Impact of image registration errors on the quality of hyperspectral images in imaging static Fourier transform spectrometry.

Imaging static Fourier transform spectrometry (isFTS) is used for pushbroom airborne or spaceborne hyperspectral remote sensing. In isFTS, a static two-wave interferometer imprints linear interference fringes over the image of the scene, so that the spectral information is multiplexed over several instantaneous images, and numerical reconstruction is needed to recover the full spectrum for each pixel. The image registration step is crucial since insufficient accuracy leads to artefacts on the images and the estimated spectra. In order to investigate these artifacts, we performed a theoretical study and designed a simulation program. We established that registration errors create crenellated spatial patterns, the magnitude of which depends on the radiance gradient of the scene, the amplitude of the registration error, and the wavelength. In the case of sinusoidal perturbations, which may correspond for instance to mechanical vibrations of the carrier, we established that spurious peaks appear on the spectrum, similarly to what happens in dynamic FTS, but with spatial patterns specific to static interferometers.

Improved performance of a hybrid optical/digital imaging system with fast piecewise Wiener deconvolution.

We quantitatively investigate how spatially varying deblurring algorithms can improve the imaging performance of hybrid optical/digital systems affected by field aberrations. To this end, we validate a theoretical model of the maximal gain that linear and spatially varying deblurring can bring to any given lens, and derive a practical algorithm to implement this type of deblurring with low computational complexity. The results demonstrate the usefulness to properly coordinate and balance the roles of the imaging optical system and raw image post-processing: optimal final imaging quality can be obtained by a lens that has been optically designed to reduce field aberrations at the price of lower average raw optical quality, associated with a fast and "slightly" spatially varying piecewise Wiener deconvolution algorithm.

End-to-end optimization of optical systems with extended depth of field under wide spectrum illumination.

We study a way to take into account the scene illumination spectrum during end-to-end optimization of optical-digital hybrid systems that include annular binary phase masks to enhance their depth of field (DoF). We show that a phase mask specifically optimized for wide spectrum panchromatic imaging performs better under this type of illumination than phase masks optimized under monochromatic illumination assumption. Indeed, thanks to spectral averaging, the modulation transfer functions of such a phase mask are very close to each other. This guarantees a very homogeneous image quality across the DoF range, which we demonstrate theoretically and experimentally using a dedicated optical setup.

Comparison of methods for end-to-end co-optimization of optical systems and image processing with commercial lens design software.

We compare three different methods to co-optimize hybrid optical/digital imaging systems with a commercial lens design software: conventional optimization based on spot diagram minimization, optimization of a surrogate criterion based on a priori equalization of modulation transfer functions (MTFs), and minimization of the mean square error (MSE) between the ideal sharp image and the image restored by a unique deconvolution filter. To implement the latter method, we integrate - for the first time to our knowledge - MSE optimization to the software Synopsys CodeV. Taking as an application example the design of a Cooke triplet having good image quality everywhere in the field of view (FoV), we show that it is possible, by leveraging deconvolution during the optimization process, to adapt the spatial distribution of imaging performance to a prescribed goal. We also demonstrate the superiority of MSE co-optimization over the other methods, both in terms of quantitative and visual image quality.

Influence of high numerical aperture on depth-of-field enhancing phase mask optimization in localization microscopy.

The depth-of-field (DoF) of localization microscopes can be extended by placing a phase mask in the aperture stop of the objective. To optimize these masks and characterize their performance, defocus is in general modeled by a simple quadratic pupil phase term. However, this model does not take into account two essential characteristics of localization microscopy setups: an extremely high numerical aperture (NA) and a mismatch between the refractive indices of the immersion liquid and sample. Using the more realistic high NA image formation model of Gibson & Lanni (GL), we show that the DoF extension is simply reduced by a NA-dependent scaling factor. We also show that, provided this scaled DoF extension factor is taken into account, masks optimized with the approximate quadratic model are still nearly optimal in the framework of the GL model. This result is important since it establishes that generic optimized masks can be used in setups with different NA and immersion indices.

Co-designed annular binary phase masks for depth-of-field extension in single-molecule localization microscopy.

Single-molecule localization microscopy has become a prominent approach to study structural and dynamic arrangements of nanometric objects well beyond the diffraction limit. To maximize localization precision, high numerical aperture objectives must be used; however, this inherently strongly limits the depth-of-field (DoF) of the microscope images. In this work, we present a framework inspired by "optical co-design" to optimize and benchmark phase masks, which, when placed in the exit pupil of the microscope objective, can extend the DoF in the realistic context of single fluorescent molecule detection. Using the Cramér-Rao bound (CRB) on localization accuracy as a criterion, we optimize annular binary phase masks for various DoF ranges, compare them to Incoherently Partitioned Pupil masks and show that they significantly extend the DoF of single-molecule localization microscopes. In particular we propose different designs including a simple and easy-to-realize two-ring binary mask to extend the DoF. Moreover, we demonstrate that a simple maximum likelihood-based localization algorithm can reach the localization accuracy predicted by the CRB. The framework developed in this paper is based on an explicit and general information theoretic criterion, and can thus be used as an engineering tool to optimize and compare any type of DoF-enhancing phase mask in high resolution microscopy on a quantitative basis.

Joint digital-optical design of complex lenses using a surrogate image quality criterion adapted to commercial optical design software.

Like classical optical design, joint digital-optical design of complex lenses requires a skilled optical designer helped by powerful optical design software. Consequently, if optimization criteria have to be modified to take into account digital post-processing, the convenient optimization environment provided by commercial optical design software needs to be preserved. For that purpose, we define a joint-design criterion based on a merit function that contains terms classically implemented in optical design software but used in a non-standard way. After validation on a simple design problem, the proposed method is applied to the design of a very fast (f/0.75) complex lens. The obtained joint-designed lens is shown to be superior to a classically designed one in terms of weight and image quality in the field.

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.

Miniature and cooled hyperspectral camera for outdoor surveillance applications in the mid-infrared.

We present the design and the realization of a compact and robust imaging spectrometer in the mid-infrared spectral range. This camera combines a small static Fourier transform birefringent interferometer and a cooled miniaturized infrared camera in order to build a robust and compact instrument that can be embedded in an unmanned aerial vehicle for hyperspectral imaging applications. This instrument has been tested during a gas detection measurement campaign. First results are presented.

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.

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.

Fully tunable active polarization imager for contrast enhancement and partial polarimetry.

We present the design and the practical implementation of a polarimetric imaging system based on liquid-crystal modulators that allows generation and analysis of any polarization state on the Poincaré sphere. This system is more versatile than standard Mueller imagers that are based on optimized, but limited, sets of illumination and analysis states. Examples of benefits brought by these extra degrees of freedom are illustrated on two different applications: contrast enhancement and extraction of partial polarimetric properties of a scene.

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.

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.

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.