Optimized Stokes imaging for highly resolved optical speckle fields, Part III: topological analysis of polarimetric state distributions with optimized data representations.

In this last article of a three-paper series focusing on Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, experimental results are provided on test samples of varying nature and polarization properties, and are analyzed extensively. For this purpose, a review of the classical ways of displaying Stokes polarimetric information is provided. Then, some original alternative graphical representations are introduced that ensure optimal readability and interpretability of the Stokes imaging data in the context of speckle field polarimetry, and it is shown how they can be adapted to various observation scales. Finally, these tools are implemented in order to provide a topological analysis of the distribution of the states of polarization across a speckle pattern, and in the vicinity of polarimetric singularities of the field.

Optimized Stokes imaging for highly resolved optical speckle fields, Part I: optimized experimental setup.

In this first article of a three-part series focusing on the Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, a review of the state-of-the-art techniques for such experimental investigations is provided. An optimized experimental setup is then extensively described, which allows polarimetric Stokes measurements on such complex interference patterns to be carried out at each location of the speckle field without disturbing the wavefront. Specific calibration procedures are also described to provide an estimation of the reliable polarimetric properties of light across a resolved speckle field.

Optimized Stokes imaging for highly resolved optical speckle fields, Part II: optimal acquisition and estimation strategies.

In this second paper of a three-paper series focusing on Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, a theoretical study based on numerical simulations is presented in order to establish the optimum sensing, estimation, and processing strategies that guarantee the best precision, accuracy, and robustness for Stokes polarimetry in this specific context. In particular, it is demonstrated that the so-called state of polarization analysis by full projection on the Poincaré space (SOPAFP) approach can be optimized in order to ensure best estimation performance. These numerical simulations also make it possible to establish that the SOPAFP approach provides better results in terms of robustness to residual experimental imperfections of the setup when compared to classical Stokes polarimetry approaches.

Polarization coherence frustration.

From the joint analysis of polarization and coherence properties of light, a remarkable concept referred to as polarization coherence frustration is introduced and analyzed. It is shown that two kinds of partially polarized and partially coherent light, with different levels of complexity, can be distinguished and that they mathematically correspond to different equivalence classes. On the one hand, light has polarization coherence properties that are not frustrated in a spatial domain D when there exists a configuration of local polarization devices at each location of the light field that allows the maximization of the modulus of the scalar degree of coherence between any couple of points in D. Two conditions are shown to hold for light to be polarization coherence unfrustrated and their physical interpretations are analyzed. On the other hand, if one of these conditions is not verified, polarization coherence frustration occurs. These notions are discussed in analogy with well-known concepts of frustration and gauge transformations developed in statistical physics for spin glasses. Their relevance in the field of statistical optics is demonstrated through different theoretical results and examples.

Probing nonaffine expansion with light scattering.

In disordered materials under mechanical stress, the induced deformation can deviate from the affine one, even in the elastic regime. The nonaffine contribution was observed and characterized in numerical simulations for various systems and reported experimentally in colloidal gels. However, low amplitude of nonaffinity and its local character makes the experimental study challenging. We present a method based on the phase compensation of the wave scattered from a thermally dilated amorphous material using fine wavelength tuning of the optical probe beam. Using a glass frit as a sample, we ensure complete reversibility of the material deformation, while experimental observations enable us to confirm the occurrence of nonaffinity in the elastic regime. We develop a model for the coupled effect of the thermal expansion or contraction of the material and the dilatation of the incident wavelength, which allows us to estimate the magnitude of the nonaffine displacement and the spatial extent of its correlation domain.

Label-free microscopy of mitotic chromosomes using the polarization orthogonality breaking technique.

We report how a recently developed polarization imaging technique, implementing micro-wave photonics and referred to as orthogonality-breaking (OB) imaging, can be adapted on a classical confocal fluorescence microscope, and is able to provide informative polarization images from a single scan of the cell sample. For instance, the comparison of the images of various cell lines at different cell-cycle stages obtained by OB polarization microscopy and fluorescence confocal images shows that an endogenous polarimetric contrast arizes with this instrument on compacted chromosomes during cell division.

Orthogonality-breaking polarimetric sensing modalities for selective polarization imaging.

Polarimetric sensing/imaging by orthogonality breaking is a microwave-photonics-inspired optical remote sensing technique that was shown to be particularly suited to characterize dichroic samples in a direct and single-shot way. In this work, we expand the scope of this approach in order to gain sensitivity on birefringent and/or purely depolarizing materials by respectively introducing a circular or a linear polarization analyzer in the detection module. We experimentally validate the interest of these two new, to the best of our knowledge, induced orthogonality-breaking modalities in the context of infrared active imaging.

An all-optical technique enables instantaneous single-shot demodulation of images at high frequency.

