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The use of refractometers to investigate the nature of liquids is very common. Here it is shown that surface relief diffraction gratings can be used to measure the refractive index of liquids. Calibration plots showing the relation between first order intensity as a function of refractive index are shown. We also developed a microfluidic device behaving as a grating which is used as refractometer where a very small amount of liquid (microliters) is used.

Variations of the induced retardance in the aperture of liquid-crystal variable retarders LCVR and spatial light modulators LC-SLM are measured. It is found that the induced retardance, in LCVR, shows variations over the aperture which depend on the wavelength of the light used and the voltage applied. Larger retardance variations appear near to the edges of the cell. There are also larger variations in the maximum and minimum unwrapped retardances in the retardance versus voltage curves. These voltage values and the edges positions of the cells should be avoided in applications of these devices. On the other hand, the induced retardance is calculated pixel by pixel in LC-SLM. For the same gray level over the entire LC-SLM screen, there are differences in the induced retardance between pixels located in a central area and pixels located in the edges. For correct calibration of the LC-SLM, the retardance value as a function of gray level was determined, pixel by pixel.

The design and construction of a Full-Stokes Imaging polarimeter is presented. The device uses a telescope optical system and a polarization state analyzer (PSA) to obtain polarimetric images on a CCD. The PSA employs two liquid crystal variable retarders (LCVR) and a linear polarizer to measure the four Stokes parameters. The Stokes polarimetry method used in this paper is based on the application of six combinations of retardance values on the LCVRs. A well-known method is used to extract all the Stokes vector parameters from this intensity data. Due to experimental errors, a calibration is necessary. The calibration method used in this paper, also calculates the errors in the experimental set-up by fitting the experimental intensity measurements for the calibration samples to a theoretical polarimeter with errors. In this case, we used incident 45° polarized light to control the output polarization, and six calibration samples. The errors calculated in the method include the axes alignment errors and the errors in the retardance values of both LCVRs. The acquisition of Stokes images used a telescope optical system with a CCD camera.

The effect of Seidel aberrations on the focusing of ultrashort optical pulses by a perfectly conducting spherical mirror, which is a dispersionless system, is presented in this paper showing that aberrations change the pulse duration.

Here we present a refractometer for liquids based on a sinusoidal relief grating immersed in a small cuvette. He – Ne light is sent to the cuvette + grating device where it is diffracted. Zero, +1 and -1 orders appear. It is possible to calibrate the device by measuring +1 order intensity, when different liquids with known refractive index are poured in the cuvette. A theoretical study has been developed that supports the experimental results.

In this work we present a method used to study the spherical and chromatic aberrations contribution near the focal point of a refractive optical system. The actual focal position is measured by scanning a pinhole attached on the front of a power detector, which are scanned along the optical axis using a motorized stage with 1 μm resolution. Spherical aberration contribution was analyzed by changing the pupil aperture, by modifying the size of the input iris diaphragm and for each case, measuring the actual laser power vs the detector position. Chromatic aberration was analyzed by performing the same procedure but in this case we used an ultra-broad-band femtosecond laser. The results between ML and CW operation were compare. Experimental results are presented.

A comparison between two experimental techniques to characterize retardance as a function of applied voltage of liquid crystal variable retarders (LCVR) is presented. In the first method the variable retarder was rotated between two polarizers with their transmission axes parallel, and the retardance was calculated from the Fourier series coefficients for each applied voltage. The second method involved using two polarizers with their transmission axes perpendicular to each other, the variable retarder was placed between the polarizers with its optical axis at 45° from the horizontal, and a final stage known as "phase unwrapping" is used on experimental data to obtain the voltage-retardance function. With these two experimental methods, the voltage-retardance relationship was obtained. To verify the accuracy of this characterization a second experiment involving the production of specific polarization states was performed as the basis of a Mueller polarimeter. A method based on measuring the optical signal resulting from the application of a predetermined set of fixed values of retardance in each retarder was used. 16 elements of the Mueller matrix of a polarizer with its transmission axis at 0° and 90° were measured, and the results are compared to the expected theoretical values.

