This PDF file contains the front matter associated with SPIE Proceedings Volume 9526, including the Title Page, Copyright information, Table of Contents, Invited Panel Discussion, and Conference Committee listing.

We present two piecewise linear parameterization schemes for the parameterized coordinate transformation method (the C method) to enable it to model gratings of deep and smooth grooves. This work generalizes and elaborates our previous work [Opt. Lett. 39(23), 6644 (2014)]. The previous bilinear transformation is replaced with a general multi-linear transformation. This gives us flexibility to handle more general grating profiles while retaining the simplicity of the linear transformation. We give some general, simple, and empirical rules on composing the piecewise linear transformation function. Both enlarged convergence range and increased groove depth-to-period ratio, which can be at least 10, are achieved with the parameterized C method for a wide class of smooth grating profiles.

This paper focuses on specialized scatterometry methods for two types of featured grating structures: highly asymmetric triangular grating on a transparent substrate (type I), and standing-wave photoresist mask grating on a reflective substrate (type II). Compared with the conventional microstructures occurring in semiconductor metrology, both type I and type II have distinct groove profiles, which makes their specialized scatterometry methods also different from the conventional ones. Combining with two specific cases, by using the asymmetry of triangular profile in type I grating, and the strong dispersion property of the specific substrate in type II grating, the paper shows the feasibility of specialized scatterometry methods with high profile reconstruction sensitivity.

Finding a fast and precise method to measure the side-wall angle of periodic (or non-periodic) structures is still a very challenging problem in lithographic applications. For this reason, over the years, many techniques have been proposed to circumvent this limitation, with the final goal to give the most precise geometrical description of particular targets. Recently, the investigation of the optical angular momentum, which is encoded in the light's spiral spectrum, has brought new ways to acquire information about objects. In this work, we built an optical setup to put forward a new method to detect the side-wall angle in a fast and reliable way. The novelty of this work is the use of the spiral spectrum of a light beam for angle measurements, i.e. the light transmitted by a particular structure is projected onto properly tailored spatial modes and only the most sensitive mode to the side wall angle is detected and processed.

Phase errors are one of the sources of insufficient measurement accuracy of optical 3D surface sensors based on the fringe projection technique. In this paper phase error analysis and compensation is presented which successfully improves the measurement results of disturbed input data. The origins of the phase errors are analyzed and systematic and random errors are distinguished. An error model is introduced which allows the description of arbitrary and locally distinguishing phase errors. The presented new method includes phase error determination and correction independently from the origin of the phase error. Different compensation algorithms are presented which were successfully applied to selected examples of real measurement data.

Homodyne laser interferometers for the measurement of movement are well-known optical systems used in many applications where exact and contactless velocity sensing is an essential requirement. While the detector output signal of such a system using a long coherence length laser is easily modeled using the Doppler shift, a short coherence length source, e.g. a broad spectrum semiconductor laser, demands a more elaborated approach for simulation.

The work being presented takes a look at a method for efficiently simulating a short coherence length Lorentzian laser source and calculating the interference signal for many point scattering sources moving through space within a continuously changing coherence function. The detector’s time domain signal and its frequency domain spectrum will be calculated and evaluated. The results of the proposed simulation method are then compared to theoretical analyses found in literature.

The European XFEL is a large facility under construction in Hamburg, Germany. It will provide a transversally fully coherent x-ray radiation with outstanding characteristics: high repetition rate (up to 2700 pulses with a 0.6 milliseconds long pulse train at 10Hz), short wavelength (down to 0.05 nm), short pulse (in the femtoseconds scale) and high average brilliance (1.61025 photons / s / mm2 / mrad2/ 0.1% bandwidth). Due to the very short wavelength and very high pulse energy, all the mirrors need to have high quality surface, to be very long, and at the same time to implement an effective cooling system. Matching these tight specifications and assessing them with high precision optical measurements is very challenging. In order to measure the mirrors and to characterize their interaction with the mechanical mounts, we equipped a Metrology Laboratory with a Large Aperture Fizeau. The system is a classical 100 mm diameter commercial Fizeau, with an additional expander providing a 300 mm diameter. Despite the commercial nature of the system, special care has been done in the polishing of the reference flats and in the expander quality. In this report, we show the preparation of the instrument, the calibration and the performance characterization, together with some preliminary results. We also describe the approach that we want to follow for the x-rays mirrors measurements. The final goal will be to characterize very long mirrors, almost 1 meter long, with nanometer accuracy.

Adaptive optics (AO) schemes are often applied to the inertial confinement fusion (ICF) system, such as SG-Ⅲ Prototype which has been set in China. This laser systm mainly includes a pulsed seed laser source, a multi-pass laser amplifier with the configuration of beam rotate-90° and expansion. When AO system is employed in this sytem, the beam bounces twice on the deformable mirror (DM) which works as the cavity mirror (CM) of the multi-pass laser amplifier, moreover, after the first bounce on the DM, the beam rotate 90° and expansion with a ratio. Therefore, the relationship between the DM’s correction stroke and the aberrations within the laser sytem must be known before applying a adaptive correction. This paper demonstrates that any output wave-front aberrations within the DM’s correction stroke range can be well corrected, as well as illuminates that the expansion ratio of beam and the types of output wave-front aberrations both affect the correction stroke range of DM. Furthermore, through building a theoretical calculating model and some simulation. the relationship between the DM’s surface stroke needed and different aberrations within the laser sytem is ascertained clearly. Results show that this configuration is proper for compensting most low order aberrtions besides some special ones. As a result, it will provides a useful guidance for those rotate-90°laser systems adopting adaptive optics technique.

