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Malignant melanoma is considered the most serious type of skin cancer. In clinical practice, the conventional technique based on subjective visual examination has a high rate of misdiagnosis for malignant melanoma and benign nevus. Polarization imaging techniques have great potential in clinical diagnosis due to the advantages of improving sensitivity to functional structures, such as microfiber. In this paper, a set of human skin tissue sections, including 853 normal, 851 benign nevus, and 874 malignant melanoma, were analyzed and differentiated using a homemade high-fidelity Mueller matrix imaging polarimeter. The quantitative result using support vector machine algorithms confirmed that, while scalar retardance yields lower accuracy rates, vectorial retardance results in greater accuracy for both the training and testing sets. In particular, the cross-validation accuracy for the training set increased from 88.33% to 98.60%, and the prediction accuracy for the testing set increased from 87.92% to 96.19%. This tackles the limitation of the examination based on clinical experience and suggests that vectorial retardance can provide more accurate diagnostic evidence than scalar retardance. Unfortunately, it is inconvenient and time-consuming to read and analyze each component of the vectorial retardance simultaneously in the qualitative assessment. To address this clinical challenge, a color-encoded vectorial retardance imaging method was implemented. This method can provide superior tissue-specific contrast and more fiber details than scalar retardance. The anisotropic microfiber variation among different skin lesions, including the orientation and distribution, can be clearly highlighted. We believe that this work will not only enable early and rapid diagnosis of skin cancer but also provide a good observation and analysis of the state of cancer progression.

This paper highlights the application of decomposition methods in Mueller polarimetry for the discrimination of three groups of barley leaf samples from Hordeum vulgare: Chlorina mutant, Chlorina etiolated mutant and Cesaer varieties in the visible wavelength at λ = 632.8 nm. To obtain the anisotropic and depolarizing properties of the samples under study, the additive and multiplicative decompositions of experimental Mueller matrices were used. We show how a rich set of anisotropy and depolarization parameters obtained from decompositions can be used as effective observables for the discrimination between different varieties of the same plant species.

Recently, Mueller matrix polarimetry (MMP) has been widely applied in many aspects, such as radar target decomposition, monitoring the glucose level, tissue diagnostics, biological samples, etc., but it is still challenging for the complex light–matter interactions of rough surfaces and non-uniform structures such as 3D composite materials. In this work, a unitary matrix-based Mueller matrix decomposition (UMMMD) is proposed for non-destructive testing (NDT) of unmanned aerial vehicles (UAVs) skin. The decomposition model is constructed by the unitary matrix transformation of coherency matrices. In the model, the non-uniform depolarization caused by multiple scattering is quantified with the depolarization matrix and the entropy. From this model, the Mueller matrix of multiple scattering media can be completely decomposed. The proposed method can provide more polarization information than some traditional methods for multiple scattering under different polarization states. The contrast of the obtained polarization image can be improved by about 13 times compared to that of the original image. In addition, the key features of UAV skin such as deformation, shear angles, and density are obtained. The shear angles vary from 17° to 90°, and the average density is about 20/cm2. The provided experimental results show that this method is effective for the NDT of UAVs skin. The method also shows great potential for applications in target decomposition, NDT of 3D composite materials, 3D polarization imaging, light–matter interactions of non-uniform complex structures, etc.

Advances in vectorial polarization-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis. Imaging polarimetry requires determination of the Mueller matrix (MM) at every point, providing a complete description of an object’s vectorial properties. Despite forming a comprehensive representation, the MM does not usually provide easily interpretable information about the object’s internal structure. Certain simpler vectorial metrics are derived from subsets of the MM elements. These metrics permit extraction of signatures that provide direct indicators of hidden optical properties of complex systems, while featuring an intriguing asymmetry about what information can or cannot be inferred via these metrics. We harness such characteristics to reveal the spin Hall effect of light, infer microscopic structure within laser-written photonic waveguides, and conduct rapid pathological diagnosis through analysis of healthy and cancerous tissue. This provides new insight for the broader usage of such asymmetric inferred vectorial information.

The Jones matrix and the Mueller matrix of the coherent Rayleigh backscattering (RB) in single-mode fibers (SMFs) have been derived recently. It has been shown that both matrices depict two polarization effects—birefringence and polarization-dependent loss (PDL)—although the SMF under investigation is purely birefringent, having no PDL. In this paper, we aim to perform a theoretical analysis of both matrices using polar decomposition. The derived sub-Jones/Mueller matrices, representing birefringence and PDL, respectively, can be used to investigate the polarization properties of the coherent RB. As an application of the theoretical results, we use the derived formulas to investigate the polarization properties of the optical signals in phase-sensitive optical time-domain reflectometry (φ-OTDR). For the first time, to our knowledge, by using the derived birefringence–Jones matrix, the common optical phase of the optical signal in φ-OTDR is obtained as the function of the forward phase and birefringence distributions. By using the derived PDL–Mueller matrix, the optical intensity of the optical signal in φ-OTDR is obtained as the function of the forward phase and birefringence distributions as well as the input state of polarization (SOP). Further theoretical predictions show that, in φ-OTDR, the common optical phase depends on only the local birefringence in the first half of the fiber section, which is occupied by the sensing pulse, irrelevant of the input SOP. However, the intensity of the φ-OTDR signal is not a local parameter, which depends on the input SOP and the birefringence distribution along the entire fiber section before the optical pulse. Moreover, the PDL measured in φ-OTDR is theoretically proven to be a local parameter, which is determined by the local birefringence and local optical phase distributions.

