Angular reflectance model for ridged specular surfaces, with comprehensive calculation of inter-reflections and polarization.

The color of a surface structured at the mesoscopic scale differs from the one of a flat surface of the same material because of the light inter-reflections taking place in the concavities of the surface, as well as shadowing effects. The color variation arises not only in scattering materials, but also in the absence of scattering, e.g., in metals and clear dielectrics, just as a consequence of multiple specular reflections between neighboring flat facets of the surface. In this paper, we investigate such color variation in the case of an infinitely long V-shaped groove, having in mind the visual appearance of a surface composed of many structures of that sort, all parallel and identical. We develop a full model of multiple specular reflections, accounting for the ray position and orientation and the polarization effects occurring at each reflection. We compare that situation with two approximate models, more usual and easier to compute, where light is assumed to remain unpolarized all along, or where the $p$p- and $s$s-polarized components are treated separately. Spectral reflectances were predicted for various materials and angles of cavities, under diffuse illumination. In most cases, the three models predict very similar bi-hemispherical reflectances, but the hemispherical-directional reflectances can vary noticeably in certain observation directions. This study might help achieve a more physically realistic rendering of dielectric or metallic ridged surfaces in computer graphics.

Numerical modeling of nominal and stray waves in birefringent interferometers: application to large-field-of-view imaging Fourier transform spectrometers.

Birefringent interferometers are often used for compact static Fourier transform spectrometers. In such devices, several uniaxial birefringent parallel or prismatic plates are stacked, with their optical axes set so that there is an efficient coupling from ordinary to extraordinary and extraordinary to ordinary eigenmodes of two successive plates. Such coupling, aside from few particular cases, is, however, not perfect, an effect that may adversely affect performance. In order to help the design and the tolerancing of these interferometers, we have developed a numerical modeling based on the propagation of plane waves inside and through the interface of birefringent media. This tool evaluates the traveled optical path length and the amplitude of the different polarization modes, enabling prediction of both the optical path differences on the interferometer outputs and the unwanted coupling strengths and related stray wave amplitudes. The tool behavior is illustrated on Savart and double-Wollaston interferometers and compared with experimental characterization of a calcite double-Wollaston prism.

Reduction of material mass of optical component in cryogenic camera by using high-order Fresnel lens on a thin germanium substrate.

We designed a compact infrared cryogenic camera using only one lens mounted inside the detector area. In the field of cooled infrared imaging systems, the maximal detector area is determined by the dewar. It is generally a sealed and cooled environment dedicated to the infrared quantum detector. By integrating an optical function inside it, we improve the compactness of the camera as well as its performances. The originality of our approach is to use a thin integrated optics which is a high quality Fresnel lens on a thin germanium substrate. The aim is to reduce the additional mass of the optical part integrated inside the dewar to obtain almost the same cool down time as a conventional dewar with no imaging function. A prototype has been made and its characterization has been carried out.

Modeling the specular spectral reflectance of partially ordered alumina nanopores on an aluminum substrate.

Anodizing of aluminum generates a porous alumina layer comprising cylindrical nanopores (300 nm diameter) extending essentially perpendicular to the substrate. The pore distribution over the surface exhibits a short-distance order close to hexagonal arrangement. On the contrary, long-distance order cannot be defined: the arrangement is not periodic. Visual observation of such nanoporous layers shows a reddish specular reflectance consistent with reflectance spectrum measurements. This work is a parametric study aiming at demonstrating that color effects are caused by the presence of disorder illustrated by the deviations from periodicity in terms of nanopore location and nanopore radius. Using the method of Rigorous Coupled Wave Analysis (RCWA), the reflectance spectrum has been simulated. Although our calculations were done using a simple one-dimensional (1D) model, a fair fit with experimental results is found.

Extra-thin infrared camera for low-cost surveillance applications.

We designed a cheap broadband uncooled microimager operating in the long-wavelength infrared range using only one lens at a minimal cost for the manufacturing process. The approach is based on thin optics where the device volume is small and therefore inexpensive materials can be used because some absorption can be tolerated. We have used a Fresnel lens on a thin silicon substrate. Up to now, Fresnel lenses have not been used for broadband imaging because of their chromatic properties. However, working in a relatively high diffraction order can significantly reduce chromatism. A prototype has been made for short range or indoor low-cost surveillance applications like people counting, and experimental images are presented.

Spatial angular multiplexing for enlarging the detected area in off-axis digital holography.

In off-axis digital holography, e.g., for detecting and imaging ultrafast phenomena, the interference region is confined to a limited region due to the short extent of the light pulse along the propagation axis. Therefore, the detected area of the object wavefront is limited. A recording method for enlarging the detected area in the above case is proposed in this Letter, in which multiple interferences between the object and the reference waves are obtained by spatial angular multiplexing. Experimental results demonstrate the validity of this method.

Angular acceptance analysis of an infrared focal plane array with a built-in stationary Fourier transform spectrometer.

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis to explain and describe the fringe formation inside the FTIR-FPA structure when illuminated by an extended source positioned at a finite distance from the detection plane. The results are then exploited to propose a simple front lens design compatible with a handheld package.

On the influence of noise statistics on polarimetric contrast optimization.

In active scalar polarimetric imaging systems, the illumination and analysis polarization states are degrees of freedom that can be used to maximize the performance. These optimal states depend on the statistics of the noise that perturbs image acquisition. We investigate the problem of optimization of discrimination ability (contrast) of such imagers in the presence of three different types of noise statistics frequently encountered in optical images (Gaussian, Poisson, and Gamma). To compare these different situations within a common theoretical framework, we use the Bhattacharyya distance and the Fisher ratio as measures of contrast. We show that the optimal states depend on a trade-off between the target/background intensity difference and the average intensity in the acquired image, and that this trade-off depends on the noise statistics. On a few examples, we show that the gain in contrast obtained by implementing the states adapted to the noise statistics actually present in the image can be significant.