Optical detectors developed on base of thermo elastic effect In quartz crystalline (PTEK) attributed to the thermal detectors group. Such detectors occurred very effective for the registration of pulsed light energy or power of harmonically modulated laser radiation flux in a wide spectral (from UV to far IR) and dynamic ranges (from 10-6 to 300 W / cm2 with cooling) with a time constant up to10-6 seconds. When exposed to electromagnetic radiation occurs at the receiver thermal field which causes mechanical stress in the transient crystalline quartz, which in turn leads to a change in the polarization of crystalline quartz and, as a consequence, to an electric potential difference at the electrodes (the front surface with a conductive coating and damper). The capacitive characteristic of the detector, based on a thermo elastic effect in crystalline quartz, eliminates the possibility of working with constant flow of radiation, which also affects at the frequency response of the detector, since the potential difference appearance in the piezoelectric plate depends on the direction of the forces relative to the axes X, Y, Z of the crystal. Therefore, a certain choice of orientation of the receiving element is necessary in accordance with the physical properties of crystalline quartz. In this paper, a calculation of the sensitivity and frequency characteristics of optical detectors based on the thermo elastic effect in crystalline quartz at the harmonic effects of electromagnetic radiation flux are reported.

Radiometric calibration and non-uniformity correction are key operations in a signature measurement, which is a special challenge in the infrared range where a large number of parameters need to be characterized. The radiation hitting the camera's pixels will not only be due to the target, but will also depend on the atmosphere and optical components like lens and spectral filters. To obtain broadband radiative properties of a target, the spectral properties of these components must be accurately characterized. In addition to signal contributions from the incident radiation, the pixel’s digital numbers will also depend on the individual responses of the pixels. Results are presented for an infrared camera of the following examined parameters: stabilization period, dynamic response, dynamic range, ambient temperature dependence and non-uniformity. In radiometric calibrations using area blackbody sources, an estimate of the sensor signal is obtained by pixel averaging (which reduces the influence of non-uniformity), and the spectral distributions of the sources are known (via the Planck distribution). These conditions do not normally apply for signature measurements e.g. of small hot spots involving only a few pixels. The measurement uncertainty is compared between calibrations based on mean values and pixel-wise calibration. It is shown that the pixel-by-pixel variation should be included in an analysis of the measurement uncertainty. A discussion is given of the effects of unknown spectral distributions on the measurement uncertainty.

With the rapid evolution of new, energy-efficient solid-state lighting (SSL) systems, a requirement has risen for new performance metrics and measurement methods to address their unique construction and operating conditions. In this paper, light propagation characteristics in light emitting diodes are analyzed for measurement uncertainty through numerical modeling and simulation. A general 2D EM simulator with PML boundary conditions is formulated to solve Maxwell's equations using finite-difference time domain (FDTD) numerical method to describe the light propagation in LEDs.

A practical GaN LED used in SSL systems is simulated for light propagation. The optical properties of dispersive materials are modeled using multi-pole Lorentz-Drude model. The input dipole source for the LED structure is modeled explicitly through a Gaussian pulse line source at a central wavelength of 460 nm corresponding to GaN emission. Finally, the expression for combined standard uncertainty in the light extraction efficiency due to uncertainties in inputs such as emission in the active layer and EM fields is developed using the GUM law of propagation of uncertainties. The uncertainty in GaN LED emission wavelength obtained from Full Width Half Maximum (FWHM) of the emission spectrum is computed to be 16.98 nm. Therefore, the uncertainty analysis model is then used to compute the corresponding uncertainties in the LED output measurements i.e. light extraction efficiency, LED output power and EM fields.

Wind energy is one of the leading sustainable energies. To attract further private and state investment in this technology, a broad scaled drop of the cost of energy has to be enforced. There is a trend towards using Laser Doppler Velocimetry LiDAR systems for enhancing power output and minimizing downtimes, fatigue and extreme forces. Since most used LiDARs are horizontally setup on a nacelle and work with two beams, it is important to understand the geometrical configuration which is crucial to estimate reaction times for the actuators to compensate wind gusts. In the beginning of this article, the basic operating modes of wind turbines are explained and the literature on wind behavior is analyzed to derive specific wind speed and wind angle conditions in relation to the yaw angle of the hub. A short introduction to the requirements for the reconstruction of the wind vector length and wind angle leads to the problem of wind shear detection of angled but horizontal homogeneous wind fronts due to the spatial separation of the measuring points. A distance is defined in which the wind shear of such homogeneous wind fronts is not present which is used as a base to estimate further distance calculations. The reaction time of the controller and the actuators are having a negative effect on the effective overall reaction time for wind regulation as well. In the end, exemplary calculations estimate benefits and disadvantages of system parameters for wind gust regulating LiDARs for a wind turbine of typical size. An outlook shows possible future improvements concerning the vertical wind behavior.

