon wafer coated with a photosensitive material. In the past few decades, continuous technological progress in this field allowed the industry to follow Moore’s law by reducing the size of the printed features. This was achieved by progressively increasing the numerical aperture of the projection system and reducing the wavelength. The latest lithography platforms for semiconductor manufacturing employ Extreme Ultra Violet (EUV) light at a wavelength of 13.5 nm. The metrology for the optics and the components of such platforms is not fully mature yet. Specifically, the inspection of the EUV photomask is still an open issue as no commercial solutions are currently available. Here we describe a lensless approach to this problem, based on coherent diffraction imaging at EUV that overcomes the main technological issues linked to the conventional mask inspection approach.

This Conference Presentation, “Metrology for and with nanooptics,” was recorded at SPIE Optical Metrology 2019, held in Munich, Germany.

We simulate the interference patterns of solar systems, incorporating an Estrella and two Tierras, as detected by a rotational shearing interferometer, to compare with laboratory setup. Three rays are propagated to represent each wavefront in the interferometer, using the exact ray tracing technique. Then, the phase, with which light beams are incident into the detection plane is used to calculate the orientation of the incident wavefront. Finally, all the incident wavefronts are summed together to obtain the resulting interference pattern.

A method based on the fractional Fourier ridges for accurate phase demodulation of a single interferogram with quadratic phase is presented. The interferograms being analyzed may contain circular, elliptic or astigmatic fringes. In signal processing field, such interferograms can be called 2-D chirp-type signals. Since the fractional Fourier transform (FRFT) of a chirp signal is a function under the matched angle that is determined by chirp rates of the signal, so the method can be used to match the multiple chirp rates in chirp-type signals with multiple chirp components. In this work, the FRFT of all row (column) signals are firstly calculated, and the ridge of the FRFT amplitude of each row (column) signal in FRFT domain is recorded. Repeat the above process for each angle of a searching range. Then a ridge tracking approach is employed to determine the matched angle, which can be used to calculate the coefficient of the square term of row (column) coordinates. Moreover, under the matched angle, the ridge of the FRFT amplitude of each row (column) signal all lie on a straight line. The slope and constant term of the line can be used to calculate the coefficient of the linear term of row (column) coordinates and the coefficient of cross term, respectively. The same procedures are implemented to all column (row) signals to determine the coefficients of the square and liner term of column (row) coordinates. According to the obtained coefficients, the phase of the fringe pattern can be constructed without phase unwrapping operation. Furthermore, the present procedure is also capable of analysis of interferograms with or without circularly symmetry fringe distribution instead of using complex and time consuming algorithms for recovering phase from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.

The precision of Frequency-scanning interferometer(FSI) for absolute distance measurement depends much on the tunability of its laser source. However, an external cavity laser diode (ECLD) exhibits nonlinearity during optical frequency sweep due to hysteresis inherent to the piezoelectric ceramic transducer (PZT) actuator in the ECDL. As a result, the interference signal become nonstationary, and then extracting the phase of the nonstationary interference signal may cause errors. To address this problem, we propose a new method based on the Prandtl–Ishlinskii (PI) model for suppressing nonlinearity of optical frequency sweeping. For the proposed FSI, the output transmission signal of a Fabry–Perot (F-P) cavity is used to obtain the optical frequency curve of the ECLD. By using the input voltage of the linear driving signal and the optical frequency of the ECLD as input and output of the model respectively, the hysteresis model can be built based on PI modelling method. Hence, the inverse of the rate-independent PI model is employed as a feedforward controller to compensate the nonlinearity of the optical frequency sweeping. In our case, instead of driving the ECLD with a linear signal, we implement a corrected nonlinear driving signal of the PZT to suppress the nonlinearity of the sweeping frequency. Experimental results demonstrate the effectiveness of our proposed method. Compared with an external witness He–Ne incremental interferometer, the proposed method greatly improves the performance of the FSI for absolute distance measurement.

The subaperture stitching technique requires the registration of freeform subapertures into global coordinate frame before stitching in order to compute entire freeform wavefront. A scanning Shack-Hartman Sensor (SHS) utilizes translation stages to scan the freeform surface in XY plane and measure the slope data of various subapertures. The measured slope data is then integrated using weighted cubic spline (WCSLI) based integration method to compute the phase data. The positioning error during scanning causes misalignments between the measured subapertures and their nominal values. The least square based subaperture stitching methods are not capable to minimize lateral misalignment errors of freeform subapertures and therefore degrade the performance of subaperture stitching process. In this work, we have utilized fiducial added planes for correction of angular and rotation misalignments of an extended cubic phase plate. An intrinsic surface feature (ISF) based registration method is used for lateral misalignment corrections. Gaussian curvature is used as an intrinsic pattern which can be defined as one of the fundamental second order geometric properties of a surface. Any shift in the peaks of the Gaussian curvature of reference and measured subaperture corresponds to lateral misalignments in X and Y directions and need to be minimized before registration of subaperture into global frame of reference. After precise registrations, all the subapertures are stitched with consistent overlapping area by using least square fitting method. A numerical validation of the proposed scheme is carried out which demonstrates the effectiveness of the proposed method to improve the subaperture stitching accuracy.

Collinear photothermal deflection spectroscopy (PDS) is a widely used method for the spatially resolved determination of the optical attenuation coefficient. In this work we rigorously model the signal contributions in PDS on semiconductors below the band gap energy. The dependencies of the PDS signal on selected experimental parameters (pump beam intensity, crossing angle, chopper frequency and distance from the pump beam focus) are computed and compared with previous calculation results that are based on simplified assumptions. We find that for high pump beam intensities and sample materials with high two photon absorption coefficients beside the mirage effect nonlinear absorption mechanisms have a strong impact on the signal. Furthermore, we show that angular deflection effects can significantly enhance the PDS signal. For example, the conical refractive index field due to the pump beam divergence leads to an angular deflection at readout points outside the pump beam focus. Considering these additional signal contributions is crucial to determine proper absorption properties.

Metasurfaces have revolutionized the definition of compact optics. Using subwavelength periodic structures of nanostructured dielectrics, the refractive index and absorption properties of metasurfaces – which are 2D metamaterials – can manipulate light to a degree not possible with conventional bulk glasses and crystals. The phase, polarization, spin (for circularly polarized light), amplitude and wavelength of light can all be manipulated and crafted to user-specified values to mimic the action of a lens, which we refer to as a metalens (ML). MLs have four major advantages over traditional refractive lenses – superior resolution, lighter weight, miniaturization and cost. Many metasurfaces with useful functionalities have been proposed in recent years, yet although novel in their approach have few real-world applications. One such market is the use within infrared laser systems, such as laser designators. In this work, we demonstrate metasurface lenses working at a wavelength of λ = 1064 nm, with aperture d = 1 mm and four different Fnumbers (focal length f = 0.5, 1, 2 and 5 mm). The lenses are composed of 700nm high a-Si pillars – ranging from 70- 360 nm diameter – which are fabricated using electron beam lithography (EBL) and reactive ion etching processes, on top of a fused silica substrate. Such lenses are shown to have diffraction-limited performance, with focal spot-size agreeing with theoretical values of λ‧f/d. Furthermore, we have designed large area lenses with aperture d = 10 mm, where the number of pillars per lens exceeds 550 million. By using an efficient Python script, we are able to produce these 100 mm² samples with just 14 hours of EBL writing time.

