In this review paper, we present a previously proposed approach for the estimation of degree of polarization under low illumination conditions. To avoid the saturation problems, zeros from the denominator of the Degree of polarization calculation are excluded which changes the distribution of the photon detection from Poisson to a Truncated Poisson distribution. 3D polarimetric imaging experiments had been conducted via light field under low illumination environments to verify the proposed approach.
When using Shack-Hartmann wavefront sensors (SH) and Zernike coefficients (Zs) in applications where the position of the measurement and the point of interest are far apart, as it is common practice in ophthalmic optics, problems in the interpretation of the values of the Zs arise, related to how the shape of the wavefront propagates along the beam. One typical example is pupil conjugation where an auxiliary lens is added to match the size of the area of the interest of the beam with the size of the entrance pupil of the SH used for measurements. In the present work, we address this problem in the framework of a numerical scheme for modeling the beam propagation. We calculate the wavefronts with exact ray tracing plus the fitting of the impacts so as to match a rectangular grid. This procedure allows the subsequent calculation of the Zs or, similarly, the pupil function at an arbitrary plane perpendicular to the optical axis. All the numerical methods and procedures have been implemented in MATLAB code and can be illustrated by running the MATLAB script for the setup configuration that is being considered. Several examples are presented to illustrate the previous ideas and to show the real capabilities of our procedures. They will help to clarify the issues actually found in practical setups for beam manipulation, often encountered in ophthalmic optics.
Dark plasmon modes in metal nanoparticle systems are usually excited by non-optical means. We show that strongly focused illumination can lead to excitation of dark modes. We first use rigorous vectorial diffraction theory to compute the distribution of light at the focus and then numerically calculate the response of single particles and particle dimers. Controlling the distribution of light arriving at the focusing lens by pupil filters enables enhancing the excitation of dark modes. Overall, these results present guidelines for the excitation of dark plasmon modes using standard optical instrumentation.
A new phase mask typology for wavefront-coding is proposed, the meshed phase mask (MPM). It is intended
to be a flexible form in order to be easily adaptable. The use of an evaluating criterion to measure the
performance of the MPM is used to optimize its shape. The MPM is uniquely defined by the fixed phase in
a number of control points equally spaced in the pupil area. These control points define a regular mesh, and
the continuous MPM phase surface is obtained from cubic spline interpolation. A global search algorithm is
used to optimize the values at the control points, thus optimizing the MPM. The preliminary results show
an improvement over the conventional cubic phase mask, especially in reducing the undesired artefacts in
the final restored images.
Wavefront coding (WFC) is an imaging technique for enhancing some invariance capabilities of optical instruments
(typically invariance against defocus). So far, the procedure has been mostly used in practical environments where the
optical aberrations of the optical system correspond to a rotationally symmetrical one, i.e., on-axis imaging. These
problems have been extensively tackled in recent years, leading to successful designs like the cubic and petal-shaped
phase plates. An interesting aspect of the implementation of the phase plate is the use of a liquid crystal spatial light
modulator (SLM) placed at the pupil of the instrument, since it allows enhanced versatility. Under these circumstances,
the characteristics of the pupil phase plate, in order to provide invariance, refer only to spherical and defocus aberrations.
However, when the optical system is not rotationally symmetrical, like for field imaging, the theoretical framework of
the problem is quite different, as one has to deal with more general aberrations. Our aim is to analyze this field imaging
invariance problem when using WFC techniques and to try to extend the well known on-axis techniques to this new
application.
Wavefront measurements are a key point in the development of imaging techniques. Nowadays, a common tool for these
measurements is the Shack-Hartmann sensor, where the results are often given in terms of the Zernike polynomials. The
interpretation of the results, as one moves the Shack-Hartmann sensor in the axial zone, is sometimes difficult as it
involves the task of visualizing the geometrical propagation of the wavefront. We present a numerical tool based on ray
tracing that visualizes wavefronts and caustics as the beam propagates and enables the calculation of the Zernike
polynomials at any intermediate stage.
Micron-sized particles can be trapped by means of a highly focused beam; light is concentrated in a tiny spot
using a high numerical aperture objective. In this communication we describe a numerical tool we have developed
for obtaining the force exerted by a beam on a spherical dielectric particle in realistic conditions. The system
(a water immersion microscope objective) is simulated using an optical system design software that provides
the required information to feed the application. The calculation of the force is carried out using the ray-optics (Mie) approach.
We present the results of the utilization of a Spatial Light Modulator Liquid Crystal Display for the implementation of
wavefront codification procedures in an imaging system. The light modulator works in transmission mode at the pupil of the instrument. The main disadvantage is that the procedure implies a calibration of the device as well as an inherent image processing. The more interesting feature we can obtain is the versatility related to the use of an electronic device at the pupil, as compared with conventional (fixed) manufactured ones.
