Eigenvalue-based depolarization metric spaces for Mueller matrices.

We present a unified formal description and a detailed study of the depolarization spaces defined by various depolarization metrics based on the eigenvalues of the covariance matrix associated with a given Mueller matrix. By introducing natural generalizations of the common and Lorentz depolarization metrics, we likewise advance novel spaces appropriate for the description of extrinsic and intrinsic depolarization. We show the intimate relation existing between the depolarization spaces and the depolarization diagrams and solve the problem of the experimentally observed forbidden depolarization region. The theoretical developments are illustrated on numerical, analytical, and experimental examples of depolarizing Mueller matrices.

Innovative integrated numerical-experimental method for high-performance multispectral Mueller polarimeters based on ferroelectric liquid crystals.

In this work, an original and effective integrated numerical-experimental approach is proposed for building a high-performance multispectral Mueller polarimeter based on ferroelectric liquid crystals (FLCs). This method relies on accurate experimental characterization of the optical components specifically selected to construct such a system, combined with a numerical procedure used to optimize it, in the spectral range of interest, by means of a global optimization function. The proposed strategy enabled the construction of an FLC-based Mueller polarimeter in transmission configuration operating between 450 and 700 nm. The robustness of this system to various optical component misalignments, as well as the conditions to keep the measurement error less than 1% over the whole spectral range of interest, have been determined experimentally. The proposed strategy is very well suited to build optimized multispectral Mueller polarimetric systems for biomedical applications for which variations of the order of a few percent in the elements of the measured Mueller matrices need to be appreciated.

Symmetric decomposition of experimental depolarizing Mueller matrices in the degenerate case.

We propose a detailed procedure to determine the two retardance matrix factors entering the symmetric decomposition of Mueller matrices when the depolarizer matrix is partially degenerate (i.e., two out of three of its depolarization coefficients are equal), which is a common occurrence. Thanks to a relatively simple algebraic method, we show that linear retardance, as well as its eigenaxes orientation can be determined unambiguously from each retardance matrix factor. The method, applied on both experimental Mueller matrices of an ad hoc sample, as well as on that of a biological tissue, shows its efficiency for decoupling the different polarimetric effects of retardance that occur during the propagation of light throughout a complex medium.

On the equivalence between Young's double-slit and crystal double-refraction interference experiments.

We show, both analytically and experimentally, that under common experimental conditions the interference pattern produced in a classic Young's double-slit experiment is indistinguishable from that generated by means of a doubly refracting uniaxial crystal whose optic axis makes a skew angle with the light propagation direction. The equivalence between diffraction and crystal optics interference experiments, taken for granted by Arago and Fresnel in their pioneering research on the interference of polarized light beams, is thus rigorously proven.

Polar decompositions of negative-determinant Mueller matrices featuring nondiagonal depolarizers.

We generalize an existing algebraic procedure for the polar decomposition of Mueller matrices with negative determinants [Opt. Commun.281, 2406 (2008)OPCOB80030-401810.1016/j.optcom.2007.12.076] to the case of nondiagonal depolarizer matrix factors. The generalized procedure is applied to experimental Mueller matrices illustrating its potential for the phenomenological interpretation of complex polarimetric data.

Algebraic invariants for reflection Mueller polarimetry via uncompensated double pass illumination-collection optics.

We report on the identification of the two algebraic invariants inherent to Mueller matrix polarimetry measurements performed through double pass illumination-collection optics (e.g., an optical fiber or an objective) of unknown polarimetric response. The practical use of the invariants, potentially applicable to the characterization of nonreciprocal media, is illustrated on experimental examples.

One shot endoscopic polarization measurement device based on a spectrally encoded polarization states generator.

We report a novel technique for polarimetric characterization of samples through a flexible fiber endoscope, with a single shot measurement per pixel. The sample is simultaneously probed with a large diversity of polarization states, and both degree of polarization and linear retardance are determined thanks to specific processing of data. The probe polarization states are spectrally encoded on the 10 nm bandwidth of the source. The key component of the endoscope is a 3 m long specially designed optical fiber which consists of the optimized concatenation of highly birefringent fiber pieces. For a proof of principle, different calibrated or manufactured samples were successfully characterized. The proposed technique is attractive in view of reducing the measurement time of polarimetric images, in endoscopic applications.

Demonstration of full 4×4 Mueller polarimetry through an optical fiber for endoscopic applications.

A novel technique to measure the full 4 × 4 Mueller matrix of a sample through an optical fiber is proposed, opening the way for endoscopic applications of Mueller polarimetry for biomedical diagnosis. The technique is based on two subsequent Mueller matrices measurements: one for characterizing the fiber only, and another for the assembly of fiber and sample. From this differential measurement, we proved theoretically that the polarimetric properties of the sample can be deduced. The proof of principle was experimentally validated by measuring various polarimetric parameters of known optical components. Images of manufactured and biological samples acquired by using this approach are also presented.