Autocollimation systems are widely used to measure angular values, in particular, angular deformations in the critical points of large objects, angles of optical components, and for controlling the straightness and parallelism. Autocollimator measures the rotation angle of the mirror as the sensitive element at angular deformation point with a potential accuracy up to 0.005 ". In fact, the error may significantly exceed the specified value because of systematic error existence, one of which main components is the error due to vignetting of working beam. The reason of vignetting error is changing of irradiance distribution of the image on the autocollimator analyzer due to cutting of a bundle of optical beams at a mirror deviation in case of angular deformation. On the basis of a computer simulation image model was investigated the influence of vignetting error and was found compensation algorithm of this error

We report on the experimental realization of locking a Fabry-Perot interferometer (FPI) onto a stabilized diode laser for the calibration of astronomical spectrographs. The external cavity diode laser (ECDL) is stabilized to the ⁸⁵Rb+ F* = 2 → F = 3 transition with a pump-probe setup. The stability of the ⁸⁵Rb+ reached between optical clocks is on the order of 10^-13.¹ and can be used to reduce the linewidth / drift of the ECDL to a few kHz.² The measured linewidth of the transition is around 20 MHz due to unavoidable misalignment between pump- and probe-beam, power- and Doppler-broadening at room temperature.² The aim is to transfer this stability to a FPI that can be used as optical frequency standard: Therefore the phase of the light reflected from the FPI is observed using the Pound-Drever-Hall method. The theoretically reachable stability of a few mHz/Hz³ is limited by different noise factors. In order to identify these noise factors we a) follow the calculation of noise factors given by, ⁴ b) calculate the contribution of misalignment and insufficient mode matching by applying the generalized matrix-formalism, ⁵ and c) estimate the contribution of the initial laser linewidth and the present electronic noise sources.

The simulation, design and tolerancing of optical systems for wafer inspection is a challenging task due to the different feature sizes, which are involved in these systems. On the one hand light is propagated through macroscopic lens systems and on the other hand light is diffracted at microscopic structures with features in the range of the wavelength of light. Due to this variety of scale plenty of different physical effects like refraction, diffraction, interference and polarization have to be taken into account for a realistic analysis of such inspection systems. We show that all of these effects can be included in a system simulation by field tracing, which combines physical and geometrical optics. The main idea is the decomposition of the complex optical setup in a sequence of subdomains. Per subdomain a different approximative or rigorous solution of Maxwell’s equations is applied to propagate the light. In this work the different modeling techniques for the analysis of an exemplary wafer inspection system are discussed in detail. These techniques are mainly geometrical optics for the light propagation through macroscopic lenses, a rigorous Fourier Modal Method (FMM) for the modeling of light diffraction at the wafer microstructure and different free-space diffraction integrals. In combination with a numerically efficient algorithm for the coordinate transformation of electromagnetic fields, field tracing enables position and fabrication tolerancing. As an example different tilt tolerance effects on the polarization state and image contrast of a simple wafer inspection system are shown.

Instrumental errors of measurement wide-aperture laser beam diameter were modeled to build measurement setup and justify its metrological characteristics. Modeled setup is based on CCD camera and transmission diffuser. This method is appropriate for precision measurement of large laser beam width from 10 mm up to 1000 mm. It is impossible to measure such beams with other methods based on slit, pinhole, knife edge or direct CCD camera measurement. The method is suitable for continuous and pulsed laser irradiation. However, transmission diffuser method has poor metrological justification required in field of wide aperture beam forming system verification. Considering the fact of non-availability of a standard of wide-aperture flat top beam modelling is preferred way to provide basic reference points for development measurement system.

Modelling was conducted in MathCAD. Super-Lorentz distribution with shape parameter 6-12 was used as a model of the beam. Using theoretical evaluations there was found that the key parameters influencing on error are: relative beam size, spatial non-uniformity of the diffuser, lens distortion, physical vignetting, CCD spatial resolution and, effective camera ADC resolution. Errors were modeled for 90% of power beam diameter criteria. 12-order Super-Lorentz distribution was primary model, because it precisely meets experimental distribution at the output of test beam forming system, although other orders were also used.

The analytic expressions were obtained analyzing the modelling results for each influencing data. Attainability of <1% error based on choice of parameters of expression was shown. The choice was based on parameters of commercially available components of the setup. The method can provide up to 0.1% error in case of using calibration procedures and multiple measurements.

Distributed fiber vibration sensing system is widely used in the field of wide area security, communication cable of long distances and pipeline security. The principle of the system is that for a vibration signal applied at a particular position along the fiber, the response, in the frequency domain, presents a series of periodic maxima and minima (or nulls). These minima depend on the position of the vibration along a fiber. Power spectral estimation method is considered to denoise the power spectrum of the system and determine these minima precisely in the paper. The parametric modelling methods such as autoregressive-moving average (ARMA) model is used to improve the positional accuracy of the system. The experimental results show the high accuracy of the position using ARMA model.

Multiple scattering of a coherent light plays important role in the optical metrology. Probably the most important phenomenon caused by multiple scattering are the speckle patterns present in every optical imaging method based on coherent or partially coherent light illumination. In many cases the speckle patterns are considered as an undesired noise. However, they were found useful in various subsurface imaging methods such as laser speckle imaging (LSI) or optical coherence tomography (OCT). All features of the speckle patterns and their connection with microstructure of scattering materials was not fully exploited. Further research on this topic may lead to a simple and inexpensive optical diagnostic methods. Theoretical and numerical research could greatly facilitate development of such methods. However, this requires simulations of coherent light propagation through a random scattering media of a length larger than few hundreds of a light wavelength. During such propagation the light can be scattered by many tens of thousands of scattering particles. The numerical methods, such as the radiative transfer theory and the Monte Carlo methods, allows to simulate propagation of the incoherent light in such a media but they do not consider the coherence properties of light. Moreover, they consider only average realization of the scattering medium and therefore does not allow to predict properties of any random fluctuations of the scattered light, such as a speckle patterns. Direct solvers of Maxwell or Helmholtz equations, such as finite-difference or finite-element methods could solve this problem but their computational complexity limits their application to media no longer than about 10 to 20 wavelengths of the light. Here we show an alternative approach based on solving the integral form of the Helmholtz equation written as a so called perturbation expansion. We show the numerical algorithm for solving this equation. The presented algorithm allows to simulate light scattering with accuracy similar to the finite difference methods but with much lower computational complexity. This can make it an useful tool in research on coherent light propagating through the random media.

