Polarimetry comprises a set of optical techniques of great interest in biophotonics due to its capability to obtain relevant information from biological samples by means of noninvasive and nondestructive methods. For instance, they are useful in pathology detection or different biological structures classification, among others. By studying the polarimetric response of biological samples we can obtain the information of how different structures produce different changes in the polarimetric characteristics of light. These changes depend on the polarimetric properties of the samples: depolarization, dichroism or retardance. From the experimental measurement of the Mueller matrix (M) of a sample, these polarimetric observables related to the mentioned tissue properties can be obtained. In this work, we propose the study of a particular set of observables derived from the Arrow decomposition of M. These parameters are used to inspect different biological tissues properties with the purpose of obtaining images with enhanced contrast of different biological structures in a tissue. In particular, we applied these observables to the study of a sample of animal origin: an ex-vivo cow brain; in order to differentiate between white and gray matter. Obtained results provide the interest of Arrow-derived polarimetric observables which may be of interest in multiple biomedical scenarios such as early pathology detection and diagnosis or enhanced visualization of different structures for clinical applications.
Complete characterization of biological samples is of potential interest in different industrial and research areas, as for instance, in biomedical applications, for the recognition of organic structures or for the early detection of some diseases. During the last decades, polarimetric methods are experiencing an increase of attention in the study of biomedical tissues, and they are nowadays used in such framework to provide qualitative (polarimetric imaging) and quantitative (data processing) information for the studied samples. Polarimetric methods are based on the analysis of polarization modifications produced by light-matter interactions which can be triggered by a number of complex internal processes but can be roughly understood as the result of the combination of three pure polarimetric features of the sample: its diattenuation, retardance and depolarization. For the analysis of the depolarization content, we propose the use of the Indices of Polarimetric Purity (IPP) to describe the sample behavior. Related with the randomness of the scattering processes, IPPs provide more information of depolarizing systems than the widely used depolarization index (p▵), which further synthetize the depolarization content of samples. Moreover, certain combinations of IPP parameters leads to p▵. As a result, IPPs allow the revelation of some structures from tissue samples hidden in regular intensity images of even in the p▵ channel, leading to better tissue classification results. In this work, we present different applications of IPPs in biomedical tissue that show its potential, which are not restricted to the biomedical framework as relevant results in plants characterization are also presented.
Light interaction with material systems may introduce depolarization to the incident light. This phenomenon comes from multiple scattering processes that take place inside the media and strongly depends on the particle characteristics. In the case of botany, plant leaves can be understood as depolarizing systems. A non-contact method to analyze these samples consist of illuminating them with well-known polarized light and study the scattered light to retrieve the physical characteristics of the sample. This physical study can be done by measuring the Mueller matrix of samples, in which the physical information of samples is encoded in their 16 elements and further mathematical treatment is required to extract the information. In the case of scattering systems, the depolarization content carries very valuable information but it is usually not inspected in the botanic field. A way to study depolarized content is by determining the so-called depolarization index PΔ, which gives an overall measure of the degree of depolarization of a system but it does not measure possible anisotropic dependence of the depolarization. For instance, a depolarizer equally depolarizing any fully polarized input polarization or a depolarizer that depolarizes them in a strongly heterogenous way, may lead to the same PΔ value. In contrast, the Indices of Polarimetric Purity (IPP) are a group of metrics that further synthesize the depolarizing content, taking into account the anisotropic depolarization. In this work, we describe the main physical characteristics of samples achieved by using these IPP through plant samples. Moreover, we show how IPP highlights some structures hidden in regular intensity measurements, highlighting the potential of these metrics for botanical applications.
Recently, a set of polarimetric indicators, the Indices of Polarimetric Purity (IPPs), were described in the literature. These indicators allow synthesize depolarization content of samples, and provide further analysis of depolarizers than other existing polarimetric indicators. We demonstrate the potential of the IPPs as a criterion to characterize and classify depolarizing samples. In particular, the method is firstly analyzed through a series of basic polarization experiments, and we prove how differences in the depolarizing capability of samples, concealed from the commonly used depolarization index PΔ, are identified with the IPPs.