High-frequency demodulation of wide area optical signals in a snapshot manner remains a technological challenge. If solved, it could open tremendous perspectives in 3D imaging, vibrometry, free-space communications, automated vision, or ballistic photon imaging in scattering media with numerous applications in smart autonomous vehicles and medical diagnosis. We present here a snapshot quadrature demodulation imaging technique, capable of estimating the amplitude and phase from a single acquisition, without synchronization of emitter and receiver, and with the added capability of continuous frequency tuning. This all-optical optimized setup comprises an electro-optic crystal acting as a fast sinusoidal optical transmission gate, and allows four quadrature image channels to be recorded simultaneously with any conventional camera. We report the design, experimental validation and examples of applications of such wide-field quadrature demodulating system that allowed snapshot demodulation of images with good spatial resolution and continuous frequency selectivity up to a few 100s of kilohertz.

Polarizer-free two-pixel polarimetric camera by compressive sensing.

We propose an original concept of compressive sensing (CS) polarimetric imaging based on a digital micromirror (DMD) array and two single-pixel detectors, without using any polarizer. The polarimetric sensitivity of the proposed setup is due to the tiny difference in Fresnel's coefficients of reflecting mirrors, which is exploited here to form an original reconstruction problem including a CS problem and a source-separation task. We show that a two-step approach, tackling each problem successively, is outperformed by a dedicated combined reconstruction method, which is demonstrated in this paper and preferably implemented through a reweighted fast iterative shrinkage-thresholding algorithm. The combined reconstruction approach is then further improved by including physical constraints specific to the polarimetric imaging context considered, which are implemented in an original constrained generalized forward-backward algorithm. Numerical simulations demonstrate the efficiency of the two-pixel CS polarimetric imaging setup at retrieving polarimetric contrast data with significant compression rate and good reconstruction quality. The influence of experimental imperfections of the DMD is also analyzed through numerical simulations, and 2D polarimetric imaging reconstruction results are finally presented.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus: erratum.

For J. Opt. Soc. Am. A33, 434 (2016)JOAOD60740-323210.1364/JOSAA.33.000434, a corrected version of Eq. (9) is provided owing to typographical errors in the original article. The original full article text and calculations are unchanged. Another typo is corrected in Eq. (A5) of Appendix A.

Generation of a coherent light beam with precise and fast dynamic control of the state and degree of polarization.

Recent developments of polarized light sources with tunable state and degree of polarization (SOP and DOP) inherently provide a temporally incoherent beam, which makes them unsuitable for applications like interferometry. We present a method for generating a coherent beam with full, precise, and independent control of the SOP and DOP. Our approach is based on an imbalanced dual-frequency dual-polarization light source. We demonstrate that it offers three different working regimes, respectively providing perfectly depolarized light, DOP modulated light, or fully polarized light with a deterministic SOP trajectory. A simple implementation of this versatile approach is described and experimentally validated.

Free-space active polarimetric imager operating at 1.55 µm by orthogonality breaking sensing.

We report the design and optimization of an active polarimetric imaging demonstrator operating at 1.55 µm that is based on the orthogonality breaking technique. It relies on the use of a fibered dual-frequency dual-polarization source raster scanned over the scene. A dedicated opto-electronic detection chain is developed to demodulate the optical signal backscattered at each location of the scene in real time, providing multivariate polarimetric image data in one single scan with limited acquisition time. We experimentally show on a homemade scene that contrast maps can be built to reveal hidden dichroic objects over a depolarizing background, as well as their orientation. Finally, experiments through air turbulence illustrate the benefit of such an imaging architecture over standard polarimetric techniques requiring multiple image acquisitions.

Theoretical optimal modulation frequencies for scattering parameter estimation and ballistic photon filtering in diffusing media.

The efficiency of using intensity modulated light for the estimation of scattering properties of a turbid medium and for ballistic photon discrimination is theoretically quantified in this article. Using the diffusion model for modulated photon transport and considering a noisy quadrature demodulation scheme, the minimum-variance bounds on estimation of parameters of interest are analytically derived and analyzed. The existence of a variance-minimizing optimal modulation frequency is shown and its evolution with the properties of the intervening medium is derived and studied. Furthermore, a metric is defined to quantify the efficiency of ballistic photon filtering which may be sought when imaging through turbid media. The analytical derivation of this metric shows that the minimum modulation frequency required to attain significant ballistic discrimination depends only on the reduced scattering coefficient of the medium in a linear fashion for a highly scattering medium.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus.

Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency-dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic, and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality-breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality-breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.

Orthogonality breaking through few-mode optical fiber.