Polarimetric imaging for cervical pre-cancer screening aided by machine learning: ex vivo studies.

Significance: Wide-field imaging Mueller polarimetry is an optical imaging technique that has great potential to become a reliable, fast, non-contact in vivo imaging modality for the early detection of, e.g., deceases and tissue structural malformations, such as cervical intraepithelial neoplasia, in both clinical and low-resource settings. On the other hand, machine learning methods have established themselves as a superior solution in image classification and regression tasks. We combine Mueller polarimetry and machine learning, critically assess the data/classification pipeline, investigate the bias arising from training strategies, and demonstrate how higher levels of detection accuracy can be achieved. Aim: We aim to automate/assist with diagnostic segmentation of polarimetric images of uterine cervix specimens. Approach: A comprehensive capture-to-classification pipeline is developed in house. Specimens are acquired and measured with imaging Mueller polarimeter and undergo histopathological classification. Subsequently, a labeled dataset is created within tagged regions of either healthy or neoplastic cervical tissues. Several machine learning methods are trained utilizing different training-test-set-split strategies, and their corresponding accuracies are compared. Results: Our results include robust measurements of model performance with two approaches: a 90:10 training-test-set-split and leave-one-out cross-validation. By comparing the classifier's accuracy directly with the ground truth obtained during histology analysis, we demonstrate how conventionally used shuffled split leads to an over-estimate of true classifier performance (0.964±0.00). The leave-one-out cross-validation, however, leads to more accurate performance (0.812±0.21) with respect to newly obtained samples that were not used to train the models. Conclusions: Combination of Mueller polarimetry and machine learning is a powerful tool for the task of screening for pre-cancerous conditions in cervical tissue sections. Nevertheless, there is a inherent bias with conventional processes that can be addressed using more conservative classifier training approaches. This results in overall improvements of the sensitivity and specificity of the developed techniques for "unseen" images.

Mueller polarimetric imaging as a tool for detecting the effect of non-thermal plasma treatment on the skin.

Non-thermal plasma (NTP) is a promising technique studied for several medical applications such as wound healing or tumor reduction. The detection of microstructural variations in the skin is currently performed by histological methods, which are time-consuming and invasive. This study aims to show that full-field Mueller polarimetric imaging is suitable for fast and without-contact detection of skin microstructure modifications induced by plasma treatment. Defrosted pig skin is treated by NTP and analyzed by MPI within 30 minutes. NTP is shown to modify the linear phase retardance and the total depolarization. The tissue modifications are inhomogeneous and present distinct features at the center and the fringes of the plasma-treated area. According to control groups, tissue alterations are primarily caused by the local heating concomitant to plasma-skin interaction.

Depolarization imaging for fast and non-invasive monitoring of cervical microstructure remodeling in vivo during pregnancy.

The cervix plays a crucial role in conception, maintenance of pregnancy, and childbirth. The mechanical properties of a pregnant woman's cervix change dramatically during gestation due to a remodeling of its microstructure, necessary for delivery. However, external factors can accelerate this process and lead to prematurity, the primary cause of perinatal mortality worldwide, due to the inefficiency of existing diagnostic methods. This study shows that polarized light is a powerful tool to probe the cervical microstructure during pregnancy. A wide-field multispectral polarimetric imaging system was fabricated to explore in vivo the cervix of full-term pregnant women. The polarimetric properties of the cervix change significantly with pregnancy progression. In particular, a set of several depolarization parameters (intrinsic and extrinsic) showed a strong linear correlation with gestational age in the red part of the visible spectral range. This trend can be attributed, among other things, to a decrease in collagen density and an increase in hydration of cervical connective tissue. Wide field depolarization imaging is a very promising tool for rapid and non-invasive analysis of cervical tissue in vivo to monitor the steady progression of pregnancy, providing the practitioner with useful information to improve the detection of preterm birth.

Mueller polarimetric imaging for fast macroscopic mapping of microscopic collagen matrix remodeling by smooth muscle cells.

Smooth muscle cells (SMCs) are critical players in cardiovascular disease development and undergo complex phenotype switching during disease progression. However, SMC phenotype is difficult to assess and track in co-culture studies. To determine the contractility of SMCs embedded within collagen hydrogels, we performed polarized light imaging and subsequent analysis based on Mueller matrices. Measurements were made both in the absence and presence of endothelial cells (ECs) in order to establish the impact of EC-SMC communication on SMC contractility. The results demonstrated that Mueller polarimetric imaging is indeed an appropriate tool for assessing SMC activity which significantly modifies the hydrogel retardance in the presence of ECs. These findings are consistent with the idea that EC-SMC communication promotes a more contractile SMC phenotype. More broadly, our findings suggest that Mueller polarimetry can be a useful tool for studies of spatial heterogeneities in hydrogel remodeling by SMCs.