Black carbon particles soon after emission interact with organic and inorganic matter. The primary goal of this work was to approximate the accuracy of the DDA method in determining the optical properties of such composites. For the light scattering simulations the ADDA code was selected and the superposition T-Matrix code by Mackowski was used as the reference algorithm. The first part of the study was to compare alternative models of a single primary particle. When only one material is considered the largest averaged relative extinction error is associated with black carbon (δC_ext ≈ 2.8%). However, for inorganic and organic matter it is lowered to δC_ext ≈ 0.75%. There is no significant difference between spheres and ellipsoids with the same volume, and therefore, both of them can be used interchangeably. The next step was to investigate aggregates composed of Np = 50 primary particles. When the coating is omitted, the averaged relative extinction error is δC_ext ≈ 2.6%. Otherwise, it can be lower than δC_ext < 0.2%.

is a well-known detection method which is applied in many different scientific and technology domains including atmospheric physics, environmental control, and biology. It allows contactless and remote detection of sub-micron size particles. However, methods for detecting a single fast moving particle smaller than 100 nm are lacking.

In the present work we report a preliminary design study of an inline large area detector for nanoparticles larger than 50 nm which move with velocities up to 100 m/s. The detector design is based on light scattering using commercially available components.

The presented design takes into account all challenges connected to the inline implementation of the scattering technique in the system: the need for the detector to have a large field of view to cover a volume with a footprint commensurate to an area of 100mm x 100mm, the necessity to sense nanoparticles transported at high velocity, and the requirement of large capture rate with a false detection as low as one false positive per week. The impact of all these stringent requirements on the expected sensitivity and performances of the device is analyzed by mean of a dedicated performance model.

The realization of improved depolarized dynamic light scattering method is presented. This technique supports measurement of non-spherical nanoparticals dimensions in liquids. The relations between translational and rotational diffusion coefficients and autocorrelation function of scattered light with polarized and depolarized components in various proportions are derived. Thus measurement of very weak cross-polarized component can be avoided. This improvement permits to reduce measurement time, to improve signal to noise ratio and results precision. The technique was applied for sizing of gold nanorods and multiwalled carbon nanotubes in liquids.

We present a method for calculating a two-dimensional refractive index field from measured boundary values of beam position and slope. By initially ignoring the dependence of beam trajectories on the index field and using cubic polynomials to approximate these trajectories, we show that the inverse problem can be reduced to set of linear algebraic equations and solved using a numerical algorithm suited for inverting sparse, ill-conditioned linear systems. The beam trajectories are subsequently corrected using an iterative ray trace procedure so that they are consistent with the ray equation inside the calculated index field. We demonstrate the efficacy of our method through computer simulation, where a hypothetical test index field is reconstructed on a 15 × 15 discrete grid using 800 interrogating rays and refractive index errors (RMS) less than 0.5% of the total index range (n_max-n_min) are achieved. In the subsequent error analysis, we identify three primary sources of error contributing to the reconstruction of the index field and assess the importance of data redundancy. The principles developed in our approach are fully extendable to three-dimensional index fields as well as more complex geometries.

Thin film thickness determination with a reflectometer suffers from two problems. One problem is the leakage in the Fast Fourier Transform caused by the fact that the two variables wavenumber 1/λ and optical thickness n⋅d are not really independent, since the refractive index n of the film material itself depends upon the wavenumber. This causes uncertainties in the thickness determination in the order of up to 5% for highly refractive materials like semiconductors. We present a simple but effective improvement of this contribution of the leakage that reduces the uncertainty to less than 2% for highly refractive materials.

Another problem that mainly affects thin films below about 2 μm arises if one uses measuring heads collimators or even microscope headers to obtain high lateral resolutions in the thickness determination. The use of a header introduces angles of incidence different from the default angle α = 0° in reflectometry. Then, the measured reflectance becomes polarization-dependent and the angle must be explicitly considered in the evaluation algorithm. For a microscope header however, all angles between 0° and the angle of aperture must be considered. We will present a solution that allows to reduce the work for each header on taking into account the polarization of the reflected light and a corresponding effective angle α_eff.

Indirect optical methods like ellipsometry or scatterometry require an optical model to calculate the response of the system, and to fit the parameters in order to minimize the difference between the calculated and measured values. The most common problem of optical modeling is that the measured structures and materials turn out to be more complex in reality than the simplified optical models used as first attempts to fit the measurement. The complexity of the optical models can be increased by introducing additional parameters, if they (1) are physically relevant, (2) improve the fit quality, (3) don't correlate with other parameters. The sensitivity of the parameters can be determined by mathematical analysis, but the accuracy has to be validated by reference methods. In this work some modeling and verification aspects of ellipsometry and optical scatterometry will be discussed and shown for a range of materials (semiconductors, dielectrics, composite materials), structures (damage and porosity profiles, gratings and other photonic structures, surface roughness) and cross-checking methods (atomic force microscopy, electron microscopy, x-ray diffraction, ion beam analysis). The high-sensitivity, high-throughput, in situ or in line capabilities of the optical methods will be demonstrated by different applications.

