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.

Bhattacharyya bound for Raman spectrum classification with a couple of binary filters.

Bhattacharyya bounds of classification error probability between two species with Raman and binary compressed Raman measurements limited by Poisson photon noise are analyzed. They exhibit the relevant physical parameters and lead to a simple expression of a minimal number of photons necessary to upper bound the optimal classification error probability.

Compressed Raman classification method with upper-bounded error probability.

Classification of different species with Raman measurements is analyzed when a total of exactly $ N $N photons are detected with binary filtered Raman spectra instead of fixing the measuring time. The optimal classification method for this problem leads to classification error probabilities upper-bounded by the Bhattacharyya bound and that are invariant to the multiplication of the spectrum intensities by an unknown factor. Furthermore, it is shown that this approach can be implemented with a number of binary filters smaller than the number of species to discriminate.

Precision of proportion estimation with binary compressed Raman spectrum.

The precision of proportion estimation with binary filtering of a Raman spectrum mixture is analyzed when the number of binary filters is equal to the number of present species and when the measurements are corrupted with Poisson photon noise. It is shown that the Cramer-Rao bound provides a useful methodology to analyze the performance of such an approach, in particular when the binary filters are orthogonal. It is demonstrated that a simple linear mean square error estimation method is efficient (i.e., has a variance equal to the Cramer-Rao bound). Evolutions of the Cramer-Rao bound are analyzed when the measuring times are optimized or when the considered proportion for binary filter synthesis is not optimized. Two strategies for the appropriate choice of this considered proportion are also analyzed for the binary filter synthesis.

Detection of imprecise estimations for polarization-resolved second-harmonic generation microscopy.

Second-harmonic generation microscopy can provide estimation of some local molecule distribution properties. However, in order not to get erroneous conclusions, it is important to detect measurements with insufficient precision. Such a detection technique is developed considering an approximation of the ultimate precision provided by the Cramer-Rao bound. This method is characterized and a simple approximation of its detection and false alarm probabilities is developed.

Precision of polarization-resolved second harmonic generation microscopy limited by photon noise for samples with cylindrical symmetry.

The estimation of parameters in polarization-resolved two-photon microscopy response perturbed by photon noise is analyzed in the context of second harmonic generation for the distribution of molecules presenting cylindrical symmetry. The estimation task is investigated using the Cramer-Rao lower bound for Poisson photon noise. It is shown that a noniterative technique can lead to estimation results that have good efficiencies for most of the physical possible values of the sample parameters for sufficiently high photon levels. The trade-off, between the number of incident polarization states and the total number of measured photons, that can be obtained with the Cramer-Rao lower bound is also discussed.

Van Cittert-Zernike theorem and symmetry properties of the normalized cross-spectral density matrix.

The van Cittert-Zernike theorem is formulated for the normalized cross-spectral density matrix of fields emitted by spatially incoherent sources. This formulation shows that sources with homogeneous polarization characteristics at second-order lead in the far field to normalized cross-spectral density matrices that possess high-symmetry properties. These symmetry properties are lost with polarization inhomogeneities of the source. These results are illustrated with ring-shaped sources.

Isotropic bicomponent partially polarized and partially coherent light.

The degree of coherence of scalar light remains constant when the fields are modified by the same random linear transformation, which can be represented by the multiplication by a random complex number. This shows that the coherence properties of scalar light at order two are not modified with the increase of disorder of each field that results from these transformations. We analyze the generalization of this property to partially polarized light. We determine the class of fields that can possess this property for any couple of points in a space-frequency or space-time domain after modification with deterministic Jones transformations. We show that the second-order coherence properties of this class of light can be generated experimentally with two uncorrelated totally polarized sources that have the same scalar coherence properties.

Evolution of 3D degrees of polarization with random unitary transformations.

The irreversible behavior of polarization properties that appears when random unitary transformations are applied to three-dimensional (3D) random optical fields is investigated. The ability of 3D degrees of polarization not to increase and to evolve independently of each other with such transformations is analyzed.

Maximal polarization order of random optical beams: reversible and irreversible polarization variations.

We discuss the degrees of polarization (DoP) of electromagnetic beams in time and frequency domains. The mean spectral DoP corresponds to the maximal temporal DoP when unitary transformations are applied in frequency domain. We demonstrate that random unitary transformations in frequency domain cannot increase the mean spectral DoP, implying that this quantity is a useful measure of the polarization order of light beams. This leads to a classification of time-domain polarization changes into reversible and irreversible processes.

