We demonstrate here that it is possible to fabricate 1D and 2D diffraction gratings on the (001) surface of RbTiOPO4
(RTP) and KTiOPO4 (KTP) single crystals. We analyzed the linear and nonlinear optical properties of 1D and 2D
nonlinear photonic crystals. We show enhanced second harmonics when the samples were illuminated with a pulsed
Nd:YAG laser, when compared to non-structured surface of the same materials and mainly there exists an asymmetry on
the diffraction patterns of the second harmonic generated light, showing higher intensity in diffraction orders different to
the zero order in the reflection configuration.
Wave-front coding techniques are being used nowadays in vision systems to obtain invariance to aberrations and,
especially, extended depth of focus capabilities. Besides using a phase mask for coding, one of the basic steps of the
method is the digital processing of the images captured by means of a pixelated sensor (for example a CCD device).
This capture process can become crucial for the overall performance of the procedures, since the effects due to the
averaging within a pixel and to the related noise inherent to the detection can be indeed the most determinant ones.
This work presents a simulation tool for fully assessing the role of a pixelated sensor in a vision system working by
wave-front coding techniques, including diffractive effects, the averaging in detection, the modeling of the noise that
might be added and the influence in the restoration algorithm. The numerical tool computes (in order): diffraction
during image formation, averaging at the pixels and digital image processing. Similarly, noise could be added to the
detection as well as other effects influencing the final image quality.
The influence of these topics in the design of the phase masks is analyzed for several cases. Our results show that the
pixelated character of the detector can not be considered a final refinement only and can not be obviated in the design
stage of phase plates for wave-front coding.
The effect of the 2D structured noise on the post-processing of images in hybrid optical-digital imaging systems is studied on the basis of the Wiener restoration filter. 2D structured noise is modeled as an additive noise that has the same random value along a row or a column in the image. The restoration is carried out with the Wiener filter in an unsupervised way by the use of well established procedures to determine the filter constant as a function of the noise power. We show that the classical Wiener filter is not satisfactory for the case of systems affected by 2D noise and we conclude that this is caused by an overdetermantion of the 2D noise in the procedure to find the filter constant. From this conclusion we propose a new filter based on the separability of the Optical Transfer Function of the optical system that depends on two constants, one for each principal direction of the 2D noise. Furthermore, we define a procedure for the unsupervised determination of these constants and we evaluate the quality of the restoration obtained by this procedure.
We analyze the performances of the most known phase filter design (the cubic phase plate) in wavefront coding systems with respect to on- and off-axis imaging. To this end, the PSF will be calculated at different off-axis positions and the contribution of coma and astigmatism aberration terms to its spatial variation will be evaluated. The study will include the subsequent digital image processing procedure as well, so that a clear idea of the overall system performance will be drawn.
Omnidirectional mirrors are multilayer periodic structures that reflect light in a wide range of wavelengths for all angles of incidence and for all polarizations of the incident light. These structures can be made using the porous silicon technology: the layers are electrochemically etched to have different porosities, corresponding to different refractive indices. Since the porosity depends on the current density of the electrochemical etching process, the layers may have any refractive index value from 1.2 to 2.7. In opposition to classical evaporated thin films where the refractive indices are fixed, this offers a new degree of freedom in the design of such structures. In this work, the four main parameters of a basic omnidirectional mirror (refractive index of the two kinds of layers and their optical thicknesses) are analyzed to find the condition to obtain the maximum width of the omnidirectional reflection band. The analysis is made using the framwork of the Photonic Band Gap materials and considering the omnidirectional mirrors as 1-D Photonic Crystals.
The effect of considering dissipation in the model for the metallic component of metallo-dielectric photonic crystals is studied. The study has been carried out with the Transfer-Matrix Method with the help of the TRANSLIGHT software package. The influence of the filling fraction and of the background dielectric constant on the width of the second band gap and on the cut-off frequency for E-polarization has been analyzed. The influence of different levels of dissipation on the transmittance and reflectance spectra and on the absorption has been calculated, with special attention to the absorption induced at the plasmonic resonances in H-polarization.