Scatterometry is a fast indirect optical method for the determination of grating profile parameters of photomasks. Profile parameters are obtained from light diffracted intensities by solving an inverse problem. There are diverse methods to reconstruct profile parameters and to calculate associated uncertainties. To fit the upcoming need for improved accuracy and precision as well as for the reduction of uncertainties different measurements should be combined. Such a combination increases the knowledge about parameters and may yield smaller uncertainties. The Bayesian approach provides an appropriate method to evaluate combined measurements and to obtain the associated uncertainties. However, for computationally expensive problems like scatterometry, the direct application of Bayesian inference is very time consuming. Here, we use an approximation method based on a polynomial chaos expansion. To probe the quality of this approximation, we reconstructed geometry parameters, quantify uncertainties and study the effect of different prior informations onto the obtained grating profile parameters by using simulation data superimposed by noise.

In hybrid metrology two or more measurements of the same measurand are combined to provide a more reliable result that ideally incorporates the individual strengths of each of the measurement methods. While these multiple measurements may come from dissimilar metrology methods such as optical critical dimension microscopy (OCD) and scanning electron microscopy (SEM), we investigated the hybridization of similar OCD methods featuring a focus-resolved simulation study of systematic errors performed at orthogonal polarizations. Specifically, errors due to line edge and line width roughness (LER, LWR) and their superposition (LEWR) are known to contribute a systematic bias with inherent correlated errors. In order to investigate the sensitivity of the measurement to LEWR, we follow a modeling approach proposed by Kato et al. who studied the effect of LEWR on extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Similar to their findings, we have observed that LEWR leads to a systematic bias in the simulated data. Since the critical dimensions (CDs) are determined by fitting the respective model data to the measurement data by minimizing the difference measure or chi square function, a proper description of the systematic bias is crucial to obtaining reliable results and to successful hybridization. In scatterometry, an analytical expression for the influence of LEWR on the measured orders can be derived, and accounting for this effect leads to a modification of the model function that not only depends on the critical dimensions but also on the magnitude of the roughness. For finite arrayed structures however, such an analytical expression cannot be derived. We demonstrate how to account for the systematic bias and that, if certain conditions are met, a significant improvement of the reliability of hybrid metrology for combining both dissimilar and similar measurement tools can be achieved.

In thin optoelectronic devices, like organic light emitting diodes (OLED) or thin-film solar cells (TFSC), light propagation, which is initiated by a local point source, is of particular importance. In OLEDs, light is generated in the layer by the luminescence of single molecules, whereas in TFSCs, light is coupled into the devices by scattering at small surface features. In both applications, light propagation within the active layers has a significant impact on the optical device performance. Scanning near-field optical microscopy (SNOM) using aperture probes is a powerful tool to investigate this propagation with a high spatial resolution. Dual-probe SNOM allows simulating the local light generation by an illumination probe as well as the detection of the light propagated through the layer. In our work, we focus on the light propagation in thin silicon films as used in thin-film silicon solar cells. We investigate the light-in-coupling from an illuminating probe via rigorous solution of Maxwell's equations using a Finite-Difference Time-Domain approach, especially to gain insight into the light distribution inside a thin layer, which is not accessible in the experiment. The structures investigated include at and structured surfaces with varying illumination positions and wavelengths. From the performed simulations, we define a "spatial sensitivity" which is characteristic for the local structure and illumination position. This quantity can help to identify structures which are beneficial as well as detrimental to absorption inside the investigated layer. We find a strong dependence of the spatial sensitivity on the surface structure as well as both the absorption coefficient and the probe position. Furthermore, we investigate inhomogeneity in local light propagation resulting from different surface structures and illumination positions.

A plenoptic imaging system records simultaneously the intensity and the direction of the rays of light. This additional information allows many post processing features such as 3D imaging, synthetic refocusing and potentially evaluation of wavefront aberrations. In this paper the effects of low order aberrations on a simple plenoptic imaging system have been investigated using a wave optics simulations approach.

Standard tomographic algorithms applied to optical limited-angle tomography result in the reconstructions that have highly anisotropic resolution and thus special algorithms are developed. State of the art approaches utilize the Total Variation (TV) minimization technique. These methods give very good results but are applicable to piecewise constant structures only. In this paper, we propose a novel algorithm for 3D limited-angle tomography – Total Variation Iterative Constraint method (TVIC) which enhances the applicability of the TV regularization to non-piecewise constant samples, like biological cells. This approach consists of two parts. First, the TV minimization is used as a strong regularizer to create a sharp-edged image converted to a 3D binary mask which is then iteratively applied in the tomographic reconstruction as a constraint in the object domain. In the present work we test the method on a synthetic object designed to mimic basic structures of a living cell. For simplicity, the test reconstructions were performed within the straight-line propagation model (SIRT3D solver from the ASTRA Tomography Toolbox), but the strategy is general enough to supplement any algorithm for tomographic reconstruction that supports arbitrary geometries of plane-wave projection acquisition. This includes optical diffraction tomography solvers. The obtained reconstructions present resolution uniformity and general shape accuracy expected from the TV regularization based solvers, but keeping the smooth internal structures of the object at the same time. Comparison between three different patterns of object illumination arrangement show very small impact of the projection acquisition geometry on the image quality.

