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.

Self-organized arrays of dislocations in thin smectic liquid crystal films.

Combining optical microscopy, synchrotron X-ray diffraction and ellipsometry, we studied the internal structure of linear defect domains (oily streaks) in films of a smectic liquid crystal 8CB with thicknesses in the range of 100-300 nm. These films are confined between air and a rubbed PVA polymer substrate which imposes hybrid anchoring conditions (normal and unidirectional planar, respectively). We show how the presence or absence of dislocations controls the structure of highly deformed thin smectic films. Each domain contains smectic layers curved in the shape of flattened hemicylinders to satisfy both anchoring conditions, together with grain boundaries whose size and shape are controlled by the presence of dislocation lines. A flat grain boundary normal to the interface connects neighboring hemicylinders, while a rotating grain boundary (RGB) is located near the axis of curvature of the cylinders. The RGB shape appears such that dislocation lines are concentrated at its summit close to the air interface. The smectic layers reach the polymer substrate via a transition region where the smectic layer orientation satisfies the planar anchoring conditions over the entire polymer substrate and whose thickness does not depend on that of the film. The strength of planar anchoring appears to be high, larger than 10(-2) mJ m(-2), compensating for the high energy cost of creating an additional 2D defect between a horizontal smectic layer and perpendicular ones of the transition region. This 2D defect may be melted, in order to avoid the creation of a transition region structure composed of a large number of dislocations. As a result, linear defect domains can be considered as arrays of oriented defects, straight dislocations of various Burger vectors, whose location is now known, and 2D nematic defects. The possibility of easy variation between the present structure with a moderate amount of dislocations and a structure with a large number of dislocations is also demonstrated.

Differential Mueller matrix of a depolarizing homogeneous medium and its relation to the Mueller matrix logarithm.

The different z-dependence and non-commutativity of the two components of the differential Mueller matrix of a homogeneous depolarizing medium prevent its formal identification with the Mueller matrix logarithm. By using a classic linear differential equation expansion, we advance a procedure for the extraction of the elementary polarization properties, in terms of mean values and variances-covariances, from the Mueller matrix logarithm. The approximate solution, based on the immediate identification of the differential matrix with the matrix logarithm, turns out to remain satisfactory up to relatively high depolarization levels. Physically interpreted experimental examples from the literature illustrate the formal developments.

Optimization of Picrosirius red staining protocol to determine collagen fiber orientations in vaginal and uterine cervical tissues by Mueller polarized microscopy.

Polarized microscopy provides unique information on anisotropic samples. In its most complete implementation, namely Mueller microscopy, this technique is well suited for the visualization of fibrillar proteins orientations, with collagen in the first place. However, the intrinsic optical anisotropy of unstained tissues has to be enhanced by Picrosirius Red (PR) staining to enable Mueller measurements. In this work, we compared the orientation mapping provided by Mueller and second harmonic generation (SHG) microscopies on PR stained samples of vaginal and uterine cervix tissues. SHG is a multiphoton technique that is highly specific to fibrillar collagen, and was taken as the "gold standard" for its visualization. We showed that Mueller microscopy can be safely used to determine collagen orientation in PR stained cervical tissue. In contrast, in vaginal samples, Mueller microscopy revealed orientations not only of collagen but also of other anisotropic structures. Thus PR is not fully specific to collagen, which necessitates comparison to SHG microscopy in every type of tissue. In addition to this study of PR specificity, we determined the optimal values of the staining parameters. We found that staining times of 5 min, and sample thicknesses of 5 µm were sufficient in cervical and vaginal tissues.

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.

Determination of collagen fiber orientation in histological slides using Mueller microscopy and validation by second harmonic generation imaging.