Light scattering has been used as a method of characterizing material or surface roughness in different areas of the science and technology, usually the surface is illuminated with light and the pattern of scattering is measured above the surface. In the literature, the scattered light has been measured using an incident beam with a diameter on the order of a few cm for surfaces with roughness scales of the order of microns, mainly to avoid problems with the speckle pattern of light. However, this kind of measurement does not give information on local variations in roughness or defects present in the sample. Also, it has been reported in many studies that the polarization of the scattered light is affected by the surface material and roughness. In this paper we present a novel experimental device used to identify local defects on surfaces by the measurement of the scattered light pattern using laser light focused onto the surface. We present results of experimental measurements for two surfaces with roughness and defects of the order of 6 to 60 microns using sizes of incident beam of the same order and we compare the results of experimental cases with results of numerical calculation based on the Kirchhoff Approximation of light scattering by rough surfaces. We include preliminary results from the effect on the pattern of light scattering as a function of the polarization state by using focused light to illuminate the surface, we calculate the Mueller matrix for the equivalent period of the surface micro-manufactured experimentally. Finally we conclude about the validity of the method.

A recently developed numerical method is used to calculate the double-scattered Mueller matrices for scattering of vector-electromagnetic waves from rough surfaces. The method is based on a modified version of the Kirchhoff approximation and is valid for surfaces with vertical walls and for any surface material. Calculations are performed for the case of a single groove and a single rib on silicon and gold surfaces and results are compared to published experimental results. The calculated results of the 16 elements of the Mueller matrix as functions of the scatter angle show good qualitative agreement with the experimental results for the groove cases. Results for the rib cases show poorer agreement, possibly due to variations from the optimum parameters of the surface structure.

We present an experimental method to characterize a liquid-crystal variable retarder (LCVR). In addition, experimental results using LCVR’s to measure the four Stokes parameters of a light beam simultaneously are presented. We use known waveplates (half-wave and quarter-wave) as devices to provide controlled polarization states to the Stokes polarimeter, and we use the measured Stokes parameters as functions of the orientation of the axes of the waveplates as an indication of the quality of the polarimeter. Also, we present results of simulations for comparison.

We compare the radial profiles of light pattern distributions formed in the retina and the exit pupil of a computational model eye, when the wavelength is varying. The computational eye simulates the presence of cataracts, as a particle distribution in the lens. We use three different wavelengths (400, 550 and 700 nm) for the incident light. The results show that for the shorter wavelength the effect of scattering is bigger around the center of the images while for the longest wavelength the light distribution is larger in the edges of the images. The distance from the center of the scattered light pattern to the zone where the profiles cross is inversely proportional to the size of the particles.

Stokes polarimetry using variable retardance elements such as Pockel´s cells and liquid crystals is a well-developed technique. There are two standard methods of analysis to extract the Stokes vector from the data using only one detector. One is to use only certain values of the retardances to obtain data for a number of fixed polarization combinations. The other is to use all the polarization combinations of the retardances for an oscillating voltage applied to the cells, and perform a Fourier analysis on the time varying signal. This method requires a linear relationship between the applied voltage and the obtained retardance. However, in general, for liquid-crystal variable retarders, this relationship is not linear. We present an analysis of a proposed method to use a nonlinear voltage-retardance relation to extract the Stokes parameters of a light beam. The method assumes a known nonlinear function relating the voltage and the retardance and uses a least-squares fit of the measured data to the calculated Mueller matrix of the polarimeter.

We analyze the Gaussian temporal envelope of pulses with an initial duration of 200fs and a carrier wavelength of 810nm at the paraxial focal plane of an achromatic doublet lens designed in the IR region. The Seidel aberrations for thin lenses are evaluated for a well-collimated beam. We analyze the effect of these aberrations in the focusing of ultrashort pulses for gaussian illumination and experimental results are presented for 200fs incident pulses and for three incident angles: 0°, 5°, and 8°.

