Temperature dependence of birefringence in ethanol-filled suspended core fiber

The temperature dependence of the birefringence in a suspended core fiber (SCF) has been experimentally analyzed by using a polarimetric setup. The used configuration consists of two linear polarizers and the SCF as birefringent medium. A theoretical study based on Jones matrices has been carried out to analyze the experimental observed behavior. For this, a polarimetric all-fiber configuration was used whose sensitivity depends on the wavelength variation with temperature. Results obtained show that it is strongly affected when the air holes of SCF are partially filled with ethanol.

Design of superachromatic quarter-wave retarders in a broad spectral range

A superachromatic quarter-wave retarder using an arbitrary number of waveplates in a broadband spectral range has been proposed. Their design is based on the optimization of a merit function, the achromatism degree (AcD), which represents a global behavior metric for the retardation. By means of this technique, the thickness and azimuth of each waveplate is determined. The achromatism degree is a measure of the distance between the overall retardation and a target retardation weighted by the spectrum of the incident light. We report on a particular case where all waveplates are made of quartz. As application examples, the design of a quarter-wave retarder using two, three, and four waveplates in the spectral ranges of 500-700 nm and 400-1000 nm was studied. The numerical results show that for these ranges, the best designs obtained present a maximum difference of 0.013° and 0.010° with respect to the target retardation, respectively. In addition, an analysis of their achromatic stability is presented. These results can be applied in the aerospace industry, spectroscopic ellipsometry, and spectrogoniometry, among others.

Self-imaging technique for beam collimation

A simple collimation technique based on measuring the period of one self-image produced by a diffraction grating is proposed. Transversal displacement of the grating is not required, and then automatic single-frame processing can be performed. The self-image is acquired with a CMOS camera, and the period is computed using the variogram function. Analytical and experimental results are obtained, which show the simplicity and accuracy of the proposed technique.

Circularly polarized light with high degree of circularity and low azimuthal error sensitivity

The generation of circularly polarized light with a high circularity degree and low azimuthal error sensitivity was analyzed using a system composed by two waveplates. It is shown how the high circularity degree is achieved using a combination of a half- (λ/2) and a quarter- (λ/4) waveplate λ/2+λ/4 configuration. However, the lowest azimuthal sensitivity under small variations in the azimuths of the waveplates is obtained by employing a λ/4+λ/2 configuration. Analytical calculus particularized for quartz and MgF₂ waveplates is presented.

Optimal achromatic wave retarders using two birefringent wave plates: reply

This reply attempts to cast some more light on the achromatic systems composed by wave plates, in particular to the calculus of the overall retardation and the use of the Jones matrix equivalence theorem. An equivalent expression for the overall retardation of the system in terms of the trace is also given.

Optimal achromatic wave retarders using two birefringent wave plates

Two plates of different birefringence material can be combined to obtain an achromatic wave retarder. In this work, we achieve a correction for the overall retardation of the system that extends the relation to any azimuth. Current techniques for the design of achromatic wave retarders do not present a parameter that characterizes its achromatism on a range of wavelengths. Thus, an achromatic degree has been introduced, in order to determine the optimal achromatic design composed with retarder plates for a spectrum of incident light. In particular, we have optimized a quarter retarder using two wave plates for the visible spectrum. Our technique has been compared to previous results, showing significant improvement.

Fast optical source for quantum key distribution based on semiconductor optical amplifiers

A novel integrated optical source capable of emitting faint pulses with different polarization states and with different intensity levels at 100 MHz has been developed. The source relies on a single laser diode followed by four semiconductor optical amplifiers and thin film polarizers, connected through a fiber network. The use of a single laser ensures high level of indistinguishability in time and spectrum of the pulses for the four different polarizations and three different levels of intensity. The applicability of the source is demonstrated in the lab through a free space quantum key distribution experiment which makes use of the decoy state BB84 protocol. We achieved a lower bound secure key rate of the order of 3.64 Mbps and a quantum bit error ratio as low as 1.14×10⁻² while the lower bound secure key rate became 187 bps for an equivalent attenuation of 35 dB. To our knowledge, this is the fastest polarization encoded QKD system which has been reported so far. The performance, reduced size, low power consumption and the fact that the components used can be space qualified make the source particularly suitable for secure satellite communication.