We studied the azimuthal orientations of collagen fibers in histological slides of uterine cervical tissue by two different microscopy techniques, namely Mueller polarimetry (MP) and Second Harmonic Generation (SHG). SHG provides direct visualization of the fibers with high specificity, which orientations is then obtained by suitable image processing. MP provides images of retardation (among other polarimetric parameters) due to the optical anisotropy of the fibers, which is enhanced by Picrosirius Red staining. The fiber orientations are then assumed to be those of the retardation slow axes. The two methods, though fully different from each other, provide quite similar maps of average fiber orientations. Overall, our results confirm that MP microscopy provides reliable images of dominant fiber orientations at a much lower cost that SHG, which remains the "gold standard" for specific imaging of collagen fibers using optical microscopy.

Modeling the optical properties of self-organized arrays of liquid crystal defects.

Local full Mueller matrix measurements in the Fourier plane of a microscope lens were used to determine the internal anisotropic ordering in periodic linear arrays of smectic liquid crystal defects, known as 'oily streaks'. We propose a single microstructure-dependent model taking into account the anisotropic dielectric function of the liquid crystal that reproduces the smectic layers orientation and organization in the oily streaks. The calculated Mueller matrix elements are compared to the measured data to reveal the anchoring mechanism of the smectic oily streaks on the substrate and evidence the presence of new type of defect arrangement. Beyond the scientific inquiry, the understanding and control of the internal structure of such arrays offer technological opportunities for developing liquid-crystal based sensors and self-assembled nanostructures.

Multispectral Mueller polarimetric imaging detecting residual cancer and cancer regression after neoadjuvant treatment for colorectal carcinomas.

This work is devoted to a first exploration of Mueller polarimetric imaging for the detection of residual cancer after neoadjuvant treatment for the rectum. Three samples of colorectal carcinomas treated by radiochemotherapy together with one untreated sample are analyzed ex vivo before fixation in formalin by using a multispectral Mueller polarimetric imaging system operated from 500 to 700 nm. The Mueller images, analyzed using the Lu-Chipmann decomposition, show negligible diattenuation and retardation. The nonirradiated rectum exhibits a variation of depolarization with cancer evolution stage. At all wavelengths on irradiated samples, the contrast between the footprint of the initial tumor and surrounding healthy tissue is found to be much smaller for complete tumor regression than when a residual tumor is present, even at volume fractions of the order of 5%. This high sensitivity is attributed to the modification of stromal collagen induced by the cancer. The depolarization contrast between treated cancer and healthy tissue is found to increase monotonously with the volume fraction of residual cancer in the red part of the spectrum. Polarimetric imaging is a promising technique for detecting short-time small residual cancers, which is valuable information for pathological diagnosis and patient management by clinicians.

Application of spectroscopic ellipsometry and Mueller ellipsometry to optical characterization.

This article provides a brief overview of both established and novel ellipsometry techniques, as well as their applications. Ellipsometry is an indirect optical technique, in that information about the physical properties of a sample is obtained through modeling analysis. Standard ellipsometry is typically used to characterize optically isotropic bulk and/or layered materials. More advanced techniques such as Mueller ellipsometry, also known as polarimetry in the literature, are necessary for the complete and accurate characterization of anisotropic and/or depolarizing samples that occur in many instances, both in research and in real-life activities. In this article, we cover three main subject areas: Basic theory of polarization, standard ellipsometry, and Mueller ellipsometry. The first section is devoted to a short, pedagogical introduction of the formalisms used to describe light polarization. The second section is devoted to standard ellipsometry. The focus is on the experimental aspects, including both pros and cons of commercially available instruments. The third section is devoted to recent advances in Mueller ellipsometry. Application examples are provided in the second and third sections to illustrate how each technique works.

Ex vivo photometric and polarimetric multilayer characterization of human healthy colon by multispectral Mueller imaging.