In the second part of this work, the method is experimentally highlighted by studying a rabbit leg ex-vivo sample. The obtained images of the ex-vivo sample illustrate how IPPs provide a significant enhancement in the image contrast of some biological tissues and, in some cases, present new information hidden in the usual polarimetric channels. Moreover, new physical interpretation of the sample can be derived from the IPPs which allow us to synthesize the depolarization behavior.
Finally, we also propose a pseudo-colored encoding of the IPPs information that provides an improved visualization of the samples. This last technique opens the possibility to highlight a specific tissue structure by properly adjusting the pseudo-colored formula.
We highlight the interest of using the Indices of Polarimetric Purity (IPPs) for the biological tissue inspection. These are three polarimetric metrics focused on the study of the depolarizing behaviour of the sample. The IPPs have been recently proposed in the literature and provide different and synthetized information than the commonly used depolarizing indices, as depolarization index (PΔ) or depolarization power (Δ). Compared with the standard polarimetric images of biological samples, IPPs enhance the contrast between different tissues of the sample and show differences between similar tissues which are not observed using the other standard techniques. Moreover, they present further physical information related to the depolarization mechanisms inherent to different tissues. In addition, the algorithm does not require advanced calculations (as in the case of polar decompositions), being the indices of polarimetric purity fast and easy to implement. We also propose a pseudo-coloured image method which encodes the sample information as a function of the different indices weights. These images allow us to customize the visualization of samples and to highlight certain of their constitutive structures. The interest and potential of the IPP approach are experimentally illustrated throughout the manuscript by comparing polarimetric images of different ex-vivo samples obtained with standard polarimetric methods with those obtained from the IPPs analysis. Enhanced contrast and retrieval of new information are experimentally obtained from the different IPP based images.
The polarimetric properties of a material medium are summarized in the sixteen elements of its associated Mueller matrix. The quantities carrying specific information on the significant polarimetric features have to be defined on the basis of the analysis of the mathematical structure of Mueller matrices. It is found that any Mueller matrix can be parameterized through two retardance vectors and ten quantities that are invariant under dual retarder transformations. This parameterization leads to proper definitions of the retardance and depolarization properties, which together with the diattenuation and polarizance properties provide complete polarimetric characterization of the sample under consideration.
The measured Mueller matrices contain until sixteen independent parameters for each measurement configuration (spectral profile of the wave probe of the polarimeter, angle of incidence, observation direction...) and for each spatially resolved element of the sample (imaging polarimetry). Thus, the polarimetric techniques are widely used for the study of a great variety of material samples in optics and remote sensing. Nevertheless, the relevant physical information does not appear explicitly in the measured parameters and thus the best knowledge of the structure of the physical information contained in a Mueller matrix is required in order to develop appropriate procedures for the polarimetric analysis. In this paper, the physically invariant polarimetric quantities are identified and decoupled, and the main approaches for serial and parallel decompositions of measured Mueller matrices into simple components are reviewed.
The physical magnitudes involved in polarimetric phenomena are studied under a unified mathematical model based on coherency matrices. These magnitude arise as the real coefficients of the expansion of the coherency matrices on the basis constituted by n-1 the generators of SU(n) group and the nxn identity matrix. The states of polarization of light beams are analyzed in the general case where the three components of the wave field must be considered. The 3D polarization magnitudes are obtained and two non-dimensional invariant magnitudes are defined to represent the stability of the polarization ellipse and the stability of the propagation direction. These "indices of purity" derive in the well known degree of polarization when the propagation direction does not fluctuate. The model is also applied to the polarimetric properties of material media, where three non-dimensional invariant "indices of purity" are defined to represent the mixture of pure components resulting in depolarization behavior of the media as a whole.
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