Collimation method using a double grating system

We present a collimation technique based on a double grating system to locate with high accuracy an emitter in the focal plane of a lens. Talbot self-images are projected onto the second grating producing moiré interferences. By means of two photodetectors positioned just behind the second grating, it is possible to determine the optimal position of the light source for collimation by measuring the phase shift between the signals over the two photodetectors. We obtain mathematical expressions of the signal in terms of defocus. This allows us to perform an automated technique for collimation. In addition, a simple and accurate visual criterion for collimating a light source using a lens is proposed. Experimental results that corroborate the proposed technique are also presented.

Rough Fresnel zone plates over metallic surfaces

We analyze the focusing properties of Fresnel zone plates fabricated over steel tapes using laser ablation. Our intention is to implement the use of micro-optical elements when the use of conventional chrome-glass elements is not indicated. Because of the manufacture process, the surface presents a certain anisotropic roughness, which reduces the focusing properties. First, we develop numerical simulations by means of the Rayleigh-Sommerfeld approach, showing how roughness in both levels of the Fresnel zone plate affects the focalization of the lens. We also manufacture Fresnel zone plates over steel tape, and perform experimental verification that corroborates the numerical results.

Continuous self-imaging regime with a double-grating mask

We analyze the Talbot effect produced by a mask composed of two diffraction gratings. Combinations with phase and amplitude gratings have been studied in the near-field regime. For a two-phase-gratings configuration, the Talbot effect is canceled, even when using monochromatic light; that is, the intensity distribution is nearly independent of the distance from the mask to the observation plane. Therefore, the mechanical tolerances of devices that use the Talbot effect may be improved. In addition, the spatial frequency of the fringes is quadrupled, which improves the accuracy of devices that employ this mask. An experimental verification for the best case two phase gratings, has also been performed, validating the theoretical results.

Correlation technique for the compensation of diffraction widening of optical reference signals

Two-grating measurement systems are routinely employed for high-resolution measurements of angular and linear displacement. Usually, these systems incorporate zero reference codes (ZRCs) to obtain a zero reference signal (ZRS), which is used as a stage-homing signal. This signal provides absolute information of the position to the otherwise relative information provided by the two-grating incremental subsystems. A zero reference signal is commonly obtained illuminating the superposition of two identical pseudorandom codes and registering the transmitted light by means of a photodiode. To increase the resolution of the system, a reduction of the grating period and the ZRC widths is required. Due to this reduction, the diffractive effects produce a widening of the ZRS and, in turn, a loss of the measuring accuracy. In this work, we propose a method to narrow the distorted signal obtained with a Lau-based encoder, reinstating the accuracy of the ZRS. The method consists of the inclusion of a correlation mask on the detector. A theoretical model to design the mask has been developed, and experimental results have been obtained that validate the proposed technique.

Hyperparabolic concentrators

We present a family of three-dimensional concentrators constructed from the photic field generated by a Lambertian emitter. The profile of these concentrators is obtained from the field lines for a two-dimensional truncated wedge and is based on the union between a hyperbola and a tilted parabola. By revolution of this profile, we obtain hyperparabolic concentrators (HPCs). In the limiting case when the focal length of the hyperbola becomes the radius of the exit aperture, the HPC becomes the well-known compound parabolic concentrator. On the other hand, when the focal length of the hyperbola becomes infinite, the HPC achieves the thermodynamic limit of concentration.

Diffraction of gratings with rough edges

We analyze the far field and near field diffraction pattern produced by an amplitude grating whose strips present rough edges. Due to the stochastic nature of the edges a statistical approach is performed. The grating with rough edges is not purely periodic, although it still divides the incident beam in diffracted orders. The intensity of each diffraction order is modified by the statistical properties of the irregular edges and it strongly decreases when roughness increases except for the zero-th diffraction order. This decreasing firstly affects to the higher orders. Then, it is possible to obtain an amplitude binary grating with only diffraction orders -1, 0 and +1. On the other hand, numerical simulations based on Rayleigh-Sommerfeld approach have been used for the case of near field. They show that the edges of the self-images are smoother than the edges of the grating. Finally, we fabricate gratings with rough edges and an experimental verification of the results is performed.

Self-imaging of gratings with rough strips

We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low- and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work.

Q(M) and the depolarization index scalar metrics

A depolarization scalar metric for Mueller matrices, named Q(M), is derived from the degree of polarization. Q(M) has been recently reported, and it has been deduced from the nine bilinear constraints between the sixteen elements of the Mueller-Jones matrix. We discuss the relations between Q(M) and the depolarization index.