In this report we exploit numerically a novel cascaded plasmonic superlens system for far field subwavelength imaging, which is a promising solution to the current existing problem with near field superlenses. In our approach, a metamaterial composed of a double layer metallic meander cavity (DLMC) structure is used to support the propagation of waves with large transverse wave vectors. Then a planar plasmonic lens (PPL) cascaded with the DLMC is used to couple the near field waves into free space to form an image with magnification via phase compensation. We study numerically the whole coupled system in the near and far field regime to demonstrate the functionality of such a superlens and near field interaction among them is discussed.

We propose an in situ method for establishing the amplification coefficient (height scale) for an interference microscope as an alternative to the traditional step height standard technique for routine calibration. The method begins by determining the properties of the microscope illuminator equipped with a narrow-band spectral filter, using a spectrometer to provide traceability to the 546.074nm ¹⁹⁸Hg line. A data acquisition with the interference microscope links this wavelength standard to a calibration of the properties of the optical path length scanning mechanism of the interferometer. A capacitance sensor in the scanner maintains this calibration for subsequent measurements. A targeted k=1 uncertainty of 0.1% is favorable when compared to calibration using physical artifacts, and the calibration procedure is easier to perform and less sensitive to operator error.

We study and test a new technique for in-line digital holography which avoids the formation of the conjugate images. Inline digital holography is based in a common path configuration. In this case, the hologram is produced by the interference between the reference wave front and the diffracted wave front by an almost transparent object. Twin images are obtained with obscured rings that difficult the determination of the best focusing plane. To avoid the conjugated image, the information of the magnitude and phase of the wave front are needed.

In a recent work a new in-line digital holography technique was proposed. In this method the object is illuminated with a collimated wave front. A plane, close to the particles distribution is imaged onto a CCD by means of a convergent lens and at the same time, a knife edge is placed in the focal plane of the lens in order to block half of spatial frequency spectrum. In this way, by means of a numerical processing performed on the Fourier plane, it is possible to eliminate one of the components (real or conjugate) of the reconstructed images nevertheless it is observed a tiny deformation of the resulting hologram image.

To compensate this effect, we propose a new configuration in which we implement the knife edge technique on both parts of the spectrum at the same time. Finally in the computer, we process the holograms to build one complete without deformation. This hologram is used to recover the wave front at different planes without the influence of the conjugate image.

A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.

Publisher’s Note: This paper, originally published on June 21, 2015, was withdrawn at the author’s request on July 7, 2015.

Accurate and efficient measurement method is necessary to improve the testing efficiency for large optical plane. In this paper, a system is proposed for testing large optical plane in the workshop which combined dynamic interferometry with stitching algorithm. The feasibility is vibrated by an optical flat with 200mm×300mm.

A complete and punctual Stokes polarimeter based on the conical refraction (CR) phenomenon is presented. The CR phenomenon occurs when light travels along one of the optical axes of a biaxial crystal (BC), leading to a bright ring of light at the focal plane of the system. We propose using the connection between the intensity pattern of the CR ring and the state of polarization (SOP) of the incident beam as a new tool for polarization metrology. In order to implement a complete polarimeter, the instrument is designed with a beam splitter and two BCs, one BC for each sub-beam. In the second sub-beam, a retarder is introduced before the BC, allowing us to measure the ellipticity content of the input SOP.

The CR-based polarimeter presents several appealing features compared to standard polarimeters. To name some of them, CR polarimeters retrieve the SOP of an input beam with a single snapshot measurement, allow for substantially enhancing the data redundancy without increasing measuring time, and avoid instrumental errors related to rotating elements or active polarization devices.

This work shows the instrument design, in particular the parameters of the set-up have been optimized in order to reduce the amplification of noise. Then, the experimental implementation of the instrument is detailed, including the experimental calibration of the system. Finally, the implemented polarimeter is experimentally tested by measuring different SOPs, including fully and partially polarized light.

Dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) has been designed and applied as a powerful tool for the characterization of thin films and nanostructures. The compensators are indispensable optical components and their performances affect the precision and accuracy of DRC-MME significantly. Biplates made of birefringent crystals are commonly used compensators in the DRC-MME, and their optical axes invariably have tilt errors due to imperfect fabrication and improper installation in practice. The axis tilt error between the rotation axis and the light beam will lead to a continuous vibration in the retardance of the rotating biplate, which further results in significant measurement errors in the Mueller matrix. In this paper, we propose a simple but valid formula for the retardance calculation under arbitrary tilt angle and azimuth angle to analyze the axis tilt errors in biplates. We further study the relations between the measurement errors in the Mueller matrix and the biplate axis tilt through simulations and experiments. We find that the axis tilt errors mainly affect the cross-talk from linear polarization to circular polarization and vice versa. In addition, the measurement errors in Mueller matrix increase acceleratively with the axis tilt errors in biplates, and the optimal retardance for reducing these errors is about 80°. This work can be expected to provide some guidences for the selection, installation and commissioning of the biplate compensator in DRC-MME design.

Mueller matrix ellipsometry has been demonstrated as a powerful tool for nanostructure metrology in high-volume manufacturing. Many factors may induce depolarization effect in the Mueller matrix measurement, and consequently, may lead to accuracy loss in the nanostructure metrology. In this paper, we propose to apply a Mueller matrix decomposition method for the Mueller matrix measurement to separate the depolarization effect caused by the MME system. The method is based on the polar decomposition by decomposing the measured depolarizing Mueller matrix into a sequence of three matrices corresponding to a diattenuator followed by a retarder and a depolarizer. Since the depolarization effects will be only reflected in the depolarizer matrix, the other two matrices are used to extract the structure parameters of the measured sample. Experiments performed on a one-dimensional silicon grating structure with an in-house developed MME layout have demonstrated that the proposed method achieves a higher accuracy in the nanostructure metrology.