We present results of resolution and optical characterization studies of silicon dioxide nanoparticle solutions. These phantoms consist of spherical particles with a mean controlled diameter of 168 and 429 nm. The importance of this work lies in using these solutions to develop phantoms with optical properties that closely match those of human breast tissue at near-IR wavelengths, and also to compare different resolution criteria for imaging studies at these wavelengths. Characterization involves illuminating the solution with a laser beam transmitted through a recipient of known width containing the solution. Resulting intensity profiles from the light spot are measured as function of the detector position. Measured intensity profiles were fitted to the calculated profiles obtained from diffusion theory, using the method of images. Fitting results give us the absorption and transport scattering coefficients. These coefficients can be modified by changing the particle concentration of the solution. We found that these coefficients are the same order of magnitude as those of human tissue reported in published studies. The resolution study involves measuring the edge response function (ERF) for a mask embedded on the nanoparticle solutions and fitting it to the calculated ERF, obtaining the resolution for the Hebden, Sparrow and Bentzen criteria.

One of the most popular methods for calculating the scattering of light from rough surfaces is the Kirchhoff approximation. A recent modification of the Kirchhoff approximation allows calculation of the scattering of electromagnetic radiation from rough surfaces with very high, or even infinite, slopes, which occurs frequently in, for example, imaging or testing of printed circuits or remote sensing applications. The modification involves a simple change in the way the surface normal is described which removes the explicit dependence of the resulting integral equations on the surface slope, and changing the sampling of the surface, removing the requirement of small slopes for application of the method. In this paper we present the application of the method to vector electromagnetic scattering, using the Stratton-Chu equation, from 2D rough metallic surfaces with infinite slope. The single and double scatter contributions to the total scattered intensity are calculated numerically with this new formulation. Geometrical shadowing is included by using ray tracing directly on the surface. The theoretical basis and preliminary numerical results of the application of this method to vector electromagnetic scattering from simple rough metallic surfaces (plane surfaces with single grooves or with a small number of identical grooves) with infinitely sloped structure are presented.

Experimental results using Liquid-Crystal Variable Retarders (LCVRs) to measure the four Stokes parameters of a light beam simultaneously are presented. We use known waveplates (half-wave and quarter-wave) as known sources to provide controlled polarization states to the Stokes polarimeter, and we use the measured Stokes parameters as functions of the orientation of the axes of the waveplates as an indication of the quality of the polarimeter. The effects of errors in optical alignment and nonlinearity of the retardance variation on the results are presented and discussed. We also present results of simulations for comparison. Finally, we present the advances obtained in the development of a Mueller matrix polarimeter for use in a goniometric scatterometer.

We analyze the Gaussian temporal envelope of pulses with a duration of 20fs and a carrier wavelength of 810nm at the paraxial focal plane of an achromatic doublet lens. The incident pulse beam is well-collimated and we use the Seidel aberration theory for thin lenses. In a set of cemented thin lenses with the stop at the lens, there is only spherical aberration, coma, astigmatism and field curvature. The distortion aberration introduced by the lens is zero. We analyze the effect of these aberrations in the focusing of ultrashort pulses for homogenous illumination.

We analyze the focusing of 20fs and 15fs ultrashort pulses using achromatic lenses by expanding the wave numbers of the pulse around the center frequency of the incident pulse up to the third order.

This paper presents calculations of a new formulation of the 3D Kirchhoff approximation which allows calculation of the scattering of vector waves from 2D rough surfaces containing infinite slopes. This type of surface has applications, for example, in remote sensing and in testing or imaging of printed circuits. The equivalent 1D surface formulation is presented to introduce the method in a physically simpler form. Some preliminary calculations for rectangular-shaped grooves in a plane are presented for the 2D surface method and are compared with the equivalent 1D calculations for the Kirchhoff and integral equation methods. Good agreement is found between the methods.

We have recently developed a scatterometer for bi-dimensional rough surfaces which uses an elliptical mirror to direct the light toward the rough surface and to collect the scattered light and direct it to a CCD camera. This device has advantages over similar previous devices such as the time needed for measurement and operation range. We have calculated and measured the Mueller matrix of the elliptical mirror and we have compared them to test the validity of our method. Preliminary results show differences between theory and experiment that must be explained.

We have recently developed a scatterometer which uses an elliptical mirror to direct the light scattered from a rough surface onto a CCD camera. This scatterometer is faster than the traditional arm based devices, and can measure the bi-dimensional scatter pattern. In the present work we present results for the calculation of the Mueller matrix of the elliptical mirror with the aim of using this information to correct the measured Mueller matrix for the instrumental contribution, to obtain the Mueller matrix of the scattering process.