Optical microscopy is widely used for the characterization of micro- and nanostructures in the field of unidirectional and bidirectional dimensional metrology. Despite the general high recognition in the metrological community, the inherent difficulties which are bound to optical bidirectional measurements using commercial vision-based metrology tools are not sufficiently investigated, yet, and require additional insight, which we intend to provide here. We demonstrate the need for sophisticated analysis methods to find a threshold value which locates the correct physical edge position within the microscopical image. The common assumption for the threshold to be at 50% of the intensity level of the edge signal is in essentially any imaging configuration wrong and leads to large systematic measurements errors. For example, the correct threshold values for transmission light microscopy using high NA objectives on chrome on quartz photomasks, are within 15% and 35% of the intensity level in the simulated images. For other measurement configurations the threshold variation can be even much larger. Since the correct threshold values depend on the illumination and imaging parameters of the imaging system as well as on the geometrical and optical parameters of the measurement object, we showcase a selection of them and their respective influence on the determination of the threshold values. Rigorous simulations are the key feature for this analysis since they require all the relevant parameters to be included in the simulation of a microscopical image which enables the correct threshold determination and to extract the correct bidirectional quantities out of the optical images.

The challenging environment of in situ micro-geometry measurements in fluids (e.g. for laser- or electrochemical machining), such as refractive index fluctuations, small dimensions and high surface gradients, hinder many conventional measurement techniques. Confocal microscopy remains most suitable with uncertainties < 1μm, but complex micro-geometries with edge slopes > 75° often produce unwanted artifacts. To prevent the formation of artifacts, the isotropically emitting fluorescence light of a fluid layer covering the specimen is measured instead. The geometry reconstruction for in situ-relevant fluid depths >100 μm is not trivial and requires a signal model that includes the contributions of light absorption and the confocal volume shape. For model validation, the surface position of a reference step-object (nominal height: 250 μm), submerged in a fluid layer > 1 mm, is determined using a fluorescence signal model that is fitted to the measured data. First experiments yield a step height uncertainty of 8.8 μm, about one order of magnitude above the requirement. In order to identify optimization potential, the minimum achievable measurement uncertainty is estimated for both a signal with experiment-equivalent variance and a shot noise limited signal. The estimated uncertainties are 3.8 μm and 0.1 μm, respectively, and decrease with lower fluorophore concentration and fluid thickness. The differing experimental and estimated uncertainties result from model simplifications such as the missing contribution of reflected light at the specimen surface where the current model assumes that the confocal volume is cut off. Expanding the model promises to reduce the measurement uncertainty and to converge estimation and experiment, enabling geometry measurements of complex micro-geometries with different surface reflectivities under challenging in situ conditions in fluids.

In principal, optical measurement methods suffer from physical limits related to finite wavelengths and diffraction. In laser focus scanning, vertical resolutions below 1 nm can be achieved while the lateral accuracy is more or less restricted by the diameter of the focused laser beam, i.e. values of half the wavelength can be reached in the best case. We present a model based approach having the potential to show a way out of this limitation. It is based on the rigorous modeling of the complete measurement device including sophisticated ray tracing in combination with Maxwell based modeling of the sample diffraction and scattering providing a simulated signal for an assumed sample profile. Furthermore, the sample profile is parametrized on the basis of a priori information. The simulated signal is then iteratively compared with the measured signal while updating the floating parameters of the model in order to improve the match between the two signals. Eventually, the improved sample profile obtained in this way is considered to represent the real sample profile as soon as a certain goodness of fit is achieved. On the other hand, the profile model has to be changed in case there is no satisfying fit. In this way, the lateral accuracy can be increased considerably. Edge detection errors below a few tens nanometer or even below 10 nm become possible while measuring with visible light. This is demonstrated by first comparisons of modeled and measured signals and validation by alternative metrology techniques.

The topography fidelity TF_i indicates the accuracy of the estimation of the real surface, describes the instrument influenced deviation of a measured topography image and depends on the interaction of the surface topography with the instrument. To understand and investigate the topography fidelity of optical surface measurement instruments, and interference microscopes in particular, an analytical model based on the fraction of the total illumination criteria and a numerical model based on Richards-Wolf theory are used to characterize the topography fidelity of 3D optical microscopy. As reference artefacts step-like micro-structures with varying spatial frequency and therefore different aspect ratios are numerically investigated with the aforementioned models. To testify the feasibility of the numerical analysis, a commercial white light interference microscope has been employed to measure these reference artefacts. The relationship between the measured heights and the spatial frequency of the samples under investigation are detailed in this paper. The aspect ratio influences on measurement results predicted by the simulation models and the agreements with the experimental results are investigated and reported in detail.

Reflectorless electro-optical distance measurement (RL-EDM) relies on measuring the round-trip time of optical signals transmitted from the instrument and reflected by natural surfaces. It is the backbone of laser scanning technology, which allows easily digitizing the environment and obtaining 3d models that represent the geometry of the scanned objects. However, the measured distances do not refer to single, well-defined target points at the object surface but rather correspond to a weighted average of effective distances within the respective footprint of the laser beam. This increases the uncertainty of the measurements and may cause systematic deviations significantly exceeding the mm-or sub-mm level precision that would otherwise be attainable with EDM technology. In this paper we introduce a numerical simulation of the measurement process for phase-based RL-EDM with I/Q-demodulation assuming a Gaussian beam profile. The beam is discretized into a fixed number of rays for each of which the corresponding phase delay and attenuation are calculated. The I- and Q-components are obtained by integration over the footprint taking the beam profile into account. By deflection of the beam into incrementally changed spatial directions we extend the simulation to one of the 3d scanning process. The scanned surfaces are represented by triangular irregular meshes (TINs) with high spatial resolution. Each triangle is associated with a reflectivity, as a starting point for the modelling of surface properties. The simulation takes the interplay between the energy distribution within the laser footprint, the surface geometry and the surface reflectivity into account. Herein, we use the simulation framework to study the effects of the angle of incidence, of surface curvature and of mixed pixels in absence of measurement noise. The results indicate that the angle of incidence at a planar surface and the surface curvature within the footprint are on the order of 0.1 mm or less for small footprint and angles of incidence below about 60 deg. If the footprint and the angle of incidence are very large the biases may reach mm-level, however even then the impact of measurement noise and surface roughness will typically exceed these biases, such that they are negligible. On the other hand we show using simulations and real scans of a cylinder in front of a planar background, that the impact of mixed pixels or beams only partially hitting an object may introduce large biases and is practically relevant.

In this work we report the design of a null-screen for corneal topography. Here we assume that the corneal surface is an ellipsoid with a diameter of 12 mm and a radius of curvature of 7.8 mm. To avoid difficulties in the alignment of the test system due to the face contour (eyebrows, nose, or eyelids), we designed a compact conical null-screen with spots drawn in such a way that its image, which is formed by reflection on the test surface, it becomes an exact semi-radial array of circular spots if the surface is perfect. To validate our proposal, we perform topography measurements of a reference surface and some human corneas using a probabilistic algorithm. The results obtained with our algorithm were consistent and we can recover the shape of the surface with accuracy.

Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse problem. To comply with the upcoming need for improved accuracy and precision and thus for the reduction of uncertainties, typically computationally expansive forward models have been used. In this paper we use Bayesian inversion to estimate parameters from scatterometry measurements of a silicon line grating and determine the associated uncertainties. Since the direct application of Bayesian inference using MarkovChain Monte Carlo methods to physics-based partial differential equation (PDE) model is not feasible due to high computational costs, we use an approximation of the PDE forward model based on a polynomial chaos expansion. The expansion provides not only a surrogate for the PDE forward model, but also Sobol indices for a global sensitivity analysis. Finally, we compare our results for the global sensitivity analysis with the uncertainties of estimated parameters.

The successful combination of electromagnetic scattering simulations and optical measurements allows for the quantification of deep-subwavelength features, including thicknesses via ellipsometry and parameterized geometries via scatterometry. Although feature size reduction has slowed in recent years, nanoelectronics still yields ever-smaller structures, thus optical measurement capabilities are ever-challenged. The critical problem is that the optical properties of materials often become thickness dependent at sub-5 nm, greatly complicating accurate fitting. These optical properties can be characterized empirically using ellipsometry and used with other prior information to reduce uncertainties via hybrid metrology, but atomistic modeling offers a unique perspective on the macroscopic optical response from features with dimensions only a few atoms in width. To illustrate the potential of such modeling, we have performed a series of density-functional theory (DFT) calculations for an ultrathin film, Si with hydrogen-terminated Si(111) surfaces. Kohn-Sham wavefunctions determined in DFT are instrumental in solving for the dielectric tensor of these configurations, as the in-plane and out-of-plane components can differ greatly with respect to incident wavelength and Si thickness. Techniques for DFT and dielectric tensor determination are reviewed, highlighting both their limitations and potential for improving optics-based metrology. The thickness- and wavelength-dependence of the resulting tensor components are parameterized using Tauc-Lorentz and Lorentz oscillators. Using an illustration from goniometric reflectometry, the quantitative effects upon dimensional metrology of employing the full thickness-dependent dielectric tensor are compared against simpler approximations of these optical properties. Reductions in parametric uncertainty in the thickness and optical constants are evaluated with a prior knowledge of the ultrathin film’s thickness with uncertainties.

For the reliable fabrication of the current and next generation of nanostructures it is essential to be able to determine their material composition and dimensional parameters. Using the grazing incidence X-ray fluoresence technique, which is taking advantage of the X-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to the structural and elemental composition. This is demonstrated using lamellar gratings made of Si₃N₄. Rigorous field simulations obtained from a Maxwell solver based on the finite element method allow to determine the spatial distribution of elemental species and the geometrical shape with sub-nm resolution. The increasing complexity of nanostructures and demanded sensitivity for small changes quickly turn the curse of dimensionality for numerical simulation into a problem which can no longer be solved rationally even with massive parallelisation. New optimization schemes, e.g. machine learning, are required to satisfy the metrological requirements. We present reconstruction results obtained with a Bayesian optimization approach to reduce the computational effort.

In several different research disciplines, modelling and simulating light propagation through volume scattering materials is a key necessity. Simulating diffusing and fluorescent materials in solid-state lighting and the interactions between intense light and skin tissue in biomedicine are just some examples of the widespread need for accurate volume scattering models. Although modelling volume scattering materials is important for several research fields, there is still no widespread reporting of model properties or of accurate and robust tools to estimate them, especially for lighting research. Most often, researchers estimate the scattering model properties, i.e. the absorption and scattering coefficients and the anisotropy factor, using Mie solutions. These are generally based on rough estimates of the scattering particle’s properties and assume that the particle is perfectly spherical or cylindrical. This approach is not well suited for the myriad of volume scattering materials available for illumination research. Our work uses the intensity-based inverse adding-doubling (i-IAD) method to estimate the volume scattering model properties of samples. In this work, we investigate the feasibility of this method in an experimental scenario by studying samples made with two different scattering particles embedded in a transparent polymer with different scattering particle concentrations and sample geometries. The light scattered by the samples is measured and their volume scattering properties estimated with i-IAD. We show the accuracy and robustness of i-IAD by extrapolating the scattering parameters obtained for low concentration samples to higher concentrations and comparing simulations with experiments for these higher concentrations. Furthermore, measurements of samples that contain both types of scattering particles were also accurately simulated using the model parameters estimated from low concentration samples. This work demonstrates that the intensity-based inverse adding-doubling method provides accurate estimates for the volume scattering model parameters and that they can be generalized for different concentrations, geometries and scattering particle mixtures.

Optical scatterometry is one of the most important techniques for measuring the critical dimension (CD) and overlay of nanostructures in current semiconductor manufacturing due to its inherent noncontact, nondestructive, time-effective, and relatively inexpensive merits over other metrology techniques, such as scanning electron microscopy (SEM) and atomic force microscopy. Along with the advantages of optical scatterometry, there are some challenges or limitations to this technique with the ever-decreasing dimensions of advanced technology nodes (22 nm and beyond) [1], such as the parameter correlation issue. In addition, optical scatterometry is mostly suitable for measuring repetitive dense structures while infeasible for the measurement of isolated or the general non-periodic structures. To address the challenges or limitations in conventional optical scatterometry, we have developed a novel instrument called the tomographic Mueller-matrix scatterometer (TMS) [2], which is a combination of a dual rotating-compensator Mueller matrix ellipsometer (MME) [3] and a reflection microscope. In this talk, I will present the development of TMS as well as its application for nanostructure metrology. As shown in Fig. 1, the position of the focal point of the light beam on the back focal plane (BFP) of a high-numerical-aperture objective lens OL can be changed by rotating the flat mirror FM, which further leads to the change of illumination direction on the sample. An epi-illumination setup is designed to collect the scattered-field distribution associated with each illumination direction by imaging the BFP of the OL. Thanks to the dual rotating-compensator configuration, a 4-by-4 Mueller matrix associated with each point on the BFP of the OL can be obtained. Since the 16 elements of a Mueller matrix contain all polarization information that one can extract from a linear polarization scattering process, the full polarization properties of the scattered field are thus achieved. Details about the principle as well as the calibration of the TMS can be found in Ref. [4, 5] and are omitted here for the sake of brevity. As a demonstration of the potential of the develop instrument, the TMS was employed for the measurement of a Si grating and a photoresist (PR) grating. For the Si grating, its geometrical profile is characterized by top CD x1, grating height x2, and sidewall angle x3. For the PR grating, its geometrical profile is characterized by top CD x1, grating height x2, sidewall angle x3, and top corner rounding x4. The period of the Si grating is 800 nm, and the nominal dimensions of other structural parameters are x1 = 350 nm, x2 = 470 nm, and x3 = 88 degree, respectively. The period of the photoresist grating is 412 nm, and the nominal dimensions of other structural parameters are x1 = 200 nm, x2 = 311 nm, and x3 = 90 degree, respectively. Figure 2 presents the fitting result of the measured and calculated best-fit Mueller matrices of the Si and PR gratings at different measurement configurations. Good agreement can be observed from this figure for both the two grating samples. References [1] N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, Nat. Electron. 1, 532-547 (2018). [2] Y. Tan, C. Chen, X. Chen, W. Du, H. Gu, and S. Liu, Rev. Sci. Instrum. 89, 073702 (2018). [3] C. Chen, X. Chen, Y. Shi, H. Gu, H. Jiang, and S. Liu, Appl. Sci. 8, 2583 (2018). [4] S. Liu, X. Chen, and C. Zhang, Thin Solid Films 584, 176-185 (2015). [5] C. Chen, X. Chen, H. Gu, H. Jiang, C. Zhang, and S. Liu, Meas. Sci. Technol. 30, 025201 (2019). (See attached documents for the cited figures).