Liquid Crystals on Silicon (LCOS) displays are a type of LCDs that work in reflection. Such devices, due to the double pass that the light beam performs through the LC cells, lead to larger phase modulation than transmissive LCDs with the same thickness. By taking advantage of this modulation capability exhibited by LCOS displays, we propose a new experimental set-up which is able to provide customized state of polarization spatial distributions just by means of a single LCOS display. To this aim, a double reflection on different halves of the display is properly performed. This fact is achieved by including a compact optical system that steers the light and performs a proper polarization plane rotation.

The set-up has been experimentally implemented and some experimental concerns are discussed. The suitability of the system is provided by generating different experimental spatial distributions of polarization. In this regard, well-known polarization distributions, as axial, azimuthal or spiral linear polarization patterns are here provided. Based on the excellent results obtained, the suitability of the system to generate different spatially variant distributions of polarization is validated.

A novel autocollimating method for measuring the focal distances is presented. It may be used for measuring the focal distances of lenses and single optical elements in the visible, infrared and ultraviolet range. The relative uncertainty of this method is about 0.1%. The limited uncertainty is over 0.03%.

The main reasons of catastrophes and accidents are high level of wear of equipment and violation of the production technology. The methods of nondestructive testing are designed to find out defects timely and to prevent break down of aggregates. These methods allow determining compliance of object parameters with technical requirements without destroying it. This work will discuss dye penetrant inspection or liquid penetrant inspection (DPI or LPI) methods and computer model of microcracks image treated with fluorescent dye.

Usually cracks on image look like broken extended lines with small width (about 1 to 10 pixels) and ragged edges. The used method of inspection allows to detect microcracks with depth about 10 or more micrometers.

During the work the mathematical model of image of randomly located microcracks treated with fluorescent dye was created in MATLAB environment. Background noises and distortions introduced by the optical systems are considered in the model.

The factors that have influence on the image are listed below:

1. Background noise. Background noise is caused by the bright light from external sources and it reduces contrast on the objects edges.

2. Noises on the image sensor. Digital noise manifests itself in the form of randomly located points that are differing in their brightness and color.

3. Distortions caused by aberrations of optical system. After passing through the real optical system the homocentricity of the bundle of rays is violated or homocentricity remains but rays intersect at the point that doesn’t coincide with the point of the ideal image.

The stronger the influence of the above-listed factors, the worse the image quality and therefore the analysis of the image for control of the item finds difficulty.

The mathematical model is created using the following algorithm: at the beginning the number of cracks that will be modeled is entered from keyboard. Then the point with random position is choosing on the matrix whose size is 1024x1024 pixels (result image size). This random pixel and two adjacent points are painted with random brightness, the points, located at the edges have lower brightness than the central pixel. The width of the paintbrush is 3 pixels. Further one of the eight possible directions is chosen and the painting continues in this direction. The number of ‘steps’ is also entered at the beginning of the program. This method of cracks simulating is based on theory A.N. Galybin and A.V. Dyskin, which describe cracks propagation as random walk process. These operations are repeated as many times as many cracks it’s necessary to simulate. After that background noises and Gaussian blur (for simulating bad focusing of optical system) are applied.

The aim of the paper is to discuss the possibility of non-invasive sizing of a step-index optical fiber with the use of a beam of light of low temporal coherence. For this purpose we examine the angular profile of light scattered from the fiber at a high angle. The scattered pattern comprises chiefly two coupled, twin rainbows and depends on the fiber physical characteristics, i.e. its dimensions, shape, and refractive index profile. In order to find a causal link between the scattering pattern and the fiber morphology, a spectral analysis (Fast Fourier Transform, FFT) is performed over the scattering intensity. From the spectral data, the core diameter of a step-index optical fiber is extracted inversely.

Autoreflection scheme is based on the scheme of measuring angles by autoreflection method, according to which the radiant stamp that was registered in the plane of the analysis is at a finite distance from the front of the lens. The main advantages and disadvantages of using autoreflection and autocollimation schemes for constructing the measuring channel, which is designed to control the relative position of the elements of the optical system Space Telescope are described in this paper. Results of modeling in the Zemax software complex are given.

The paper presents the Λ-ridge and V-trough concentrator system with a low concentration ratio. Calculations and simulations have been made in the program created by the author. The results of simulation allow to choose the best parameters of photovoltaic system: the opening angle between the surface of the photovoltaic module and mirrors, resolution of the tracking system and the material for construction of the concentrator mirrors. The research shows the effect each of these parameters on the efficiency of the photovoltaic system and method of surface modeling using BRDF function. The parameters of concentrator surface (eg. surface roughness) were calculated using a new algorithm based on the BRDF function. The algorithm uses a combination of model Torrance-Sparrow and HTSG. The simulation shows the change in voltage, current and output power depending on system parameters.