Far field of gratings with rough strips

In this work, we analyze the far-field pattern produced by a grating made of strips with two different random roughness levels. The efficiency and shape of the diffraction orders is obtained, which are shown to depend on the statistical properties of roughness. We assume for the calculations that the grating can be used in a mobile mechanical system. A preliminary experimental approach which partially corroborates the theoretical results is also performed.

Invariant grating pseudoimaging using polychromatic light and a finite extension source

The Talbot effect is a well studied phenomenon by which grating pseudoimages appear at certain periodic distances when monochromatic light is used. Recently, numerical simulations have shown a new phenomenon; when a polychromatic light beam is used in a double grating system, the intensity of the pseudoimages presents a transverse-profile that remains unaffected over a wide range of propagation distances. This effect can be used to increase the tolerances of gratings based optical devices, such as displacement measurement systems, interferometers, and spectrometers. The pseudoimages formation with a polychromatic and finite extension light source is analytically and experimentally demonstrated. Relatively simple analytical expressions for the intensity and the contrast allow us to predict when pseudoimages present a constant contrast and when they disappear. Furthermore, we experimentally obtain the pseudoimages using the proposed configuration, corroborating the theoretical predictions.

Hemispheric laterality and dissociative tendencies: Differences in emotional processing in a dichotic listening task

The present work investigates whether the hemispheric processing of both verbal and emotional stimuli, studied by means of a dichotic listening task, differs between normal high and low dissociators as assessed by the Dissociative Experiences Scale (DES; Bernstein & Putnam (1986). Development, reliability and validity of a dissociation scale. Journal of Nervous and Mental Disease, 174(2), 727-735). Two groups of subjects (50 high and 50 low dissociators), participated in the experiment. The task consisted in identifying both verbal and emotional stimulus-targets, respectively, on successive sessions. Reaction time and response accuracy were registered and analysed using ANOVA (Analysis of Variance). The interaction between stimuli (verbal, emotional), channel (right ear, left ear), and dissociation level (high, low) reached statistical significance in terms of accuracy measures (d': F(1,98)=4.75; p<.05). Both high and low dissociators exhibited the expected right ear advantage (REA effect) on verbal targets. On the other hand, whereas low dissociators exhibited the expected left ear advantage (LEA effect) on emotional targets, high dissociators failed to follow this typical pattern of hemispheric asymmetry: both hemispheres exhibited similar performances. These results confirm the hypothesis that dissociation is related to changes in hemispheric processing, specifically of emotional information.

Variogram-based method for contrast measurement

We present a technique for determining the contrast of an intensity distribution in the presence of additive noise and other effects, such as undesired local amplitude or offset variations. The method is based on the variogram function. It just requires the measurement of the variogram at only four points and, as a consequence, it is very fast. The proposed technique is compared with other standard techniques, showing a reduction in the error of the contrast measurement.

Talbot effect with rough reflection gratings

The Talbot effect is analyzed when steel tape gratings are used. These gratings are made on a steel substrate, and, because of the manufacture process, both levels of the grating are rough with different roughness parameters. A theoretical analysis based on Fresnel regime, which considers the statistical properties of roughness, is developed. Analytical formulas that show a decreasing exponential dependence on the intensity in terms of the distance between the grating and the observation plane are obtained, and an experimental verification is also performed.

Elliptical concentrators

Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.

Uncertainty estimation by convolution using spatial statistics

Kriging has proven to be a useful tool in image processing since it behaves, under regular sampling, as a convolution. Convolution kernels obtained with kriging allow noise filtering and include the effects of the random fluctuations of the experimental data and the resolution of the measuring devices. The uncertainty at each location of the image can also be determined using kriging. However, this procedure is slow since, currently, only matrix methods are available. In this work, we compare the way kriging performs the uncertainty estimation with the standard statistical technique for magnitudes without spatial dependence. As a result, we propose a much faster technique, based on the variogram, to determine the uncertainty using a convolutional procedure. We check the validity of this approach by applying it to one-dimensional images obtained in diffractometry and two-dimensional images obtained by shadow moire.

Design of two-dimensional zero reference codes with a genetic algorithm

In mask-alignment systems a reference signal is needed to align the mask with the silicon wafers. The optical reference signal is the autocorrelation of two two-dimensional (2D) codes with binary transmittance. For a long time, one-dimensional codes have been used in grating-measurement systems to obtain a reference signal. The design of this type of code has needed a great computational effort, which limits the size of the code to about 100 elements. Recently, we have applied genetic algorithms to design codes with arbitrary length. We propose the application of these algorithms to design 2D codes to generate 2D optical signals used in mask-alignment systems.