This paper describes an instrument and method for high-resolution characterization of lens components and assemblies for DUV retardance performance at various stages of manufacture. The instrument is a bespoke rotating analyzer Stokes polarimeter designed for DUV wavelengths (e.g. 193 nm, 213 nm, 266 nm, etc.). Using a laser source, the polarimeter delivers a small diameter beam with a characterized polarization state to the optical lens element or objective assembly at the “as-used” design angles of incidence (AOI) to characterize the retardance through the lens or objective at an arbitrary location. The polarization characteristics are usually described by the retardance at specific locations on a component or sub-assembly that can be used to characterize components during development and manufacturing or optimize performance of an assembly.

We have recently developed a high-numerical-aperture (high-NA) Mueller-matrix ellipsometer (MME). By adopting a high-NA objective lens, the scattered light can be collected and the image with high lateral resolution is acquired to obtain the spatially resolved Mueller matrix of the sample. In this manuscript, we propose a model of the image formation of the high-NA MME based on the rigorous coupled-wave analysis (RCWA) and vector diffraction theory. The proposed imaging formation model consists of four parts: scattering on the sample, collecting by the optical system, propagating in the optical system, and imaging on the image plane. Each part can be modeled and calculated separately. Utilizing the proposed model, we have performed a numerical simulation for two types of gratings. The results reveal the potential of the proposed model in predicting the measured Mueller matrix and analyzing the sensitivity of the high-NA MME to different nanostructures.

Accurate metrology of nanostructures gains more and more importance and for efficiency reasons optical methods play a significant role here. Unfortunately, conventional optical microscopy is subject to the well-known resolution limit. The necessity to resolve objects smaller than this limit led to the development of superresolution methods which however are barely used in metrology for practical reasons. Non-imaging indirect optical methods like scatterometry and ellipsometry however are not limited by diffraction and are able to determine the critical dimensions of nanostructures. We investigate the application of different approaches for specifically manipulated near-fields in Mueller matrix ellipsometry to achieve an enhanced sensitivity for polarization based sub-wavelength topological information. To this end, we present first numerical simulations of these approaches. To examine the relationship between structural properties and Mueller matrix elements we designed individual structures based on geometrical shapes of varying parameters as well as small arrays. They are realized by lithography as holes in PMMA resist. First, we characterize SEM images of the structures to validate the fabrication process. Numerical simulations of the Mueller matrices of the structures by finite element method are discussed. Results indicate that conventional Mueller matrix ellipsometry alone is unsuitable but the extension to imaging Mueller matrix microscopy is promising for the characterization of sub-wavelength features.

Spectroscopic ellipsometry is a versatile tool to measure dimensional or optical parameters of surface layers or surface structures. The determination of these parameters requires to solve an inverse problem. This is achieved by a fitting procedure, where a merit function is optimized. This merit function compares simulated with measured polarization quantities for each measurement configuration, i. e. for each wavelength and angle of incidence. For the simulation of unstructured samples Fresnel-equations can be used, while for structured surfaces the Maxwells equations must be solved using so-called Maxwell-solvers. For depolarizing samples Mueller ellipsometry must be used, because only the Mueller-stokes formalism is capable to describe depolarization. However, in common approaches to evaluate Mueller matrix measurements depolarization is treated in a nonoptimal way, which leads to inadequate measurement uncertainty estimations and in the worst case may lead to systematic measurement errors. Especially for surfaces with strong depolarization such as rough or textured surfaces this is a problem. To treat these issues, we developed an improved analysis method to attain reliable sample parameters and reliable and mathematically well-founded uncertainty estimations from Mueller ellipsometry measurements. While deterministic non-depolarising samples can be fully described within the well-known Jones formalism and can be simulated by Fresnel- or Maxwell-solvers, a complete simulation of depolarizing samples would require very high computational expenses which are too elaborate or even impossible in practice. Thus the question arises, how to treat depolarization in the optimization process. Commonly used merit functions treat it as a residual error, which is minimized and accept the fit solution with the smallest overall depolarization as the best approximation. However, depolarization is a sample property, which must not be minimized. Therefore, instead we use the depolarization to derive a weight-factor for each residual contribution to the merit-function. We will present the underlying mathematics. The evolved theory is applicated on measurement data obtained with a Sentech SE 850 system. The Mueller-matrices for each measurement configuration are computed from an overdetermined system of raw data achieved with analyzer-scans at discrete polarizer-steps (step-scan-mode). Thus the raw measurement data can additionally be exploited to get statistical information to the measured Mueller matrices and included in the merit function. Embedded into a Bayesian approach the best-fit values and their uncertainties are determined from the posterior distribution in a much more realistic and reliable way. Applied on both virtual and real measurement data, we demonstrate the advantages of this new method and compare the results with different standard analysis methods.

Channeled spectropolarimeter (CSP) measures the spectrally resolved Stokes vector of light from only one single spectral acquisition, which makes it possible to accurately measure dynamic events. The accurate reconstruction of Stokes vector plays a key role in this snapshot technique shifting the main burden of measurement to computational work. The state-ofthe-art algorithm runs the Fourier transform of the channeled spectrum or linear operator model of the system and its pseudo-inverse to reconstruct Stokes vector. However, they may suffer from the lack of signal-to-noise ratio (SNR) then reduce the accuracy of reconstruction. To accurately reconstruct Stokes vector from noise-contaminated data, we propose an effective method called fast compressed channeled spectropolarimeter (FCCSP). In our FCCSP method, the spectrum from spectrometer is seen as the compressive representation of Stokes vector, thus the FCCSP algorithm is to solve an underdetermined problem, where we reconstruct the 4N×1 Stokes vector from only N×1 spectral data acquisition points. Simulation results show that our FCCSP method is more accurate to reconstruct Stokes vector changing gradually with wavelength from noise-contaminated spectrum than Fourier and linear operator methods. Besides, it is faster and more memory and computation-friendly than other compressed CSP method.

