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.

Regularized image reconstruction for continuously self-imaging gratings.

In this paper, we demonstrate two image reconstruction schemes for continuously self-imaging gratings (CSIGs). CSIGs are diffractive optical elements that generate a depth-invariant propagation pattern and sample objects with a sparse spatial frequency spectrum. To compensate for the sparse sampling, we apply two methods with different regularizations for CSIG imaging. The first method employs continuity of the spatial frequency spectrum, and the second one uses sparsity of the intensity pattern. The two methods are demonstrated with simulations and experiments.

Fabrication of concave and convex potassium bromide lens arrays by compression molding.

A new simple and cost-effective method has been developed for the fabrication of both plano-convex and plano-concave lens arrays with potentially important sag heights. The process is based on the use of potassium bromide (KBr) powder. At ambient temperature and under pressure, KBr powder is compressed on a molding die with the desired shape to form a solid lens array. The quality of the lens arrays has been assessed, and we present the first image produced by a converging KBr lens array.

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.

Compact infrared cryogenic wafer-level camera: design and experimental validation.

We present a compact infrared cryogenic multichannel camera with a wide field of view equal to 120°. By merging the optics with the detector, the concept is compatible with both cryogenic constraints and wafer-level fabrication. The design strategy of such a camera is described, as well as its fabrication and integration process. Its characterization has been carried out in terms of the modulation transfer function and the noise equivalent temperature difference (NETD). The optical system is limited by the diffraction. By cooling the optics, we achieve a very low NETD equal to 15 mK compared with traditional infrared cameras. A postprocessing algorithm that aims at reconstructing a well-sampled image from the set of undersampled raw subimages produced by the camera is proposed and validated on experimental images.

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.

Influence of band selection and target estimation error on the performance of the matched filter in hyperspectral imaging.

The matched filter is a widely used detector in hyperspectral detection applications because of its simplicity and its efficiency in practical situations. We propose to estimate its performance with respect to the number of spectral bands. These spectral bands are selected thanks to a genetic algorithm in order to optimize the contrast between the target and the background in the detection plane. Our band selection method can be used to optimize not only the position but also the linewidth of the spectral bands. The optimized contrast always increases with the number of selected bands. However, in practical situations, the target spectral signature has to be estimated from the image. We show that in the presence of estimation error, the maximum number of bands may not always be the best choice in terms of detection performance.

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.

Inverse problem approaches for stationary Fourier transform spectrometers.

A design of a miniaturized stationary Fourier transform IR spectrometer has been developed that produces a two-dimensional interferogram. The latter is disturbed by effects like parasitic interferences or disparities in the cutoff wavelength of the pixels. Thus, a simple Fourier transform cannot be used to estimate the spectrum of the scene. However, as these defects are deterministic, they can be measured and taken into account by inversion methods. A regularization term can also be added. The first experimental results prove the efficiency of this processing methodology.

Random phase mask in a filamentation regime: application to the localization of point sources.

We present a optical system with an extended point-spread function (PSF) for the localization of point sources in the visible and IR spectral ranges with a subpixel precision. This compact system involves a random phase mask (RPM) as its unique component. It exhibits original properties, because this RPM is used in a particular regime, called the "filamentation regime," before the speckle region. The localization is performed by calculating the phase correlation between the PSF and the image obtained under off-axis illumination. Numerical simulations are presented to assess the basic optical properties of this RPM in the filamentation regime.

Design strategies to simplify and miniaturize imaging systems.

We present the range of optical architectures for imaging systems based on a single optical component, an aperture stop, and a detector. Thanks to the formalism of third-order Seidel aberrations, several strategies of simplification and miniaturization of optical systems are examined. Figures of merit are also introduced to assess the basic optical properties and performance capabilities of such systems; by this way, we show the necessary trade-off between simplicity, miniaturization, and optical performance.

Modulation transfer function measurement of a multichannel optical system.

We present a new method to measure the modulation transfer function (MTF) beyond the Nyquist frequency of a multichannel imaging system for which all the channels have parallel optical axes. Such a multichannel optical system produces a set of undersampled subimages. If the subimages contain nonredundant information, high spatial frequencies are folded between low spatial frequencies, leading to the possible extraction of frequencies higher than the Nyquist frequency. The measurement of the MTF of the multichannel system leads to the estimation of the resolution enhancement of the final image that can be obtained by applying a postprocessing algorithm to the collection of undersampled subimages. Experimental images are presented to validate this method.

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.

Demonstration of an infrared microcamera inspired by Xenos peckii vision.

We present an original and compact optical system inspired by the unusual eyes of a Strepsipteran insect called Xenos peckii. It is designed for a field of view of 30 degrees and is composed of multiple telescopes. An array of prisms of various angles is placed in front of these telescopes in order to set a different field of view for each channel. This type of camera operates in the [3-5 microm] spectral bandwidth and is entirely integrated in a Dewar in order to maximize its compactness. Experimental images are presented to validate this design.

Compact infrared pinhole fisheye for wide field applications.

The performances of a compact infrared optical system using advanced pinhole optics for wide field applications are given. This concept is adapted from the classical Tisse design in order to fit with infrared issues. Despite a low light gathering efficiency and a low resolution in comparison with classical lenses, pinhole imagery provides a long depth of field and a wide angular field of view. Moreover, by using a simple lens that compresses the field of view, the angular acceptance of this pinhole camera can be drastically widened to a value around 180°. This infrared compact system is named pinhole fisheye since it is based on the field lens of a classical fisheye system.

Demonstration of image-zooming capability for diffractive axicons.

Diffractive axicons are optical components producing achromatic nondiffracting beams. They thus produce a focal line rather than a focal point for classical lenses. This gives the interesting property of a long focal depth. We show that this property can be used to design a simple imaging system with a linear variable zoom by using and translating a diffractive axicon as the only optical component.

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.