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.
We study different effective medium theories for describing the optical behaviour of composites consisting of spherical metallic inclusions embedded in a dielectric matrix. The analysis is performed according to the Bergman spectral density theory. This theory establishes that any effective medium model has an integral representation in terms of a function (the spectral density) that depends on the geometry of the two-phase mixture and is independent of the optical constants of the composing materials. We review classical effective medium theories (Maxwell-Garnett and Bruggeman models) according to their spectral density. Furthermore, numerical simulations based in recent works allow studying the influence of different geometric parameters in the spectral density and compare the results with the classical theories.
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 time evolution of the optical properties of nanostructured silicon nitride (ns-SiNx:H) thin films was studied by FTIR
phase-modulated ellipsometry. The samples were produced by RF-PECVD and ellipsometric measurements were performed after the deposition and at different time intervals in the spectral range between 950 and 3500 cm-1. The experimental data show an evolution from an initial not-oxidized state to a final oxidized state. The oxidation process of ns-SiNx:H films is modeled with two different approaches: i) assuming that the oxidation starts at the film surface and diffuses towards the substrate and ii) assuming a homogeneous oxidization through the entire volume of the film. The final best fitting of the data suggests that the oxidization occurs homogeneously in all the thickness of the film.
This paper is a work-in progress report on the development of sol-gel coatings for high power laser systems in the near-UV, infrared region. Silica, titania and titania-silica acid catalysed sols were prepared by using tetraethoxysilane and titanium isoproxide as precursors. Single and multi-layer coatings were generated by dipping on fused silica substrates. The single films were heated at 500°C and 900°C after deposition in order to investigate the role of the sintering temperature either on the optical properties and on the film laser-induced damage threshold at 1064 nm (Nd:YAG c.w. laser) and 351 nm (XeF excimer laser). The ageing effects due to the exposure to humidity was investigated by testing the damp heat resistance of the coatings in agreement with the ISO environmental test for optical coatings. The silica coatings have been assessed before and after the damp heat test with regard to their laser-induced-damage resistance, reflectance and transmittance properties. The optical parameters (refractive index and extinction coefficient) have been determined by UV-VIS-NIR spectrometry. A global fit procedure based on the simultaneous characterisation of several samples was used for the evaluation of the optical properties of the materials both as single films and inside multi-layer stacks.
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.
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 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.
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.
Optical properties of materials inside a multilayer stack may differ from those of single layers. This fact is specially noticeable in the case of sol-gel films obtained by dip coatings. We propose a method to determine the refractive index and thickness of materials inside a multilayer stack, based on the simultaneous characterization of several samples. The procedure increases the reliability of the results and helps in improving quality in optical coating production. (Summary only available)
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.
On the basis of a representation of the general solution of the Maxwell equations in terms of the angular spectrum of the electromagnetic field, the concept of the so-called closest solution to a given field is analyzed. In particular, we investigate the spatial profile and the polarization structure of the closest field to a polarized Gaussian beam.
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.
The intrinsic absorption of fluoride coating materials tends to higher values in the DUV/VUV spectral range. In respect to applications of this material class for DUV/VUV multilayer systems, like high reflecting mirrors and anti- reflective coatings, the control of absorption is essential for further improvement of the coating quality. However, the reliable determination of absorption losses by photometric techniques has to overcome various obstacles caused by light absorption in air, scattering effects of the coating, and absorption related to contamination of the employed fluoride material. In this contribution spectrophotometric measurements for the characterization of optical data of MgF2 and LaF3 single layers and multi layer systems are presented. An advanced VUV/DUV-spectrophotometer, which has been developed at the Laser Zentrum Hannover for the optimization of thin film production processes, is described. The subsequent optical data evaluation for fluoride single layer coatings is reported and the optical data, n and k, of MgF2 and LaF3 for the spectral range from 130 to 660 nm are presented. Transmittance and reflectance measurements of multilayer coating systems are compared to theoretical calculations for these systems on the basis of the evaluated optical data of the single layers. Observed deviations are discussed under respect of contaminations of the fluoride layer systems.
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.
Plasma polymerized hexamethyldisiloxane (PP-HMDSO) thin films have been obtained in a DC glow discharge from oxygen/HMDSO gas mixtures. Such films are successfully applied to the pr otection of Al metallisations on plastic substrates. The composition of the films (SiOxCy:H) may be varied from organic (polymer-like) to inorganic (SiO2-like) by varying the oxygen-to-monomer ration in the precursor gas mixture. The structural and functional properties of the films are studied as a function of the plasma parameters.