Optimal design of optical reference signals by use of a genetic algorithm

A new technique for the generation of optical reference signals with optimal properties is presented. In grating measurement systems a reference signal is needed to achieve an absolute measurement of the position. The optical signal is the autocorrelation of two codes with binary transmittance. For a long time, the design of this type of code has required great computational effort, which limits the size of the code to approximately 30 elements. Recently, the application of the dividing rectangles (DIRECT) algorithm has allowed the automatic design of codes up to 100 elements. Because of the binary nature of the problem and the parallel processing of the genetic algorithms, these algorithms are efficient tools for obtaining codes with particular autocorrelation properties. We design optimum zero reference codes with arbitrary length by means of a genetic algorithm enhanced with a restricted search operator.

Determination of the optimum sampling frequency of noisy images by spatial statistics

In optical metrology the final experimental result is normally an image acquired with a CCD camera. Owing to the sampling at the image, an interpolation is usually required. For determining the error in the measured parameters with that image, knowledge of the uncertainty at the interpolation is essential. We analyze how kriging, an estimator used in spatial statistics, can generate convolution kernels for filtering noise in regularly sampled images. The convolution kernel obtained with kriging explicitly depends on the spatial correlation and also on metrological conditions, such as the random fluctuations of the measured quantity, and the resolution of the measuring devices. Kriging, in addition, allows us to determine the uncertainty of the interpolation, and we have analyzed it in terms of the sampling frequency and the random fluctuations of the image, comparing it with Nyquist criterion. By use of kriging, it is possible to determine the optimum-required sampling frequency for a noisy image so that the uncertainty at interpolation is below a threshold value.

Design of two-dimensional zero reference codes by means of a global optimization method

A method to obtain the absolute measure of the position is by means of the autocorrelation of two zero reference marks. In one-axis measurement systems one dimensional mark are used and the design of these marks is relatively complex. When the movement is in two-axes, two dimensional reference marks are required and they are even harder to design. We report a method of global optimization to calculate the optimal two dimensional zero reference marks which generate the reference signal with the highest central peak. This method proves to be a powerful tool for solving this problem.

Estimation of the standard deviation in three-dimensional microscopy by spatial statistics

Usually, the calibration process for three-dimensional microscopy involves the use of a reference flat surface. The random fluctuations of the topographic image for this reference surface are used for determining the uncertainty of the microscope. When the sample material or the measuring conditions of the microscope are modified (such as the objective used in a confocal microscope, or the tip in an atomic force microscope), the measuring conditions vary and thus a new calibration is required. In this work, a technique based on spatial statistics methods (more specifically, the variogram function) is proposed to determine accurately the standard deviation for three-dimensional microscopy that does not require a reference flat surface and therefore eliminates the need for a previous calibration process of this parameter.

Design of zero reference codes by means of a global optimization method

The grating measurement systems can be used for displacement and angle measurements. They require of zero reference codes to obtain zero reference signals and absolute measures. The zero reference signals are obtained from the autocorrelation of two identical zero reference codes. The design of codes which generate optimum signals is rather complex, especially for larges codes. In this paper we present a global optimization method, a DIRECT algorithm for the design of zero reference codes. This method proves to be a powerful tool for solving this inverse problem.

Detection and measurement of waviness on thin metallic wires

We propose a model for determining the far-field diffraction pattern of wires with waviness. Analytical solutions are obtained by means of the stationary phase method, which allows us to determine dimensional parameters such as wire diameter and waviness factor. Experimental results are presented, which are in accordance with our theoretical description.

Zero reference signal for displacement measuring systems by use of speckle

An optical method for generating a reference signal for an incremental displacement measurement system is proposed. We achieved this zero reference signal by comparing two speckle patterns arriving from two symmetric diffusers, which are used as natural random codes that are identical only when the reading head is located equidistantly between the diffusers. The comparison of the speckles is obtained either by interference, as in a Michelson interferometer, or by intensity correlations.