We develop a method for the calculation of the integrals arising in the diffraction theory of aberrations. This method is developed from in a previous one based in the division of the diffracting aperture in semiperiodic zones, which enabled the exact calculation of the Point-Spread Function of an optical system. By a careful analysis of the integration process and of the properties of the semiperiodic zones, we develop a set of formulae that give an approximate value of the result of the diffraction integrals. This permits to avoid the numerical calculation of the integrals, which is a computationally intensive procedure and enables a substantial reduction of the computation times. The method has been tested on aberration-free optical systems and real optical systems and has shown a good accuracy, although some minor problems require further investigation.
Many practical approaches have been developed for computing the point spread function (PSF) of imaging systems and the subject has been extensively studied for many years, since this has been a classical topic in optics. In recent times, the exact numerical calculation of the diffraction integrals and, hence, of the PSF of image forming systems has been successfully addressed. These methods are based on the determination of the critical points and the semi-periodic zones of the integrand on the plane of the aperture, followed by the summation for each of the zones. In the present work we address a comparison between an approximate calculation method based on the classical approach and the cited exact numerical procedures, mainly regarding the required computational effort involved.
The improvement in production process of high quality optics needs routinary accurate characterization of the optical properties of the sample. Whereas some commercial instruments allow accurate measurements of the transmitted and reflected light, the measurement of the scattered light very often falls below the detection level when standard attachments, like the Ulbricht integrating sphere, are used. In order to characterize scattering levels below 10-3 dedicated set ups are usually used which are quite complicate to run and often do not fit the need of a production department. In this work we present the design and test of scatterometers based on the Coblentz sphere that fit inside a Perkin-Elmer λ-900 spectrophotometer. They are aimed to the measurement of light scattering in both the transmittion and the reflection hemisphere with a detection limit in the range of 50 ppm. The Coblentz sphere is a mirror like collector of the scattered light and does not suffer of the typical limitations of the Ulbricht sphere in terms of low collecting efficiency and spectral limitation in the UV edge. As an example, LaF3 films on silica samples were first characterized with both conventional photometric techniques (specular reflectance and direct transmittance) and ellipsometry and the film thicknesses and refractive indices, as well as inhomogeneity and interface layers, were determined. The scattering data were also independently analysed by considering the vector theory of scattering and the effect on the simulated spectral TS of several power spectrum densities obtained with different hypothesis on the correlation between interfaces.
The optical behavior of multilayer coatings for the VUV region is determined by dispersion and absorption of the used materials, non-ideal interfaces between layers and thickness of each component layer. Therefore, an accurate characterization of a multilayer stack encounters the inherent difficulties related to dealing with a high number of defining parameters. The use of on-line data (data acquired during the deposition process) allows a more precise characterization of the coatings, in comparison with the use of standard spectrophotometric measurements obtained after the deposition of the layers. Here we present the results of the characterization of a high reflecting coating where the component materials are fluorides (LaF3 and MgF2). Several models with an increasing degree of complexity and assuming different multilayer growing concepts have been applied for the description of the analyzed sample.
We report the comparison between two methods to evaluate optical systems. The flux-tracing method is an extension of the classical ray-tracing methods with additional energetic features. The direct integration method involves the calculation of the integral appearing in the diffraction theory of aberrations. We give a brief outline of the two methods and compare the results on a standard optical system. This will help to put in common the two methods to try to formulate new algorithms for the design of optical systems.
The diffraction theory of aberrations involves the calculation of the Rayleigh-Sommerfeld (RS) integral taking into account that the wave arriving to the diffracting aperture is affected by the aberrations of the optical system and assuming the exit pupil (EP) as the diffracting aperture. This last assumption is just an approximation, since the actual diffracting aperture is the aperture stop (AS) of the system. In this work we show that using the geometrical-numerical approach for the calculation of the RS integral developed at the Optics Laboratory of the Universitat de Barcelona, it is possible to perform the calculation of the point spread function (PSF) of an optical system using as diffracting aperture the AS or the EP. We will prove that the results may indeed be different in some cases and we will present experimental evidences.