The evaluation of inertial sensor’s frequency response is a crucial step during the development of such sensors (gyroscope, accelerometer…) or of embedding systems. An accurate measurement of the sensor’s gain and phase requires a test equipment, usually a motion simulator, able to create accurately controlled motions over a wide frequency band, with minimum amplitude and phase uncertainty. State-of-the-art motion simulators use permanent magnet synchronous motors as actuators and optical encoders as angular position sensor. They also include a servo-loop whose bandwidth is necessarily limited either for theoretical reasons, like the Bode Integral Theorem, or for physical ones, such as the inevitable time-lags occurring in the loop, or even mechanical resonances. Nevertheless, the appropriate bandwidth is required to allow for an accurate inertial sensor characterization. A well-known way of coping with the intrinsic limitations of the feedback control structure in a servo-drive consists in introducing a specific filter (called feedforward) between the motion trajectory generator and the feedback loop, to provide an anticipation independently of the feedback structure. This compensation requires a good modelling of the controlled system transfer function but is never perfect. Moreover, in a motion simulator, the tested inertial equipment is subject to change, and a unique feedforward filter cannot provide an accurate enough compensation. Thus, iXblue has introduced an adaptive feedforward structure in the controllers of their motion simulators, leading to a more accurate tracking of sine commands, beyond the initial closed-loop bandwidth. The benefits of this control structure are quite significant: the sine tracking is very accurate, having very little amplitude attenuation and phase lag.

Interferometer-based optical setups play an important role in modern optical metrology for different applications. Such setups often consist of multi-disciplinary components. This reveals new ways of improving the performance or enriching the functionality of the system, while at the same time leading to complexities and difficulties in system modeling and analysis. To overcome this, we present a physical-optics-based simulation approach. It is founded on a fully electromagnetic representation of light, and therefore includes the coherence and polarization effects which are of growing interest for modern interferometers. As examples, several typical optical interferometer setups are built up and analyzed. With the physical-optics modeling technique, we demonstrate and understand the functionalities of such setups, so as to help in the design of advanced optical interferometers.

Phase diversity is a powerful methodology technique for measuring the wavefront aberrations of optical systems and surfaces by solving an unconstrained optimization problem from multiple images whose pupil phases differ from one another by a known amount. However, it often fails for large wavefront aberrations. A modified phase diversity technique to improve the sensing dynamic range was proposed. We conducted computer simulations of the reconstruction of large aberrations of an optical system with the proposed phase diversity method. We fitted the wavefront to Zernike polynomials to reduce the number of variables. The limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used for optimizing process. The study shows that the method can extend the dynamic range from about 2λ to about 11λ and the paper gives practical guidelines for the application of phase diversity methods to characterize large wavefront aberrations.

Newton’s rings are the fringe patterns of quadratic phase, the curvature radius of optical components can be obtained from the coefficients of quadratic phase. Usually, the coordinate transformation method has been used to the curvature radius, however, the first step of the algorithm is to find the center of the circular fringes. In recent years, deep learning, especially the deep convolutional neural networks (CNNs), has achieved remarkable successes in object detection task. In this work, an new approach based on the Faster region-based convolutional neural network (Faster R-CNN) is proposed to estimate the rings’ center. Once the rings’ center has been detected, the squared distance from each pixel to the rings’ center is calculated, the two-dimensional pattern is transformed into a one-dimensional signal by coordinate transformation, fast Fourier transform of the spectrum reveals the periodicity of the one-dimensional fringe profile, thus enabling the calculation of the unknown surface curvature radius. The effectiveness of this method is demonstrated by the simulation and actual images.

Sets of chromatic and neutral ceramic tiles are widely used as measurement standards for reflectance factors in color applications. The usual instrument for color measurements is a spectrophotometer that measures the tiles using either a 0:45 or 45:0 illumination and viewing geometry, or with an integrating sphere in order to measure the reflectance factor in either specular excluded or specular included conditions. Having the corresponding measurements of the tile set from a calibrated instrument, systematic errors in the instrument under study can be diagnosed and corrected using a model of the errors and fitting it to the difference in measurements. One such is the Berns-Petersen model, which models photometric scale errors as well as wavelength registration and bandwidth errors using the spectra and its derivatives from the studied instrument. This allows for a simple multilinear regression to be used for recovering the model coefficients either collectively or separately for each wavelength band. In this study we examine the potential of a ceramic tile set for transferring the calibration from a calibrated spectrophotometer to a hyperspectral imager using the Berns-Petersen model. In particular we compare different approaches that are needed for matching the measurements from the two instruments with respect to the differences in the spectral and spatial resolution that need to be considered for the application of the regression procedure to be possible. We also compare the effectiveness of the procedure when using single model parameters for the whole imaging sensor to that obtained by doing the procedure separately for different spatial regions of the imager. The accuracy of the imager before and after the procedure is evaluated both in absolute radiometric terms as well as colorimetric quantities. We also examine the effect of using different subsets of the available full set of ceramic tiles for the resulting model fit.

In the field of earth-observation, on-board calibration is often necessary to guarantee the radiometric accuracy of space instruments. A typical method is to use large diffusers in front of the instrument, illuminated with a reference source like the sun [1]. Hence, it is necessary to characterize the scattering properties of the diffuser with excellent accuracy. Given the large size and weight of the diffusers to characterize, CSL have developed a bench which uses a robot arm to manipulate the sample. For the most stringent applications, the typical accuracy of robotic arms is not good enough to measure the BSDF with a satisfactory accuracy. A method have been developed which uses laser tracker measurements of the sample during a calibration phase and compensate for the robot errors. This paper describes the principle of the method and the results obtained. We also present the model of how the orientation error of the sample affects the BSDF relative error.

Cameras are common imaging elements in optical measurement systems. A different approach to imaging utilizes only a single pixel sensor and is nevertheless capable of producing two-dimensional images: In computational ghost imaging (CGI) a projector illuminates the object with a known set of patterns and a single photodiode records the resulting radiation powers. These are passed on to a reconstruction algorithm. Such setups can be advantageous where classical camera systems might fail or be too expensive, but cannot currently compete with them in high speed imaging applications. Although the idea is not new, it represents a very different and rarely used paradigm compared to conventional approaches to two- and three-dimensional imaging. Three-dimensional reconstruction through CGI can be achieved through well-known techniques such as photogrammetric stereo reconstruction. Theoretical work has shown that for an actual setup having a single projector and two photodiodes arranged in a parallax is not sufficient. Instead, two projectors and a single photodiode in combination with a computer are necessary for the production of two images suitable for stereo reconstruction. Two characteristics of a CGI setup should play an important role in its technical implementation. These are the type of projected patterns and the sensor dynamic range. A two-dimensional simulation showed that the type of patterns, the sensor’s dynamic range and also the dynamic range of the projector are crucial design aspects. A threedimensional photometric simulation of the setup was designed. It adds a proof of concept to CGI with backscattered light and showed that it can be used for stereo reconstruction. Experiments in the future shall reveal more details about the technical implementation. In this submission we present the introduced novel 3D sensor approach and the most significant details of the simulation results.