Fourier-based automatic alignment for improved Visual Cryptography schemes.

In Visual Cryptography, several images, called "shadow images", that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image.

Experimental results from an airborne static Fourier transform imaging spectrometer.

A high étendue static Fourier transform spectral imager has been developed for airborne use. This imaging spectrometer, based on a Michelson interferometer with rooftop mirrors, is compact and robust and benefits from a high collection efficiency. Experimental airborne images were acquired in the visible domain. The processing chain to convert raw images to hyperspectral data is described, and airborne spectral images are presented. These experimental results show that the spectral resolution is close to the one expected, but also that the signal to noise ratio is limited by various phenomena (jitter, elevation fluctuations, and one parasitic image). We discuss the origin of those limitations and suggest solutions to circumvent them.

Fourier optics heuristics for diffraction at infinity by an index discontinuity in a one-dimensional slab.

We study the far-field reflected diffraction pattern of an index discontinuity in a thin one-dimensional slab illuminated by a plane wave and show that a time-saving modeling technique based on plane wave expansion approaches fairly well the Maxwell-based rigorous models. This method is simple to implement, and it furthermore allows a good understanding of the optical phenomena involved in the propagation of light through the slab.

Compactness of lateral shearing interferometers.

Imaging lateral shearing interferometers are good candidates for airborne or spaceborne Fourier-transform spectral imaging. For such applications, compactness is one key parameter. In this article, we compare the size of four mirror-based interferometers, the Michelson interferometer with roof-top (or corner-cube) mirrors, and the cyclic interferometers with two, three, and four mirrors, focusing more particularly on the last two designs. We give the expression of the translation they induce between the two exiting rays. We then show that the cyclic interferometer with three mirrors can be made quite compact. Nevertheless, the Michelson interferometer is the most compact solution, especially for highly diverging beams.

Reducing the diffraction artifacts while implementing a phase function on a spatial light modulator.

Spatial light modulators are often used to implement phase modulation. Since they are pixelated, the phase function is usually approximated by a regularly sampled piecewise constant function, and the periodicity of the pixel sampling generates annoying diffraction peaks. We theoretically investigate two pixelation techniques: the isophase method and a new nonperiodic method derived from the Voronoi tessellation technique. We show that, for a suitable choice of parameters, the diffraction peaks disappear and are replaced by a smoothly varying halo. We illustrate the potential of these two techniques for implementing a lens function and wavefront correction.

Minimization of diffraction peaks of spatial light modulators using Voronoi diagrams.

It is possible to reduce the diffraction peaks of a Spatial Light Modulator (SLM) by breaking the periodicity of the pixels shape. We propose a theoretical investigation of a SLM that would be based on a Voronoi diagram, obtained by deforming a regular grid, and show that for a specific deformation parameter the diffraction peaks disappear and are replaced with a speckle-like diffraction halo. We also develop a simple model to determine the shape and the level of this halo.

Spatiotemporal distortions of attosecond pulses.

In this article, we report that usual multilayer mirror configurations to focus attosecond pulses generate geometric aberrations and can significantly stretch pulses. The numerical simulations show that the effects can be strong enough to delay some parts of the pulses of an attosecond pulse train and make them interfere with the next pulses of the train. The influence of the numerical aperture on the pulse duration is also studied, showing that such effects can occur even with very low numerical apertures.

Shape of diffraction orders of centered and decentered pixelated lenses.

We consider diffraction by pixelated lenses when the lens size is significantly smaller than the diffraction pattern of single pixels. In that case, the diffraction orders show shapes that have not been identified in earlier studies and that are quite sensitive to the pixel filling ratio as well as to decentering.

Heuristic models for diffraction by some simple micro-objects.

Electromagnetic optics is normally expected to be the only appropriate approach to describe structures with features of just a few wavelengths. But in some cases, these structure can be well described by simple heuristic arguments relying on geometrical optics and on diffraction by known elementary primitives. Such an approach allows a better understanding of the involved physical phenomena and reduces the computation time. We investigate the case of a microcomponent with a triangular section by using two approximate models with increasing complexity and explore their limits as the size of the structure decreases. Results are compared with a rigorous electromagnetic approach and discussed on the basis of near-field and far-field diffraction patterns.

Probing multilayer stack reflectors by low coherence interferometry in extreme ultraviolet.

We use low coherence interferometry to investigate the depth structure of a complex multilayer stack reflector. The probing instrument is an interferometer based on a Fresnel's bi-mirror illuminated by relatively wide-band synchrotron undulator light near 13.5 nm. Simulations clearly confirm that our test object generates two back propagated signals that behave as if reflected on two effective planes. First results in this spectral range may open the way to a new physical approach to extreme ultraviolet sample characterization in the form of line-scan optical coherence tomography.

Nonparaxial analysis of continuous self-imaging gratings in oblique illumination.

Tolerance in angles of continuously self-imaging gratings (CSIGs) is explored. The degradation in angle of the shape of the point-spread function is theoretically investigated and illustrated by simulations and experiments. The formalism presented is inspired by the one used for classical lenses and can be easily generalized to diffraction gratings. It turns out that well-designed CSIGs could be used for scanning optical systems requiring a large field of view.

Entropy of partially polarized light and application to statistical processing techniques.

We have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection tasks.