In high quality otpical coating systems for the DUV-spectral range, MgF2 is one of the preferred deposition materials. MgF2-coatings exhibit relatively low optical losses as well as high stability and laser induced damage thresholds. In the present joint research effort of several European laboratories, the potentiality of MgF2 is evaluated in respect to the production of improved optical coatings for applications in laser technology and semiconductor lithography. For this purpose, single layers of MgF2 were deposited on superpolished fused silica and CaF2-substrates by ion beam sputtering, boat and e-beam evaporation in different laboratories. Besides photometric inspections, the samples were characterized by an optical scatter measurement facility at 193 nm and 633 nm. The structural properties were assessed using AFM, XRD, and adapted TEM-techniques invovling conventional thinning methods for the layers. For the measurement of mechanical stress in the coatings, special silicon substrates were coated and analyzed.
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.
In this work we present the developments for the simulation of image formation through an ophthalmic lens. The procedure is, essentially an exact ray tracing taking into account the particular mobility conditions of the exit pupil. This leads to the computation of astigmatism as a function of the field angle considered. In the computer program, the use of a commercial glass with a gradient in the refractive index (GRIN material) is foreseen. This latter feature proves to be useful for two practical objectives: modifying the power and the astigmatism of the lens. To illustrate these points, an example based on a lens made by deforming a plane parallel plate of GRIN material will be presented.
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.
Thin film deposition techniques are widely used in industry because of the variety of practical applications where they may be appropriate. The manufacture of thin film coatings normally requires high vacuum equipment, with additional attachments such as electron beam evaporators, ion guns, quartz oscillator microbalance, etc. Besides the technological problems involved in the deposition of the films, the optical characterization of the coatings obtained is a major issue. For example, for wideband antireflection coating of lenses a precise control of the refractive indices and thicknesses obtained is required, together with a good uniformity inside the whole vacuum chamber. Thus, techniques for the measurement of refractive indices and thicknesses of thin films have to be available in laboratories related to the deposition plants. Several characterization apparatus are quite standard in industry, because their wide range of applications and relative low cost (spectrophotometer is the typical example). Other apparatus are much more specific and much more expensive like ellipsometers, secondary ion mass spectrometers, transmission electron microscopes--, although monochromatic ellipsometers may sometimes be accessible because of its moderate cost. Finally, very powerful desk computers are really cheap nowadays, so computation facilities are always available at any laboratory. The aim of the present work is to illustrate the combined use of three basic laboratory techniques- -spectrophotometry, monochromatic ellipsometry and computer simulation--in the development of thin film coatings and filters.
The proposal of this work is the study of a method for characterization of the focal of ophthalmic lenses whose surface refraction index has been modified by diffusion techniques based on thermal ion exchange in glass. In particular the aim is the measurement of the variations in focal length of ophthalmic lenses after undergoing a diffusion process. An interferometric technique has been used and computer simulations have also been carried out.
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.
We report quantitative evidence of the slight anisotropic behavior of several Ta2O5 dielectric thin films. Refractive indices and thickness have been determined by using the prism-film coupler setup. In order to obtain dispersion values for the refractive indices, the measurements have been realized at four different wavelengths, 632.8, 514.5, 488.0 and 457.9 nm. We have checked the results by measuring the layers with two different prisms. A new numerical approach to the problem has been useful to determine the parameters of the layers.
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.
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.
A new Fabry-Perot filter based on a silicon wafer spacer is proposed in this work. IR gas sensors based on these filters would combine excellent selectivity and signal-to-noise ratio with an overall scheme similar to that of the simplest non-dispersive IR sensors. The filter can be fitted to the fine structure of different gases, in particular those diatomic with unlike atoms as carbon monoxide among others. The spacer of the filter is a silicon wafer of defined thickness. Fine tuning to gas absorption peaks can be reached by coupling it to other multilayers. In this work the properties of silicon wafers as spacers of the proposed filters are studied. From the study it derives that the most determining factor of the filter properties is the loss of coherence caused by surface roughness. However, as we demonstrate in this work, surface roughness limitations are not very severe and easily obtained by standard polishing procedures.
Automatic inspection (locating and quality assessment) of centering marks engraved on ophthalmic lenses presents special difficulties. The scene is noisy and blurred, and the engraved marks are weak, low-contrast and partially occluded. To locate the marks, we take advantage of their binary-shaped characteristic to design a model that greatly simplifies the numerical computation of correlation without the need to binarize the scene. Three figures of merit are defined to ensure the robustness of the whole procedure: the contrast of the target against the background, the uniqueness of the correlation peak, and the similarity between target and model. By comparing these figures with suitable threshold levels, decisions can be reached based on existence, multiplicity, and completeness of the marks. The computational simplification enables a low-cost industrial implantation based on a CCD camera, a frame grabber, and a 486/33 PC. A precision of 0.1 mm in positioning is reached with a processing time of less than 1 s.