Coherence scanning interferometry (CSI) is a well-established technique for measuring surface topography based on the coherence envelope and phase of interference fringes. The most commonly used surface reconstruction methods, i.e. frequency domain analysis, the envelope detection method, and the correlogram correlation method, obtain the phase of the measured field for each pixel and, from this obtain the surface height, by assuming the two are directly proportional. For surfaces with minor deviations from a plane, it is straightforward to show that the scattered field’s phase is a linear function of surface height. An alternative approach known as the “foil model” gives more generally the scattered field as the result of a linear filtering process operating on a “foil” representation of the surface. This model assumes that the surface slowly varies on the optical scale and that there is no multiple scattering. However, for surfaces that are rough at the optical scale or have coherent features (e.g. vee-grooves), the effect of multiple scattering cannot be neglected and remains a problem for reconstruction methods. Linear reconstruction methods cannot provide accurate surface topographies for complex surfaces, since for such surfaces, the measurement process of CSI is fundamentally non-linear. To develop an advanced reconstruction method for CSI, an accurate model of the imaging process is required. In this paper, a boundary elements method is used as a rigorous scattering model to calculate the scattered field at a distant boundary. Then, the CSI signal is calculated by considering the image formation as back-propagation of the scattered field, combined with the reflected reference field. Through this approach, the optical response of a CSI system can be predicted rigorously for almost any arbitrary surface geometry. Future work will include a comprehensive experimental verification of this model, and development of the non-linear surface reconstruction algorithm.

The overview of different types of reflectometers is given. The theoretical calculation of factors, such as instability of internal reference clocks and resolution of time interval measurement device, influencing on resolution and uncertainty of signal delay (which can be calculated into length) is given. One of the ways to decrease uncertainty type A of distance measurements is suggested scheme of pulse reflectometer with multistop event timer. Due to ability of measurement averaging it is possible to reduce resolution less then 0.1 mm. In the work principle of operation of the proposed reflectometer and functional scheme are given. The impact of such factors as chromatic and polarization mode dispersion, timer trigger error, temperature fluctuations are considered. The requirements to laser module due to dispersion characteristics of measured fiber are given. The temperature variation affects mostly on signal delay in photodetector and other electronics. It also changes the delay of optical pulse in fiber coil, which is used for dead zone riddance. The results of theoretical error limits calculations for such reflectometers are presented. The results of experimental studies of reflectometer are presented. It is shown that the proposed scheme of the optical time domain reflectometer and technical solutions make possible the signal propagation delays measurements with an resolution better than 5 ps and combined uncertainty less than 100 ps.

ELT-HIRES (High Resolution Spectrograph for the Extremely Large Telescope) is a multifold fiber-fed spectrograph planned for the Nasmyth B focal station on ELT, with a large spectral coverage, ranging from 0.4 to 1.8 μ. It’s our intention to equip it with a full Stokes polarimetric facility, feeding the UBVRI and the zYJH bands. Among the most relevant scientific targets there is the detection of life signature in the extrasolar atmospheres for Earth-like planets. The polarimetric instrument will consist of two subunits: the main one intended to be installed in the intermediate focus where the optical beam is split into the two polarized components via a double Wollaston calcite prism; the other one installed in one of the four arms of the Front End on the Nasmyth platform, in charge of the atmospheric dispersion correction, field stabilization and selection of the operating modes before the fiber injection. This has been presented for the Phase A as the only possible design solution fulfilling the top level requirement of reaching a sensitivity of 10^-5 S/I (with S equivalent to one of the Stokes vectors), condition achievable only if the polarizers are installed in a rotationally symmetric focus. In the present work we illustrate novel simulations of the polarized aberrations based on an integration of the structural and thermal FEM analysis within a Zemax design with the help of Matlab and Python tools.

The reflectance factor of a surface is generally defined as the amount of radiation reflected from the surface divided by that reflected by an ideal Lambertian diffuser. In practice, the latter is estimated by measuring the reflected radiation from a reference material approximating that ideal. If both are measured exactly once concurrently in the same conditions, the estimateof the surface reflectance factor is trivial to compute. However, if we decide to do repeated measurements of the quantities, then - like the proverbial man with two watches - we already run into multiple choices for our estimate, and for our assumptions. Do we assume the reflected light from either source to stay constant during our measurements? Is it enough to measure the reference just once, but keep measuring the surface? The assumptions we choose naturally lead to different ways to estimate the reflectance factor as either the ratio of the mean measurements, the slope from the linear regression to our measurements, or possibly the mean of the ratios for each pair of measurements (i.e. the mean reflectance factor). The latter estimate is especially prevalent in the field of hyperspectral imaging where the same choices arise from assumptions made about spatial instead of temporal uniformity, and many datasets commonly used for analysis consist only of the already computed ratios. This can present problems for accurate comparison of different instruments, since in general the different estimates can and do differ even on the same data due to their different behaviour with respect to the assumptions and instrument errors. Furthermore, different estimates also have different numerical characteristics, which should be considered especially when computing with discretized values from digital instruments. In order to gain a rigorous understanding of the different estimates and their associated uncertainties, in this work we present a review of the different assumptions that can be made of such measurements from a statistical viewpoint. We will present a mathematical framework for evaluating the uncertainties of each estimate given the instrument characteristics and a statistical model for the measured quantities. The framework will then be used to map out the various combinations of assumptions and estimates in order to guide planning of measurements and analysis workflows. Furthermore, we discuss the suitability of each estimate in the context of comparison between instruments, which will be accompanied by concrete examples using real and simulated data.

The most prevalent routine for camera calibration is based on the detection of well-defined feature points on a purpose-made calibration artifact. These could be checkerboard saddle points, circles, rings or triangles, often printed on a planar structure. The feature points are first detected and then used in a nonlinear optimization to estimate the internal camera parameters. We propose a new method for camera calibration using the principle of inverse rendering. Instead of relying solely on detected feature points, we use an estimate of the internal parameters and the pose of the calibration object to implicitly render a non-photorealistic equivalent of the optical features. This enables us to compute pixel-wise differences in the image domain without interpolation artifacts. We can then improve our estimate of the internal parameters by minimizing pixel-wise least-squares differences. In this way, our model optimizes a meaningful metric in the image space assuming normally distributed noise characteristic for camera sensors. We demonstrate using synthetic and real camera images that our method improves the accuracy of estimated camera parameters as compared with current state-of-the-art calibration routines. Our method also estimates these parameters more robustly in the presence of noise and in situations where the number of calibration images is limited.