We present the study of the resolving power of real optical systems in the light of new methods for the calculation of the expressions involved in the diffraction theory of aberrations. These new methods permit the exact calculation of the diffraction integrals, thus avoiding the inaccuracies of the usual approximations. We show the effect of the phase difference between the two point sources and of the plane of observation, in the resolution capabilities of an optical system composed by a lens and a circular aperture.
We present an educational resource based in a virtual optical laboratory for undergraduate students. It consists in a web-based textbook with several applets to illustrate the theory and simplify the teaching tasks in the classroom. These programs can also be used as a method for self-learning in an on-line environment. Applets are written in Java language using the Java Network Launching Protocol (JNPL) for avoiding problems related with the use of specific browsers or Java interpreters versions.
The optical characterization of materials in thin film phase is a standard task in the field of coating technology. One typical problem is the optical characterization of a single layer of material deposited on a well-known substrate. Provided the physical model considered for the modeling is correct and the available experimental date (usually spectrophotometric or ellipsometric spectra) are accurate, a precise optical characterization is quite straightforward. However, there are experimental circumstances where several samples have been coated under very well defined conditions. As when they have been obtained in the same coating run, so that no differences are expected due to the positions of each individual sample inside the chamber during the deposition process. The aim of this work is to present an improved procedure for the optical characterization of the material deposited under the very well controlled conditions explained above. The basis of our method is to use the a priori information about the identical nature of all the samples, introducing all the spectrophotometric and/or ellipsometric data available from optical properties of the layers, as compared with the separate (individual) characterization of the samples. We will illustrate our procedures for MgF2 films in the range 200-800 nm.
For the roughness characterization of optical surfaces a new procedure based on the analysis of their power spectral density (PSD) functions has been developed. The method consists of the fitting of the PSD obtained from Atomic Force Microscopy measurements at different scan sizes to mathematical models. With this procedure the micro- structural properties of optical surfaces and coatings can be represented by a reduced set of numbers that correspond to the characteristic parameters of the mathematical models. For optical coatings this method allows a separate study of the influence of the substrate and layers on the overall sample roughness. As an example, the method is applied to MgF2 and LaF3 films for VUV applications. We investigated a set of single layers deposited onto superpolished Caf2, fused silica and Si substrates. The samples were deposited by ion beam sputtering, boat and e- beam evaporation. A comparison of the influence of the substrate on the development of the roughnesses and lateral structures has been performed, as well as a study of the dependence of the roughness properties of the coatings on the deposition process. Complementary investigations of roughness-related scattering consisting of measurements of Total Scatter at 193 nm and 633 nm and calculation of expected scattering based on the theory are presented.
The numerical calculation of diffraction integrals in systems with aberrations is addressed from the point of view of a new geometrical interpretation of the diffraction phenomena. This interpretation is based on the division of the integration domain in semiperiodic zones that isolate the integrand oscillations. Moreover, the critical points of the aperture allow to identify the zones with a net contribution to the diffracted field. With the help of this interpretation it is possible to define methods for calculating the diffraction of a spherical wave incident on an aperture. We study the problems that arise when these methods have to be applied to waves in aberrated systems and we propose a solution based on the analysis of the behavior of the optical path of the wave incident on the exit pupil of the system.
The optical characterization of materials in thin film phase is a standard task in the field of coating technology. There are experimental circumstances where the accurate comparison between several deposition processes (for the same material) is important. In these cases, several sets of substrates are coated at the different deposition plants. The samples will be subsequently analyzed using, if the plants are at different locations, different spectrophometers and finally the results of all the optical characterizations will be compared. The aim of this work is to present the results of a global procedure for the optical characterization of LaF3 in the UV-visible region, deposited at three different plants. We have used R and T spectrophotometric data and we have assumed the following model for the optical characterization: n(λ)=n0+n1/λ2, k(λ)=k0 exp(k1/(λ). Our method characterizes all the samples from the same deposition process by a single set of parameters (instead of a set for each sample), using all the available measurements to determine them in a single numerical fitting, without a significant loss in the quality of the fittins. This procedure reduces the number of parameters and makes the comparison between different deposition processes more clear. By using similar results obtained for MgF2 the optical characterization of stacks (manufactured using MgF2 and LaF3) is also presented.