Precision increase with two orthogonal analyzers in polarization-resolved second-harmonic generation microscopy.

We analyze the increase in precision of parameters estimation for polarization-resolved second-harmonic generation imaging microscopy when two intensities are measured with two orthogonal analyzers. The analysis is performed for measuring anisotropy parameters and molecule orientation for samples with cylindrical symmetry in the presence of photon noise with Poisson statistics. The improvement in comparison to global intensity measurement (i.e., without analyzer) is discussed.

Coherence and polarization properties in speckle of totally depolarized light scattered by totally depolarizing media.

When a totally unpolarized light is scattered by a medium that spatially totally depolarizes incident polarized light, the scattered field presents an increase of the order described by the temporal degree of polarization. We analyze the behavior of some polarization and coherence properties in such a physical situation.

Intensity correlations of partially polarized light: a field decomposition approach.

Intensity fluctuations of partially polarized light with Gaussian statistics are investigated using a field decomposition approach. These developments provide an enlightening interpretation of the Hanbury Brown-Twiss effect of partially polarized Gaussian light. In particular, the behavior of the intensity fluctuation correlations can be interpreted as resulting from the mixing of two incoherent lights between themselves.

Precision analysis in polarization-resolved second harmonic generation microscopy.

Polarization-resolved second harmonic generation (PSHG) imaging microscopy allows one to provide information such as anisotropy parameters and molecule orientation. We analyze the precision of parameter estimation for samples with cylindrical symmetry and a Gaussian additive noise model. We introduce improvements of existing techniques that can be useful to get rapid acquisition and processing of PSHG images, and we discuss the influence of photon noise.

Mixed segmentation-detection-based technique for point target detection in nonhomogeneous sky.

This paper deals with point target detection in infrared images of the sky for which there are local variations of the gray level mean value. We show that considering a simple image model with the gray level mean value varying as a linear or a quadratic function of the pixel coordinates can improve mixed segmentation-detection performance in comparison to homogeneous model-based approaches.

Two-point Stokes parameters: interpretation and properties.

Whereas the classic Stokes parameters are measures of intensity, the recently introduced two-point Stokes parameters characterize spatial coherence. It is shown that in analogy to the Stokes parameters, the two-point parameters have a physical interpretation as sums and differences of (scalar) cross-spectral density functions of specific electric-field components. A measurement scheme and several physical consequences of the two-point parameters are discussed.

Application of the deflection criterion to classification of radar SAR images.

An original application of the weighted deflection is proposed for radar target classification by quadratic filters. An explicit formulation of optimal filters is derived. We analyse the impact of the weighting parameter on real data recognition, and show that performances are better when the deflection coincides with the Fisher ratio.

Minimal stochastic complexity image partitioning with unknown noise model.

We present a generalization of a new statistical technique of image partitioning into homogeneous regions to cases where the family of the probability laws of the gray-level fluctuations is a priori unknown. For that purpose, the probability laws are described with step functions whose parameters are estimated. This approach is based on a polygonal grid which can have an arbitrary topology and whose number of regions and regularity of its boundaries are obtained by minimizing the stochastic complexity of the image. We demonstrate that efficient homogeneous image partitioning can be obtained when no parametric model of the probability laws of the gray levels is used and that this approach leads to a criterion without parameter to be tuned by the user. The efficiency of this technique is compared to a statistical parametric technique on a synthetic image and is compared to a standard unsupervised segmentation method on real optical images.

Nonparametric statistical snake based on the minimum stochastic complexity.

We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image are described with step functions with parameters that are estimated. The segmentation is thus obtained by minimizing a criterion that does not include any parameter to be tuned by the user. We illustrate the robustness of this technique on various types of images with level set and polygonal contour models. The efficiency of this approach is also analyzed in comparison with parametric statistical techniques.

Invariant degrees of coherence of partially polarized light.

The spatio-temporal properties of partially polarized light are analyzed in order to separate partial polarization and partial coherence. For that purpose we introduce useful invariance properties which allow one to characterize intrinsic properties of the optical light independently of the particular experimental conditions. This approach leads to new degrees of coherence and their relation with measurable quantities is discussed. These results are illustrated on some simple examples.