Holographic exposure (i.e., exposure of a photoresist coated substrate in an interference field of two light beams), followed by development in alkaline solution and subsequent ion-beam etching, remains to be the most important technique for fabricating diffraction gratings, especially large-area gratings, despite the advance of other techniques. In this process as an intermediate product the photoresist grating serves as a mask for ion-beam etching. The shape and critical dimensions of the photoresist mask directly determine the shape and critical dimensions of the etched end product, which in turn determine the performance parameters of the grating. In a crude and yet often effective approximation the shape of the mask can be taken as rectangular and the critical dimension is duty cycle (ratio of ridge width to period). The groove depth is not critical, as long as it is large enough, and it can be controlled easily by adjusting the photoresist layer thickness during spin coating and by detecting the critical turning point of the diffraction efficiency curve of one of the grating’s dispersive orders during development when the photoresist in the trough is completely removed. Once the maximum groove depth has been reached the following development process predominantly manifests as reduction of duty cycle. While the efficiency monitoring method is effective for detecting the point of trough clearing, it is ineffective for measuring duty cycle. A one-dimensionally periodic grating is an optically anisotropic structure when the groove period and light wavelength are comparable. Diffraction efficiencies of TE and TM polarizations are different and their ratio is a monotonic function of duty cycle in the range of duty cycle of interest. We propose to use this property to estimate the duty-cycle of surface-relief holographic gratings during development. We will present our theoretical simulation results and experimental results.

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1,2,3,4]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface).

In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

It is shown that the applying of quaternions can successfully solve the problem of determining the unit vector of the beam reflected from an arbitrary system of flat mirrors, and the position of the image of a point object formed by this system.

Disadvantages of photovoltaic panels are their low efficiency and non-linear current-voltage characteristic. Therefore it is necessary to apply the maximum power tracking systems which are dependent on the sun exposure and temperature. Trackers, that are used in photovoltaic systems, differ from each other in the speed and accuracy of tracking. Typically, in order to determine the maximum power point, trackers use measure of current and voltage. The perturb and observe algorithm or the incremental conductance method are frequent in the literature. The drawback of these solutions is the need to search the entire current-voltage curve, resulting in a significant loss of power in the fast-changing lighting conditions. Modern solutions use an additional measurement of temperature, short-circuit current or open circuit voltage in order to determine the starting point of one of the above methods, what decreases the tracking time. For this paper, a sequence of simulations and tests in real shading and temperature conditions for the investigated method, which uses additional light sensor to increase the speed of the perturb and observe algorithm in fast-changing illumination conditions was performed. Due to the non-linearity of the light sensor and the photovoltaic panel and the influence of temperature on the used sensor and panel characteristics, we cannot directly determine the relationship between them. For this reason, the tested method is divided into two steps. In the first step algorithm uses the correlation curve of the light sensor and current at the maximum power point and determines the current starting point with respect of which the perturb and observe algorithm is run. When the maximum power point is reached, in a second step, the difference between the starting point and the actual maximum power point is calculated and on this basis the coefficients of correlation curve are modified.

This paper discusses theoretical and experimental results of the investigation of light beams that retain their intensity structure during propagation and focusing. Spiral laser beams are a family of laser beams that preserve the structural stability up to scale and rotation with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Functionality laser manipulators can be significantly enhanced by using spiral beams whose intensity remains invariable. It is well known, that these beams has non-zero orbital angular momentum. Spiral beams have a complicated phase distribution in cross section. In this paper we investigate the structural stability of the laser beams having a spiral phase structure by passing them through an inhomogeneous phase medium. Laser beam is passed through a medium is characterized by a random distribution of phase in the range 0..2π. The modeling was performed using VirtualLab 5.0 (manufacturer LightTrans GmbH). Compared the intensity distribution of the spiral and ordinary laser beam after the passage of the inhomogeneous medium. It is shown that the spiral beams exhibit a significantly better structural stability during the passage phase heterogeneous environments than conventional laser beams. The results obtained in the simulation are tested experimentally. Experimental results show good agreement with the theoretical results.

This work devoted to a comparative study of different designs of lightweighted mirrors, as well as a comparison of materials, of which these mirrors are made of. We consider such methods of lightweighting as: pockets (radial-circular, triangular, hexagonal), holes, contoured back (single arch and double arch), so-called «sandwich» and selection of materials.

Propagation invariant laser beams (PILBs) represent a class of coherent structured field distributions possessing several unique properties. PILB shapes have been traditionally produced as the output mode field distributions of stable laser resonators. To expand the diversity of possible PILB shapes, additional techniques have been developed, including PILB transformations with the aid of anamorphic optical systems.

The unique properties of PILBs make them an attractive choice in several optical metrology applications, including superresolution microscopy. In this paper, we apply novel PILB shapes produced with anamorphic optical systems to optical metrology of sub-wavelength sized phase objects. The anamorphic transformation technique is based on a single propagating laser field, and is therefore simpler to implement than interferometric beam transformations based on superposition of optical fields.

We explore the interactions between PILBs and nanoscale phase objects, representative of sub-wavelength lithographic patterns and nano-particles. We observe that the sensitivity of PILBs to phase perturbations is dependent on the beam shape. Analysis of the far field diffraction patterns produced can provide information about the location and shape of the nanoscale phase structures. Results of our study can be applied to high-resolution detection of small phase objects in a variety of fields within optical metrology.

Determination of refractive index is an important characteristic of material which is crucial parameter for physicists and engineers. Moiré deflectometry technique is convenient, easy-aligning, nondestructive, non-contact and fairly accurate method for refractive index measurement of gas, liquid, solid. In this paper we investigate the theory of the technique and simulate some relations then finally measure refractive index of a glassy lamella, n=1.536.