Analysis of nanostructured porous films by measurement of adsorption isotherms with optical fiber and ellipsometry

An optical method to determine the nanostructure and the morphology of porous thin films is presented. This procedure is based on the response of a side-polished optical fiber with the film under study, when an adsorption-desorption cycle is carried out. Spectroscopic ellipsometry provides additional information about the optical properties and adsorption behavior of the film. Pore size distribution, anisotropy, and inhomogeneity of films can be determined by use of these two complementary techniques. To check the performances and suitability of the optical method, we have characterized a typical porous material: a TiO2 film deposited by evaporation. Water vapor has been used for the adsorption cycles. The well-known columnar structure of the evaporated TiO2 has been evidenced, and the relation between the nanostructure and the optical properties of the film is showed.

Experimental measurements of generalized grating images

The term generalized grating imaging is used to describe the process of image formation of a grating using only another grating as imaging system. The moiré and the Lau effects could be regarded as particular cases of such a process. Here we deal with the less-studied case of images formed at finite distances from the gratings, using an extended monochromatic light source. Some experimental results are shown for the images obtained in this last case, and they are compared with theoretical predictions.

Calculation of optical imbalances in ophthalmic lenses using a new algorithm based on the local dioptric power matrix formalism

We present a new algorithm to calculate the optical imbalances and differential prismatic effects that appear when two eyes look at an object through correcting eyeglasses. These are important magnitudes in ophthalmic optics because large amounts of them will disturb the binocular vision of the spectacle wearer. As a practical application of our algorithm, the distribution of optical imbalances and differential prismatic powers for a pair of progressive addition lenses has been calculated, and we obtain information about the effects of this kind of lens on the binocular vision of the wearer.

Enhancement of surface inspection by Moiré interferometry using flexible reference gratings

We have extended the use of shadow Moiré technique to be implemented in simple curved surfaces by using a flexible grating. Dynamic visual inspection of surface micro-damages is significantly favored by the use of well adapted pliable gratings compared to the use of flat reference gratings. The experimental set-up consists of a plastic foil with a printed Ronchi grating stretched between three points which adapts to any cylindrical or conical convex surface independently of the relative orientation grating/surface. Static quantification of defects profiles is also possible with an attached CCD camera. Visual detection of defects in the range of ~30 microm in depth is obtainable.

Adsorption of water on porous Vycor glass studied by ellipsometry

The variation of the optical properties of porous Vycor glass (Corning, Model 7930) under different relative-humidity conditions was studied. The adsorption of water into the glass pores was investigated with spectroscopic ellipsometry. The change of the refractive index was Deltan approximately 0.04 between 5% and 90% relative humidity. A linear relation between the ellipsometer parameter tan Psi, the amount of water adsorbed in the glass pores, and information about the pore-size distributions was established. The results are in accord with the values obtained from N2 isotherms, transmission electron microscope micrographs, and the manufacturer's specifications (radius of approximately 20 A). The possibility of using this material as a transducer for implementation in a fiber-optic sensor to measure humidity was evaluated.

Thermal influences on optical properties of light-emitting diodes: a semiempirical model

The application of LED technology to fields such as alphanumerical displays and traffic control is continuously increasing. Because the technology is used outdoors, it must be able to operate under various environmental conditions. Like all semiconductor devices, LED's have properties that change with temperature. We propose a semiempirical model, based on semiconductor solid-state theory, that predicts the changes in the emission spectrum including the effect of temperature changes on the optical properties of the LED, within a range appropriate for outdoor applications (0-40 degrees C). This model permits us to evaluate the changes in the output flux and the chromaticity coordinates of the LED. We checked this model with seven different LED's.

Deflectometric measurement of mechanical spectacle lens deformation

The warpage of a set of six hard resin spherical lenses was measured when they were compressed by means of the tangential force exerted by a metal frame. The technique employed to measure the lenses improves over previous work both because greater precision is achieved, and because radii of curvature are measured in two perpendicular meridians. In this work, a representative sample of lenses has been used in order to test the way in which deformation depends on lens power and base. It is found that the induced warpage is enough to move the tested lenses between different base families, spoiling the initial design of the manufacturer.

Histogram-based method for contrast measurement

A histogram-based technique for robust contrast measurement is proposed. The method is based on fitting the histogram of the measured image to the histogram of a model function, and it can be used for contrast determination in fringe patterns. Simulated and experimental results are presented.

Reflection optical encoders as three-grating moiré systems

Reflection optical encoders are studied as three-grating moiré systems. An analysis is made of the differences that may appear between it and the standard case in which an optical encoder is regarded as a two-grating system.