Microstructural deformation observed by Mueller polarimetry during traction assay on myocardium samples.

Despite recent advances, the myocardial microstructure remains imperfectly understood. In particular, bundles of cardiomyocytes have been observed but their three-dimensional organisation remains debated and the associated mechanical consequences unknown. One of the major challenges remains to perform multiscale observations of the mechanical response of the heart wall. For this purpose, in this study, a full-field Mueller polarimetric imager (MPI) was combined, for the first time, with an in-situ traction device. The full-field MPI enables to obtain a macroscopic image of the explored tissue, while providing detailed information about its structure on a microscopic scale. Specifically it exploits the polarization of the light to determine various biophysical quantities related to the tissue scattering or anisotropy properties. Combined with a mechanical traction device, the full-field MPI allows to measure the evolution of such biophysical quantities during tissue stretch. We observe separation lines on the tissue, which are associated with a fast variation of the fiber orientation, and have the size of cardiomyocyte bundles. Thus, we hypothesize that these lines are the perimysium, the collagen layer surrounding these bundles. During the mechanical traction, we observe two mechanisms simultaneously. On one hand, the azimuth shows an affine behavior, meaning the orientation changes according to the tissue deformation, and showing coherence in the tissue. On the other hand, the separation lines appear to be resistant in shear and compression but weak against traction, with a forming of gaps in the tissue.

Polarimetric measurement utility for pre-cancer detection from uterine cervix specimens.

Prior work demonstrated significant contrast in visible wavelength Mueller matrix images for healthy and pre-cancerous regions of excised cervical tissue. This work demonstrates post-processing compressions of the full Mueller matrix that preserve detection performance. The purpose of this post-processing is to understand polarimetric measurement utility for computing mathematical observers and designing future imaging protocols. The detection performance of the full Mueller matrix, and both linear and non-linear parameters of the Mueller matrix will be compared. The area under the receiver operating characteristic (ROC) curve, otherwise known as the AUC, is the gold standard metric to quantify detection performance in medical applications. An AUC = 1 is perfect detection and AUC = 0.5 is the performance of guessing. Either the scalar retardance or the 3 smallest eigenvalues of the coherency matrix yield an average AUC of 0.94 or 0.93, respectively. When these four non-linear parameters are used simultaneously the average AUC is 0.95. The J-optimal Channelized Quadratic Observer (J-CQO) method for optimizing polarimetric measurements demonstrates equivalent AUC values for the full Muller matrix and 6 J-CQO optimized measurements. The advantage of this optimization is that only 6 measurements, instead of 16 for the full Mueller matrix, are required to achieve this AUC.

In vivo imaging of uterine cervix with a Mueller polarimetric colposcope.

Mueller polarimetric imaging enables the detection and quantification of modifications of the collagen fibers in the uterine cervix due to the development of a precancerous lesion. This information is not accessible through the use of the classic colposcope, a low magnification microscope used in current practice for cervical cancer screening. However, the in vivo application of Mueller polarimetric imaging poses an instrumental challenge: the device should be sufficiently compact, while still being able to perform fast and accurate acquisition of Mueller matrices in real-world conditions. In this study, the first wide field Mueller Polarimetric Colposcope (MPC) for the in vivo analysis of uterine cervix is presented. The MPC has been fabricated by grafting a miniaturized Mueller polarimetric imager on a classic colposcope. This new imaging tool performs the fast acquisition of Mueller polarimetric images, thus eliminating any blurring effects due to patient movements. It can be easily used by a practitioner with little change to their existing practice. Finally, the MPC was tested in vivo on a number of patients in the field.

Optical fiber-based full Mueller polarimeter for endoscopic imaging using a two-wavelength simultaneous measurement method.

This paper reports a technique based on spectrally differential measurement for determining the full Mueller matrix of a biological sample through an optical fiber. In this technique, two close wavelengths were used simultaneously, one for characterizing the fiber and the other for characterizing the assembly of fiber and sample. The characteristics of the fiber measured at one wavelength were used to decouple its contribution from the measurement on the assembly of fiber and sample and then to extract sample Mueller matrix at the second wavelength. The proof of concept was experimentally validated by measuring polarimetric parameters of various calibrated optical components through the optical fiber. Then, polarimetric images of histological cuts of human colon tissues were measured, and retardance, diattenuation, and orientation of the main axes of fibrillar regions were displayed. Finally, these images were successfully compared with images obtained by a free space Mueller microscope. As the reported method does not use any moving component, it offers attractive integration possibilities with an endoscopic probe.