Polarization sensing and imaging through optical fibers is a technological challenge motivated by promising applications for in vivo, in situ polarimetric endoscopy for biomedical diagnosis. Among the recent approaches proposed to solve this issue, the depolarization/dichroism sensing by polarization orthogonality breaking (DSOB) technique was shown to perform remotely through single-mode optical fibers for depolarization/diattenuation measurements. In this article, we investigate the applicability of such a technique in slightly multimode waveguides. Through theoretical modeling and numerical simulations, we evidence the conditions required for the polarization orthogonality to be preserved after propagation in a few-mode fiber, notably in terms of detection geometry of the spatial modes. Original experiments realized in few-mode fibers both in transmission and reflection configurations are also reported and validate the theoretical predictions. These results allow us to analyze the influence of the experimental parameters, such as detection geometry, sample tilt, or fiber length, on orthogonality preservation and on the measurement dynamics of the DSOB technique in slightly multimode waveguides.

Real-time imaging through strongly scattering media: seeing through turbid media, instantly.

Numerous everyday situations like navigation, medical imaging and rescue operations require viewing through optically inhomogeneous media. This is a challenging task as photons propagate predominantly diffusively (rather than ballistically) due to random multiple scattering off the inhomogenieties. Real-time imaging with ballistic light under continuous-wave illumination is even more challenging due to the extremely weak signal, necessitating voluminous data-processing. Here we report imaging through strongly scattering media in real-time and at rates several times the critical flicker frequency of the eye, so that motion is perceived as continuous. Two factors contributed to the speedup of more than three orders of magnitude over conventional techniques - the use of a simplified algorithm enabling processing of data on the fly, and the utilisation of task and data parallelization capabilities of typical desktop computers. The extreme simplicity of the technique, and its implementation with present day low-cost technology promises its utility in a variety of devices in maritime, aerospace, rail and road transport, in medical imaging and defence. It is of equal interest to the common man and adventure sportsperson like hikers, divers, mountaineers, who frequently encounter situations requiring realtime imaging through obscuring media. As a specific example, navigation under poor visibility is examined.

Generalized Jones matrix method for homogeneous biaxial samples.

The generalized Jones matrix (GJM) is a recently introduced tool to describe linear transformations of three-dimensional light fields. Based on this framework, a specific method for obtaining the GJM of uniaxial anisotropic media was recently presented. However, the GJM of biaxial media had not been tackled so far, as the previous method made use of a simplified rotation matrix that lacks a degree of freedom in the three-dimensional rotation, thus being not suitable for calculating the GJM of biaxial media. In this work we propose a general method to derive the GJM of arbitrarily-oriented homogeneous biaxial media. It is based on the differential generalized Jones matrix (dGJM), which is the three-dimensional counterpart of the conventional differential Jones matrix. We show that the dGJM provides a simple and elegant way to describe uniaxial and biaxial media, with the capacity to model multiple simultaneous optical effects. The practical usefulness of this method is illustrated by the GJM modeling of the polarimetric properties of a negative uniaxial KDP crystal and a biaxial KTP crystal for any three-dimensional sample orientation. The results show that this method constitutes an advantageous and straightforward way to model biaxial media, which show a growing relevance for many interesting applications.

Full characterization of dichroic samples from a single measurement by circular polarization orthogonality breaking.

We report a novel method to unambiguously determine the magnitude and orientation of linear dichroism in a simultaneous way. It is based on the use of a dedicated dual-frequency dual-polarization coherent source providing two orthogonal circularly polarized modes at the output. We show that the interaction of such a beam with dichroic media gives rise to a beatnote signal whose amplitude and phase enable the full determination of the diattenuation coefficient and axis orientation, respectively. The application of this method to polarimetric imaging provides single-shot sample characterization by its diattenuation coefficient and optical axis angle, with potential applications in biomedical imaging.

Long-range polarimetric imaging through fog.

We report an experimental implementation of long-range polarimetric imaging through fog over kilometric distance in real field atmospheric conditions. An incoherent polarized light source settled on a telecommunication tower is imaged at a distance of 1.3 km with a snapshot polarimetric camera including a birefringent Wollaston prism, allowing simultaneous acquisition of two images along orthogonal polarization directions. From a large number of acquisitions datasets and under various environmental conditions (clear sky/fog/haze, day/night), we compare the efficiency of using polarized light for source contrast increase with different signal representations (intensity, polarimetric difference, polarimetric contrast, etc.). With the limited-dynamics detector used, a maximum fourfold increase in contrast was demonstrated under bright background illumination using polarimetric difference image.

Optimal estimation in polarimetric imaging in the presence of correlated noise fluctuations.

We quantitatively analyze how a polarization-sensitive imager can overcome the precision of a standard intensity camera when estimating a parameter on a polarized source over an intense background. We show that the gain is maximized when the two polarimetric channels are perturbed with significantly correlated noise fluctuations. An optimal estimator is derived and compared to standard intensity and polarimetric estimators.