Current and future space-exploration endeavors will require new capabilities for large data transfer between Earth and other planets in the Solar system. Data communication with Earth from other planets will be completed through DSN (Deep Space Network) arrays on Earth and satellites around Earth. In an effort to develop advanced Space communication capabilities for large data transfer, NASA John H. Glenn Research Center at Lewis Field (GRC) is also investing a revolutionary concept, named iROC (integrated Radio and Optical Communication), featuring a space-communication terminal which tightly integrates a compact optical transmitter with a radio communication system. A particular design named TeleTenna (Telescope within (RF) Antenna) for future iROC flight-demonstration is being developed at GRC, in which a laser-transmission telescope is placed at the center of an RF antenna. The TeleTenna system capabilities to be demonstrated should include advanced pointing techniques for laser-transmission without a beacon over vast Space distances up to at least 2.0 AU (Astronomical Unit). The pointing-precision imposed on this TeleTenna design for beaconless optical communication should be achievable with an interferometric Star Tracker (iST) for celestial pointing calculation and the metrology for tracking the outgoing laser-beam. The outer-diameter of the Primary-Mirror (PM) of the telescope (either of Cassegrain or Ritchey-Chrétien type) in the TeleTenna concept for data transmission from Mars to Earth is 0.25 meters, and the Secondary-Mirror (SM) outer-diameter is 0.025 meters. The laser-transmission tertiary optics behind the PM include the laser-fiber port, collimator lens, focus lens, quarter-wave plate, and a beam-splitter in that order; all aligned with the telescope axis. The test-bed that the first author and GRC team setup back in 2017 for some preliminary studies on beaconless-pointing and optics alignment metrology for the TeleTenna concept, and some experimental results will be presented in this paper. The investigated metrology includes an optics alignment sensing metrology to image a beam reflected from a fiducial on the secondary mirror of the surrogate telescope onto a pixelated sensor (PixSen) behind the telescope. Additionally, the metrology includes sampling a portion of the laser beam and redirecting it onto the iST image plane. The objectives of this procedure are to determine angular change of a laser beam as it comes out of the surrogate telescope. Among other findings, the work presented here shows that the alignment measurements performed at the edge of the Fine Steering Mirror (FSM) articulation range lead to nonlinearity in the relationship between the out-going beam direction registered on the iST and the fiducial reflected beam direction on an alignment sensor placed behind the telescope. For this reason, the adjustment of FSM angular position can realign only one of the beams with its respective camera but not both, and therefore an additional metrology instrument is required for high pointing precision. In the presented proof-of-concept metrology, this additional metrology component could be the piezo-controller of the FSM and/or an autocollimator that gives with accuracy the position of the FSM. These findings are relevant to the current development and design of the iROC system at GRC.

Currently, there are various methods to control the layers thicknesses during their manufacture and optical monitoring method is the basically used most often today. In this paper, we consider a method for determining the monitoring wavelength to control the optical thickness of each layer during its fabrication. By applying the method, it is possible to reduce errors in layer thicknesses and to obtain the spectral characteristic of the transmittance (or reflection) of the experimental coating that is maximally close to the theoretical spectra. The experimental results of thin films with high spectral performance showed that the method can effectively reduce the errors in layers thickness.

The paper discusses the main stages of creating and implementing a model of a universal, inexpensive measuring system based on the principles of stereo vision. Particularly special attention had been paid to the development, analysis, study of the features and accuracy of measurements of a passive stereo vision system, as a measuring device. In the course of the presented work, the following procedures were performed: calibration of a separate camera, calibration of a stereo camera, straightening and comparison of stereo images. The software part of the work was done in the C ++ programming language in the QtCreator editor using the computer vision library OpenCV 3.2.

A model that describes polymerization unit formation in multilayer absorbing medium for direct laser writing has been proposed. Properties of separate layers including surface roughness, illumination geometry, pulsed laser source and photosensitive material are parameters of the discussed model. A set of simulations has been carried out where the influence of the refractive indexes relation, layer thickness, roughness of the particular layers with respect to the structuring depth on the structure-model match and reproducibility has been analysed and discussed.

We present a novel method for measuring the spectral phase of laser mirrors, where fringe free spectrally resolved interferograms are recorded, and a simple arcus cosine transformation is used to retrieve the spectral phase from the normalized interferograms. The method does not require time delay correction during the evaluation of the interferograms. Group-delay dispersion of a silver and a high reflection mirror is measured to test the precision of the method and it is compared with the precision provided by the cosine function fit and the Fourier-transform method.

The paper addresses the problem of low quality 3D terrain models enhancement. We propose the approach based on convolutional neural networks (CNN), namely, on Pix2Pix method that uses generative adversarial networks for imageto-image translation. We use heightmap 3D terrain models representation to use classical CNNs. The network was trained on a synthetic dataset that included 150000 images and heightmaps of different landscapes. Our model showed the relative mean absolute difference equal to 0.459% on synthetic testing dataset. In addition, we demonstrate landscapes generation on the real data from Google Maps using our model.

Measuring accuracy of Photosynthetically Active Radiation (PAR) and Plant Biology Active Radiation (PBAR) in plant growth facilities influences its commercial efficiency. Integrated measuring systems based on spectrophotometry are more accurate than systems with sensors with broadband spectral sensitivity. Optical scheme and elements parameters of spectroradiometer have an effect on measurement accuracy. The primary objective is to model error of spectroradiometer for measuring photosynthetically active radiation, investigate error introduced by unoptimized choice of array photodetector and influence of residual defocus of spectra image on photodetector for that spectroradiometric error. Theoretical investigation is carried out with computer software. Modelling is done for optical scheme with different aperture angle, which has an effect on focus surface curvature radius. Measurement error dependence on SRF for full width at half max (FWHM) and residual defocus is calculated numerically. It is demonstrated, that decreasing focal surface radius and increasing aperture angle increases inhomogeneity of spectroradiometric error.

A mathematical model of the spectral transform implemented in a diffraction grating spectral device based on the principles of radio optics, the system approach and the theory of linear systems is presenter in paper. The model is based on a sequential describing of the optical signal conversion by all elements of the device. The rejection of the principles of geometric optics when describing the operation of the device is argued. The proposed model in a strict mathematical form allows to establish important properties of the spectra in various diffraction orders: a nonlinear relationship of the spatial and frequency scale and a multiple improvement in the spectral resolution with an increase in the number of the diffraction order. In addition, a method has been established for improving the resolution of the device by applying diffraction gratings with a modified topology of the location of the strokes, which makes it possible to increase the intensity of the diffracted light into higher diffraction orders. Changing the topology consist in location of the strokes at not at an equidistant distance, i.e. introduction of spatial modulation. The results of computer simulation of a diffraction grating with the proposed topology and calculations of the theoretically achievable resolution of device with such grating are presented. A comparison is made between ordinary and high-order diffraction gratings according to their efficiency.

This paper addresses the challenges and limitations involved in the measurement of steep freeform wavefront by using Shack-Hartmann Sensor (SHS). To estimate the slope errors, Zemax simulation tool is used to design a SHS setup including array of lenslets and detector plane with predefined specifications. In first step, error due to approximation of tilted plane wavefront over curved wavefront is simulated. Plane, tilted, curved and tilted-curved wavefronts are defined using appropriate ray source objects. The centroids of the focal spots of lenslets are calculated based on the detector data obtained by using ray tracing method, which is done by an in-plane scanning aperture for segmented local wavefronts sequentially.The scanning aperture is used to block rays from more than one lenslet array. Centroids from the focus spots are calculated and the slopes are estimated with respect to collimated reference wavefront for each ray trace process. Further, matrix of slope errors is used as an input for MATLAB routines for surface reconstruction and error estimation. Based on the simulation data, it is found that the assumption used in Shack-Hartmann wavefront measurement introduce residual errors. For example a 50 wave peak to valley input and 1.19 mm thick lenslet array can give up to 9 waves of residual form error. However, very thin lenslets can have very less residual error.The effect of shift of focal plane, tilted plane wavefront and curve wavefront during the reconstruction using SHS is reported.

