It is shown that there exist three classes of temporal structural coherence anisotropy characteristics of wide-sense stationary partially polarized lights. They present different behaviors in temporal interference experiments and are theoretically well founded. In addition, these three classes have remarkable representations in a temporal polarization intrinsic coherence Poincaré sphere.

In this communication, we show how partially polarized light reveals richer physical coherence properties than fully polarized light, uncovering subtle coherence features such as polarization coherence frustration.

A Poincaré-like sphere for spatial coherence characteristics leading to “visual algorithms” is introduced. Deterministic and random Jones transformations, as well as coherence optimization between lights at two spatial locations, can be apprehended with simple geometric transformations analogous to the ones used with the standard Poincaré sphere for polarization. The joint representation of polarization and coherence characteristics in a single global polarization intrinsic coherence Poincaré sphere allows one to easily identify remarkable physical situations.

We analyze the relation between the space-frequency and space-time coherence properties of scalar optical fields when deterministic and/or random linear transformations are performed in the frequency domain. Particular attention is paid to the irreversibility of the coherence properties under random operations. We introduce two time-domain order parameters, neither of which can increase under random transformations that preserve the power spectrum. We also identify different classes of spectrally completely coherent stochastic fields that the descriptors of coherence introduce. The results can be useful in the research of light propagation through random media.

It is shown that the canonical correlation method used with the intrinsic degrees of coherence (IDOCs) to describe coherence properties of partially polarized light is effective to identify relevant properties of the photo-detection correlations of a two-photon source described with its density operator. The results are compared with other global correlation measures. (c) 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.

It is shown that a polarization coherence un-frustrated field can become polarization coherence frustrated with propagation in vacuum. Each of the two necessary conditions for light to be polarization coherence un-frustrated, which correspond to different physical properties, can be lost with propagation in free space.

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 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.

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.

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.

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.

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.

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.

It has been shown that the Cramer-Rao bound (CRB) can be helpful to characterize vegetation and ground height estimations based on the homogenous random volume over ground (RVoG) model and polarimetric interferometric SAR techniques. However, this model is a function of 20 unknown parameters, which makes the performance analysis a tedious task. We show that the group invariance property of the RVoG model can greatly reduce the complexity of the analysis since the CRB of the vegetation and ground heights only depends on four unknown parameters instead of 20. Furthermore, for the considered situations analyzed in this letter, only three of these four parameters have a nonnegligible influence and can be interpreted as contrast parameters.

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.