A numerical procedure for solving the effective medium approximation equations for ellipsometric data analysis is presented. The idea is to transform the complex root-finding problem into a minimization task in real space. Thus, the method can be implemented through a standard downhill simplex algorithm, leading to a general, simple and useful technique for ellipsometric developments.
Optical thin films are nowadays major obstacles in deep UV lithography. Scattering and absorption losses are the dominant factors which limit their optical performances. The reduction of scattering requires the development of specific deposition techniques. As a new way of manufacturing optical thin films for 193 nm applications, we applied Ion Beam Sputtering (IBS) to fluoride coatings previously developed for 355 nm. In order to check the ability of IBS to reduce the scattering losses of coatings, various quarterwave and halfwave coatings as well as multilayer stacks deposited onto fused silica and CaF2 substrates were produced and characterized by total scattering (TS) measurements at 193 nm. An AFM was used for direct imaging of the surface features and calculation of rms surface roughnesses. Subsequent data processing provided power spectral density curves containing more detailed roughness information. The evolution of the surface roughness and scattering with increasing film thickness or number of layers was analyzed and the results were discussed in order to determine the origin of the scattering and to highlight the benefits which can be expected from IBS processes.
After analyzing the problems related to finding a small shape in a scene, we introduce a nonparametric similarity measure based on the Kolmogorov-Smirnov statistic, which proves to be robust for template-matching problems where a target of binary characteristics is to be located inside a gray-scale image. We show that the Kolmogorov-Smirnov statistic gives the optimum thresholding level for the image and may be computed without actual thresholding of the image. Some interesting properties of the proposed similarity measure are exposed and compared to the corresponding properties of normalized correlation.
In this work we analyze the effects of signal-dependent noise in the input scenes of optical correlators. We propose several algorithms to process this noise and we evaluate their performance. In particular we compare the strategy of restoring the input scene with noise and perform the correlation, with the alternative of correlating directly using filters designed to take into account the noise model in the input image.
In this work we present the application of the Kolmogorov- Smirnov binary-domain measure of similarity to grey scale targets. This generalization consist of the generation of a template by thresholding the target. The threshold level is selected according to an optimality criterion with respect to a metric of performance of the detection algorithm. We examine the reduction of the computation time of the algorithm and its noise robustness, and finally we show an example of application.
The Kolmogorov-Smirnov statistical test is applied to the recognition of a binary template in gray-scale scenes. The development uses mathematical morphology to define two subsets of points in the scene deduced from the shape of the template. Then, the Kolmogorov-Smirnov statistic is computed from the histograms of the two subsets and used as a similarity measure. This method is applied to locating engraved centering marks contained in images taken from an industrial environment. Besides, the method is also used to carry out a post processing of the output given by a joint transform correlator.
The use of correlation methods in pattern recognition is a well known technique to detect the absence, presence and even the spatial or temporal position of any signal within another signal embedded in a complex background. Blurring, rotation, scaling, and noise often lead to false alarms in the correlation plane when working with images. Simple thresholding algorithms then might give the wrong correlation peak. Often, however, the human user can easily define the correct peak by taking into account the shape and surrounding of those local maxima that could represent the correlation peak. Sometimes less obvious factors have influence on the user's decision to discriminate between wrong and false peaks. These factors have to be interrogated and transferred into quantities that can be accessed by the computer. For example, it is possible in some applications (e.g., stress analysis in experimental mechanics) to predict the peak's location to be within a certain area of the correlation plane. Thus, this quantity could be used as well. In many cases, however, it is not easy to define mathematical relations between these input variables that lead to a quantity that helps to distinguish between wrong and correct peaks. All these facts lead to the introduction of fuzzy logic to be used on the correlation plane to decide which of the local maxima corresponds to the correct correlation peak. Fuzzy logic simplifies the way in which input quantities and rules that connect these quantities have to be defined. This way the discrimination capability of different correlation methods could be greatly improved.
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