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.

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.

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.

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.

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.