Linear optics and quantum maps

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.Comment: 13 pages, 8 figure

Radio Astronomical Polarimetry and the Lorentz Group

In radio astronomy the polarimetric properties of radiation are often modified during propagation and reception. Effects such as Faraday rotation, receiver cross-talk, and differential amplification act to change the state of polarized radiation. A general description of such transformations is useful for the investigation of these effects and for the interpretation and calibration of polarimetric observations. Such a description is provided by the Lorentz group, which is intimately related to the transformation properties of polarized radiation. In this paper the transformations that commonly arise in radio astronomy are analyzed in the context of this group. This analysis is then used to construct a model for the propagation and reception of radio waves. The implications of this model for radio astronomical polarimetry are discussed.Comment: 10 pages, accepted for publication in Astrophysical Journa

Depolarization metric spaces for biological tissues classification

Classification of tissues is an important problem in biomedicine. An efficient tissue classification protocol allows, for instance, the guided-recognition of structures through treated images or discriminating between healthy and unhealthy regions (e.g., early detection of cancer). In this framework, we study the potential of some polarimetric metrics, the so-called depolarization spaces, for the classification of biological tissues. The analysis is performed using 120 biological ex vivo samples of three different tissues types. Based on these data collection, we provide for the first time a comparison between these depolarization spaces, as well as with most commonly used depolarization metrics, in terms of biological samples discrimination. The results illustrate the way to determine the set of depolarization metrics which optimizes tissue classification efficiencies. In that sense, the results show the interest of the method which is general, and which can be applied to study multiple types of biological samples, including of course human tissues. The latter can be useful for instance, to improve and to boost applications related to optical biopsy.Agència de Gestió d'Ajuts Universitaris i de Recerca, Grant/Award Number: 2017-SGR-001500; Ministerio de Economía y Competitividad, Grant/Award Numbers: Fondos FEDER, RTI2018-097107-B-C3

Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix formulation is given for decoherence effects on the Stokes parameters, and a possible experiment is proposed. It is shown also that this Lorentz-group formalism leads to optical filters with a symmetry property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.

Combination of Persistent Scatterer Interferometry and Single-Baseline Polarimetric Coherence Optimisation to Estimate Deformation Rates with Application to Tehran Basin

This study reports on the monitoring of land subsidence in a rural area located in the southwest of the Tehran basin, Iran, by combining a persistent scatterer interferometry (PSI) method with a single-baseline polarimetric coherence optimisation. Owing to vegetation coverage in this rural area, coherence level experiences a decline and the performance and coverage of conventional interferometry to estimate deformation rate reduces concomitantly. Since the launch of satellites with polarimetric information, the polarimetric InSAR (PolInSAR) technique, which is vector interferometry with different polarimetric channels, has been introduced to optimise the coherence level. One of the most common criteria to select PS pixels is coherence and maximising the coherence can lead to an increased number of selected PS pixels and enhanced PSI performance. The single-baseline polarimetric coherence optimisation method assumes equal polarisation states at the end of each baseline. In order to apply this technique in our study, two different multi-look windows for coherence calculation and also two TerraSAR-X data sets with different numbers of images are used to assess their effect on the polarimetric PSI. Combination of the single-baseline coherence optimisation method with PSI shows significant improvements (more than 50%) in terms of the number of selected PS pixels in the case study even using a data set with a small number of images. A 15 × 15 multi-look window selects a greater number of PS pixels compared to a 9×9 multi-look window, although this entails reducing spatial resolution. The most effective PSI approach in terms of the density of the selected PS turned out to be polarimetric PSI using a data set with a large number of images and a selection of a 15 × 15 multi-look window. Validation of the PSI methods using a large number of images with 9×9 and 15 × 15 multi-look windows via levelling measurements confirms the accuracy and reliability of the results obtained

A Macroecological Analysis of SERA Derived Forest Heights and Implications for Forest Volume Remote Sensing

Individual trees have been shown to exhibit strong relationships between DBH, height and volume. Often such studies are cited as justification for forest volume or standing biomass estimation through remote sensing. With resolution of common satellite remote sensing systems generally too low to resolve individuals, and a need for larger coverage, these systems rely on descriptive heights, which account for tree collections in forests. For remote sensing and allometric applications, this height is not entirely understood in terms of its location. Here, a forest growth model (SERA) analyzes forest canopy height relationships with forest wood volume. Maximum height, mean, H100, and Lorey's height are examined for variability under plant number density, resource and species. Our findings, shown to be allometrically consistent with empirical measurements for forested communities world-wide, are analyzed for implications to forest remote sensing techniques such as LiDAR and RADAR. Traditional forestry measures of maximum height, and to a lesser extent H100 and Lorey's, exhibit little consistent correlation with forest volume across modeled conditions. The implication is that using forest height to infer volume or biomass from remote sensing requires species and community behavioral information to infer accurate estimates using height alone. SERA predicts mean height to provide the most consistent relationship with volume of the height classifications studied and overall across forest variations. This prediction agrees with empirical data collected from conifer and angiosperm forests with plant densities ranging between 102–106 plants/hectare and heights 6–49 m. Height classifications investigated are potentially linked to radar scattering centers with implications for allometry. These findings may be used to advance forest biomass estimation accuracy through remote sensing. Furthermore, Lorey's height with its specific relationship to remote sensing physics is recommended as a more universal indicator of volume when using remote sensing than achieved using either maximum height or H100

Complementary analysis of Mueller-matrix images of optically anisotropic highly scattering biological tissues

Background: Using optical techniques for tissue diagnostics (so-called ‘optical biopsy’) has been a subject of extensive research for many years. Various groups have been exploring different spectral and/or imaging modalities (e.g. diffuse reflectance spectroscopy, autofluorescence, Raman spectroscopy, optical coherence tomography (OCT), polarized light microscopy, etc.) for biomedical applications. In this paper, we report on using multi-wavelength imaging Mueller polarimetry combined with an appropriated image post-processing for the detection of tissue malignancy. Methods: We investigate a possibility of complementary analysis of Mueller matrix images obtained for turbid tissue-like scattering phantoms and excised human normal and cancerous colorectal tissue samples embedded in paraffin. Combined application of correlation, fractal and statistical analysis was employed to assess quantitatively the polarization-inhomogeneous scattered fields observed at the surface of tissue samples. Results: The combined analysis of the polarimetric images of paraffin-embedded tissue blocks has proved to be an efficient tool for the unambiguous detection of tissue malignant transformation. A fractal structure was clearly observed at spatial distributions of depolarization of light scattered in healthy tissues in a visible range of spectrum, while corresponding distributions for cancerous tissues did not show such dependence. We demonstrate that paraffin does not destroy a fractal structure of spatial distribution of depolarization. Thus, the loss of fractality in spatial distributions of depolarization for cancerous tissue is related to the structural changes in the tissue sample induced by cancer itself and, therefore, may serve as a marker of the disease. Conclusion: The obtained results emphasize that a combined use of statistical, correlation and fractal analysis for the Mueller-matrix image post-processing is an effective approach for an assessment of variations of optical properties in turbid tissue-like scattering media and biological tissues, with a high potential to be transferred to clinical practice for screening cancerous tissue samples