We present a complete procedure for automated inspection of engraved marks and ink marks placed on ophthalmic lenses. The engraved marks are small and weak, and are partially occluded by ink marks. The whole sense is noisy and has low contrast. A preprocessing for image enhancement is first performed. Then, a simplified numerical correlation algorithm is applied, resulting in a fast and accurate positioning of the marks. The procedure includes designing a model for the target, in a way that greatly reduces the volume of computed data. Three figures of merit are defined to ensure the robustness of the whole procedure: the contrast of the target on the background, the uniqueness of the correlation peak, and the similarity between target and model. By comparison of these figures against suitable threshold levels, decisions based on existence, multiplicity and completeness of the marks can be taken.
The generalization of a recent numerical inversion procedure for the analysis of ellipsometric data of double layer samples is described. Within this generalization, data reduction for any double absorbing layer configuration is easily accomplished. Starting from a ((Delta) , (Psi) ) measurement of a single incidence angle and single wavelength ellipsometer, our method will allow finding any two configuration parameters, provided one of them is a thickness. This reduces the constraints of previous methods, leading also to a simple 1D root- finding numerical scheme. Useful graphical procedures for the analysis of double-layer ellipsometric results are easily devised.
In the usual surface forces apparatus arrangement, the determination of the distances between interacting surfaces, as well as their mutual forces, is based on the analysis of interference fringes originated between the surfaces. To enhances the contrast and sharpness of the fringes, a thin metallic coating is applied to the mica plates that form the interaction chamber. In this paper we try to improve the performance of the basic system just described by optimizing the metallic coating and also by computer processing the images of the visible fringes.
When real time optical pattern recognition is carried out by means of spatial light modulators (SLMs), a practical situation may arise in which the size of the Fourier transform and the intensity of the light source are fixed. Then, provided the input scene and the size of the SLM allow it, an interesting possibility for improving the overall intensity in the Fourier plane is the replication of the scene. This procedure may be used in two different ways: regular along a lattice structure or non regular or random replication. In this work we analyze the usefulness of these methods, both to obtain diffraction images or cross-correlation between images in a joint transform correlator.
We present and discuss a Fabry-Perot type interferometric method that permits the concurrent measurement of the thermooptic coefficients of quartz retardation plates in the thermal range 25°-300 °C.
The design of a simple two lens system for optical diffraction operating within a fixed bench distance is analyzed. Geometrical conditions for large size Fourier transforms, as needed when using light modulators, are deduced within paraxial theory. Different configurations using different lenses but giving the same input output magnification are studied in order to specify its practical usefulness. A ray tracing based numerical criterion for assessing the quality of the diffractive system is used. Preliminary experimental results are presented.
A simple procedure to evidence inhomogeneity in the refractive index of a single
dielectric thin film included in a AR coating is developed. It requires only the
use of standard measurement equipment: a spectrophotometer and a three wavelength
e 1 lipsometer.
The results show a good agreement between different characterization methods:
reflectance, ellipsometry and single layer spectrophotometric analysis.
The limiting thickness uniformity attainable for the coating of multiple substrates
inside a thermal evaporation physical vapor deposition (PVD) unit is theoretically
analyzed. This study compares the classical spherical (dome-shaped) calotte with a plane
sectors reversible lens holder setup. This arrangement is very useful for two-sides
substrate deposition, such as antireflection coatings on lenses. The design of static
correcting shutters for this kind of configuration is also discussed. Some results of this
theoretical study are presented.
When a large scale Fourier transform is
required, the main disadvantage in the
classical architecture for optical Fourier
transforiing (froi front to back focal
planes of a lens) is its length. If special
detectors (CCD caDera), spatial
sodulators (light valve) or filters (iiquid
crystal iodulator) are to be used,
the size of the transfora has to iatch the
size of the active eleient of the device.
When perforiirig optical correlation, the
final length of the set up will be about
four times the focal length of the two
lenses (if they are equal).
Circular harionic expansion of twodiiensional
coiplex functions has proven
to be a very useful tool for the design
and experiiental realization of rotationally
invariant pattern recognition correlation
filters (1). Good practical results
iay be obtained provided that the choice
of the harionic order (nuiber of the ten
of the expansion) and the polar coordinates
origin taken are both optimized (2,3).
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