Recently a modification of the Kirchhoff approximation was presented to permit the calculation of the multiple scattered light in rough surfaces with infinite slopes. Here we present a brief description of the method and examples of the scattering of light from rough surfaces with rectangular grooves. The examples presented here show how the scattering pattern changes from a periodic surface to a random surface. The randomness is added to the groove width, separation and depth separately to investigate the effect of each of these parameters on the scattering.

The Kirchhoff approximation has been used for many years to calculate for the problem of scattering of light from rough surfaces. One of the limitations of the method is on the surface slopes for which the method can be used. For large surface slopes there is more shadowing and multiple scattering and the sampling of the surface, which is in constant intervals of the variable along the mean plane of the surface, becomes a problem. In this work, the Kirchhoff approximation is reformulated to permit the use of this method in surfaces with very high slopes. Results are presented for surfaces containing rectangular shaped grooves, surfaces which have infinite slope on the sidewalls of the grooves.

In this work we present the design of an instrument for measuring the scattering of light by a two-dimensional rough surface in the visible between 550nm and 830nm. An elliptical mirror is used to collect the light scattered by a 2D-surface which is placed at the first focus of the ellipse. A relay is placed near to the second focus of the ellipse to collect the light scattered by the surface in each direction, that is, parallel rays leaving the illuminated 2D surface at an arbitrary angle are brought to a point at the focal plane of the relay. The light is detected by a CCD camera. To cover 180 degrees field of view it is necessary to move the CCD linearly in two directions in the focal plane.

In this work we present the optical design of an instrument for measuring the scattering of light by a 2D rough surface in the visible between 550nm and 830nm. An elliptical mirror is used to collect the light scattered by a 2D-surface. The 2D-surface is placed at the first focus of the ellipse. A relay is placed at the second focus of the ellipse to collect the light scattered by the surface in each direction, that is, parallel rays leaving the illuminated 2D surface at an arbitrary angle are brought to a point at the focal plane of the relay. The light is detected by a CCD camera. To cover 180 degrees field of view it is necessary to move the CCD linearly in two directions in the focal plane.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper numerical calculations are performed to compare scattered light distributions for light reflected from randomly rough surfaces in the converging and diverging illumination geometries. It is found that the enhanced backscatter peak can be measured accurately if the source and detector are at the same distance in the diverging geometry, and if the source and detector distances are approximately 100 times the size of the illuminated surface.

Scattering from 2-dimensional randomly rough surfaces is considered using a simple ray trace. The effects of phase and polarization are taken into account. It is shown that the patterns observed experimentally are due to the interference of the double scattered rays which gives a pattern with four-fold symmetry.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The Kirchhoff approximation (KA) is used to find the double scatter contribution to the field scattered froma random rough surface. The method is to use the same approximation for each interaction with the surface as isnormally used for the single scatter term. Solution of the double scatter term using a Monte-Carlo method showsa peak in the scattered intensity in the backscatter direction. This peak is approximately a factor of 2 greater inintensity than the background intensity agreeing with a simple multiple scattering ray picture. INTRODUCTION The phenomenon of enhanced backscatter of light from rough surfaces has been observed experimentally andpredicted theoretically through numerical calculation. 2 Generally the "exact" calculations involve solving Maxwell'sequations using the exact boundary conditions and then expanding the scattered field in a suitable manner to reducethe problem to the solution of a set of solvable equations. These methods give accurate results for the scattereddistribution of intensity but very little insight into the physical processes involved, e.g. shadowing and multiplescattering, and how each of these affects the scatter pattern.There is, however, another type ofsolution, the Kirchhoff method ofsolution. In this case the boundary conditionsare satisfied approximately and the scattered field of this approximate boundary field is found exactly. Although theresults from such a method are less accurate than the exact case there is a great advantage of more physical insightinto the problem.To date only the single scatter term of the KA has been used i.e. the contribution to the scattered field ofterms which depend only on a 8lngle point on the surface. From a simple ray picture of the scattering process' themultiply scattered rays can add coherently in the backscatter direction as opposed to incoherently in other directions.This should give a peak in the diffracted intensity pattern in the backscatter direction a factor of 2 larger than thebackground.However, the condition for the KA to the surface field,E,(x, z)