At a particular frequency, most materials and objects of interest exhibit a polarization signature, or Mueller matrix, of limited dimensionality, with many matrix elements either negligibly small or redundant due to symmetry. Robust design of a polarization sensor for a particular material or object of interest, or for an application with a limited set of materials or objects, will adapt to the signature subspace, as well as the available modulators, in order to avoid unnecessary measurements and hardware and their associated budgets, errors, and artifacts. At the same time, measured polarization features should be expressed in the Stokes–Mueller basis to allow use of known phenomenology for data interpretation and processing as well as instrument calibration and troubleshooting. This approach to partial Mueller-matrix polarimeter (pMMP) design begins by defining a vector space of reduced Mueller matrices and an instrument vector representing the polarization modulators and other components of the sensor. The reduced-Mueller vector space is proven to be identical to R15 and to provide a completely linear description constrained to the Mueller cone. The reduced irradiance, the inner product of the reduced instrument and target vectors, is then applied to construct classifiers and tune modulator parameters, for instance to maximize representation of a specific target in a fixed number of measured channels. This design method eliminates the use of pseudo-inverses and reveals the optimal channel compositions to capture a particular signature feature, or a limited set of features, under given hardware constraints. Examples are given for common optical division-of-amplitude (DoA) 2-channel passive and serial/DoT-DoA 4-channel active polarimeters with rotating crystal modulators for classification of targets with diattenuation and depolarization characteristics.

Cyanine dyes are known to form H- and J-aggregates in aqueous solutions. Here we show that the cyanine dye, S0271, assembles in water into vortex induced chiral J-aggregates. The chirality of the J-aggregates depends on the directionality of the vortex. This study utilised both conventional benchtop CD spectropolarimeters and Mueller matrix polarimetry. It was found that J-aggregates have real chirality alongside linear dichroism and linear and circular birefringence. We identify the factors that are key to the formation of metastable chiral J-aggregates and propose a mechanism for their assembly.

Significance: The Mueller matrix decomposition method is widely used for the analysis of biological samples. However, its presumed sequential appearance of the basic optical effects (e.g., dichroism, retardance, and depolarization) limits its accuracy and application. Aim: An approach is proposed for detecting and classifying human melanoma and non-melanoma skin cancer lesions based on the characteristics of the Mueller matrix elements and a random forest (RF) algorithm. Approach: In the proposal technique, 669 data points corresponding to the 16 elements of the Mueller matrices obtained from 32 tissue samples with squamous cell carcinoma (SCC), basal cell carcinoma (BCC), melanoma, and normal features are input into an RF classifier as predictors. Results: The results show that the proposed model yields an average precision of 93%. Furthermore, the classification results show that for biological tissues, the circular polarization properties (i.e., elements m44, m34, m24, and m14 of the Mueller matrix) dominate the linear polarization properties (i.e., elements m13, m31, m22, and m41 of the Mueller matrix) in determining the classification outcome of the trained classifier. Conclusions: Overall, our study provides a simple, accurate, and cost-effective solution for developing a technique for classification and diagnosis of human skin cancer.

Due to the limited accuracy of experimental data, Mueller polarimetry can produce real 4×4 matrices that fail to meet required covariance or passivity conditions. A general and simple procedure to convert any real 4×4 matrix into a valid Mueller matrix by adding a portion of polarimetric white noise is presented. This approach provides deeper insight into the structure of Mueller matrices and has a subtle relation to the effective component of the Mueller matrix, which is defined through the subtraction of the fully random component of the characteristic decomposition. Up to a scale coefficient determined by the third index of polarimetric purity of the original Mueller matrix, the effective component retains complete information on the polarimetric anisotropies.

The properties of the state of polarization (SOP) and the degree of polarization (DOP) of Rayleigh backscattered light (RBL) in single-mode fibers (SMF) are investigated theoretically and experimentally when the incident probe is a perfectly coherent continuous-wave (CW) light. It is concluded that the instantaneous DOP of the coherently superposed RBL is always 100%, and the instantaneous SOP is determined by the distributions of the birefringence and the optical phase along the SMF. Therefore, the instantaneous SOP of the coherently superposed RBL does not have a constant relationship with the SOP of the incident CW probe. Furthermore, the instantaneous SOP varies randomly with time because the optical phase is very sensitive to ambient temperature and vibration even in the lab environment. Further theoretical derivation and experimental verification demonstrate, for the first time, that the temporally averaged SOP of the coherently superposed RBL has a simple constant relationship with the SOP of the incident CW probe, and the temporally averaged DOP is 1/3 in an SMF with low and randomly distributed birefringence. The derived formulas and obtained findings can be used to enhance the modelling and improve the performances of phase-sensitive optical time-domain reflectometry and other Rayleigh backscattering based fiber-optic sensors.