In optics, there are two notable groups of wavefront recovery techniques: the interferometric and geometric ones. Some intensity patterns obtained with these techniques can be quickly related to typical aberrations such as coma or astigmatism. However, the patterns obtained with phase retrieval techniques have not been studied yet. In this work, we proposed and developed a computational tool to obtain intensity distributions in any perpendicular plane of well-known and well-behaved beams, such as parabolic or Gaussian beam wavefronts.

A method of measuring the dimensionless extinction coefficient for optical thin-film layers of weakly absorbing filmforming materials using a parallelepiped form attachment is presented. The attachment uses frustrated total internal reflection to multiply radiation losses in tested thin film layers. Influences of some main factors on accuracy of the method have been studied and the results show that those influences can be compensated and as the result of it the measurement error can be reduced to 1%.

An experimental arrangement is proposed to measure the wavefront aberration associated with a plane-convex lens of PDMS. The wavefront is obtained by numerically solving the transport intensity equation (TIE) using intensity measurements in different planes. In addition, the Zernike polynomials will be used to show the contribution of each optical aberration on the wavefront.

In the present study we consider an approach to design and tolerance analysis of a spectrograph with a complex dispersive unit. The design uses a mosaic dispersive unit consisting of two VPH gratings imposed on the same substrate. This solution allows to detect spectra in two intervals – visible (375-625 nm) and near infrared (600-1000 nm) simultaneously. The modeling results show that the spectra resolution reaches 0.78 and 1.25 nm in the visible and NIR channel, respectively. The diffraction efficiency varies between 74.3% and 99.7% for the entire working range. However, the design is sensitive to the manufacturing and assembly errors. Some design parameters have influence on both the image quality and the diffraction efficiency. We developed a set of design tools allowing to include diffraction efficiency data into the tolerance analysis process. The analysis performed with these tools shown that maintenance of the nominal efficiency together with the image quality requires special control over the holographic layer parameters and also tightening of the tolerances on the lenses parameters. The developed analysis approach and tools may be useful in the future for design of spectral instruments with VPH gratings, especially when they are used to build a complex dispersive element.

This paper formulates a general thermodynamically consistent theory of the coupled solute transport and large strain to describe the transformation kinetics of precipitation in a supersaturated matrix during laser additive manufacturing (AM) by selective laser melting of powder bed using phase field method. The structure of the constitutive equations is derived utilizing multiplicative kinematic decomposition of the total deformation gradient into elastic and eigen transformation parts. Expressions for the first Piola–Kirchhoff stress and the Cauchy stress are derived. The stress-dependent diffusion potential accounts for nonlinear, finite deformation. A high nonlinear Ginsburg–Landau kinetic equations coupled to Cahn-Hilliard type of diffusion-drift equation for solute atom concentration are derived. The Voigt/Taylor homogenization theory is used to model the dependence of total stress on the phase-field, which assumes equal elastic strains in the different phases at the diffuse interface region. To describe the effects of temperature and fluid velocity distributions and thermal history on the precipitate growth mechanisms a linking of microscale model with the macroscopic AM processing conditions is discussed. To describe the effects of temperature gradient and fluid velocity distributions and thermal history on the precipitate growth mechanisms a linking of microscale model with the macroscopic AM processing conditions is discussed. Then the proposed model is applied to cylindrical precipitate growth to explore the stress evolution with taking account of finite deformation and plastic deformation.

In this paper, the processes accompanying multitrack and multilayer selective laser melting of metal powder are studied by methods of multiscale numerical simulation. The model includes the coupled macro-scale balance equations of energy and momentum, describing heat transfer, fluid flow and phase transformations, while modeling the structure of the deposited layer by the discrete elements method. The features of the processes of heat transfer and the formation of the melt pool are studied, the surface profile and the relative density (porosity) of the synthesized sample of stainless steel 304 are determined. The calculated values of the final porosity coincide with the experimental data. On the micro-scale, a phase field method characterized by a self-consistent thermodynamic approach and universality is used to describe phase transitions and structure formation dynamics. The numerical implementation of the microstructure evolution micromodel is carried out, the dynamics of morphology and growth of columnar dendritic microstructures in the process of selective laser melting is analyzed. The influence of the governing parameters of the model and the process on the formation of stress fields in dendritic crystal structures is studied.

Fringe Projection Profilometry (FPP) is a widely used technique for optical three-dimensional (3D) shape measurement. Among the existing 3D shape measurement techniques, FPP provides a whole-field 3D reconstruction of objects in a non-contact manner, with high resolution, and fast data processing. The key to accurate 3D shape measurement is the proper calibration of the measurement system. Currently, most calibration procedures in FPP rely on phase-coordinate mapping (PCM) or back-projection stereo-vision (SV) methods. The PCM technique consists in mapping experimental metric XYZ coordinates to recovered phase values by fitting a predetermined function. However, it requires accurately placing 2D or 3D targets at different distances and orientations. Conversely, in the SV method, the projector is regarded as an inverse camera, and the system is modeled using triangulation principles. Therefore, the calibration process can be carried out using 2D targets placed in arbitrary positions and orientations, resulting in a more flexible procedure. In this work, we propose a hybrid calibration procedure that combines SV and PCM methods. The procedure is highly flexible, robust to lens distortions, and has a simple relationship between phase and coordinates. Experimental results show that the proposed method has advantages over the conventional SV model since it needs fewer acquired images for the reconstruction process, and due to its low computational complexity the reconstruction time decreases significantly.

To measure the quality of optical surfaces, one of the most used methods is the deflectometry. To implement this technique, a screen is used to choose some incident rays on the surface under test. Subsequently, the intersection of the rays is measured, after having passed through the surface, in a detection plane perpendicular to the optical axis. With the coordinates of the points in the detection plane, the normal vectors are determined in each point of the surface under test. The process is simple if the incident rays are chosen in a configuration called null, that is, in the detection plane the measured points will be distributed in a uniform configuration, rectangular, circular, radial, etc. In this work we present the numerical simulations, considering an incident spherical wavefront in the null screen that is placed at an arbitrary position between the source and the flat surface of an aspheric lens that was used in the experimental arrangement. In the simulations it is expected to obtain a uniformly distributed arrangement of spots, which will be compared with the experimental results.

The design of a two-mirror telescope using a free-form surface for the primary mirror, to obtain a compensation of the spherical and coma aberrations, in the entire pupil of the telescope is proposed. In this design, the conic constant (𝑘₁ ) of the primary mirror is a function of the heights, measure from the center to the edge of primary mirror. In this method, we use the exact ray tracing to find the optical path length (OPL) for each ray that intersect the primary mirror at different distances measured from the center of the primary mirror. The OPL is calculated with the sum of the distances that each ray travels until reaching the plane of the image, and the sum of the distances for a paraxial axial ray. From the optical path difference (OPD) of a set of rays, we obtain a set of values of the conic constant that guarantees that the OPD has a value of zero for each incident ray height. With the set of values of the conic constant it is possible to obtain the shape of the surface of the primary mirror.