Healthy human colon samples were analyzed ex vivo with a multispectral imaging Mueller polarimeter operating from 500 to 700 nm in a backscattering configuration with diffuse light illumination impinging on the innermost tissue layer, the mucosa. The intensity and polarimetric responses were taken on whole tissues first and after progressive exfoliation of the outer layers afterwards. Moreover, these measurements were carried out with two different substrates (one bright and the other dark) successively placed beneath each sample, allowing a reasonably accurate evaluation of the contributions to the overall backscattered light by the various layers. For the shorter investigated wavelengths (500 to 550 nm) the major contribution comes from mucosa and submucosa, while for the longer wavelengths (650 to 700 nm) muscular tissue and fat also contribute significantly. The depolarization has also been studied and is found to be stronger in the red part of the spectrum, mainly due to the highly depolarizing power of the muscular and fat layers.

Impact of model parameters on Monte Carlo simulations of backscattering Mueller matrix images of colon tissue.

Polarimetric imaging is emerging as a viable technique for tumor detection and staging. As a preliminary step towards a thorough understanding of the observed contrasts, we present a set of numerical Monte Carlo simulations of the polarimetric response of multilayer structures representing colon samples in the backscattering geometry. In a first instance, a typical colon sample was modeled as one or two scattering "slabs" with monodisperse non absorbing scatterers representing the most superficial tissue layers (the mucosa and submucosa), above a totally depolarizing Lambertian lumping the contributions of the deeper layers (muscularis and pericolic tissue). The model parameters were the number of layers, their thicknesses and morphology, the sizes and concentrations of the scatterers, the optical index contrast between the scatterers and the surrounding medium, and the Lambertian albedo. With quite similar results for single and double layer structures, this model does not reproduce the experimentally observed stability of the relative magnitudes of the depolarizing powers for incident linear and circular polarizations. This issue was solved by considering bimodal populations including large and small scatterers in a single layer above the Lambertian, a result which shows the importance of taking into account the various types of scatterers (nuclei, collagen fibers and organelles) in the same model.

Effect of speckle on APSCI method and Mueller Imaging.

The principle of the polarimetric imaging method called APSCI (Adapted Polarization State Contrast Imaging) is to maximize the polarimetric contrast between an object and its background using specific polarization states of illumination and detection. We perform here a comparative study of the APSCI method with existing Classical Mueller Imaging(CMI) associated with polar decomposition in the presence of fully and partially polarized circular Gaussian speckle. The results show a noticeable increase of the Bhattacharyya distance used as our contrast parameter for the APSCI method, especially when the object and background exhibit several polarimetric properties simultaneously.

Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging.

Cancerous and healthy human colon samples have been analyzed ex-vivo using a multispectral imaging Mueller polarimeter operated in the visible (from 500 to 700 nm) in a backscattering configuration with diffuse light illumination. Three samples of Liberkühn colon adenocarcinomas have been studied: common, mucinous and treated by radiochemotherapy. For each sample, several specific zones have been chosen, based on their visual staging and polarimetric responses, which have been correlated to the histology of the corresponding cuts. The most relevant polarimetric images are those quantifying the depolarization for incident linearly polarized light. The measured depolarization depends on several factors, namely the presence or absence of tumor, its exophytic (budding) or endophytic (penetrating) nature, its thickness (its degree of ulceration) and its level of penetration in deeper layers (submucosa, muscularis externa and serosa). The cellular density, the concentration of stroma, the presence or absence of mucus and the light penetration depth, which increases with wavelength, are also relevant parameters. Our data indicate that the tissues with the lowest and highest depolarizing powers are respectively mucus-free tumoral tissue with high cellular density and healthy serosa, while healthy submucosa, muscularis externa as well as mucinous tumor probably feature intermediate values. Moreover, the specimen coming from a patient treated successfully with radiochemotherapy exhibited a uniform polarimetric response typical of healthy tissue even in the initially pathological zone. These results demonstrate that multi-spectral Mueller imaging can provide useful contrasts to quickly stage human colon cancer ex-vivo and to distinguish between different histological variants of tumor.

Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data.

Colon samples with both healthy and cancerous regions have been imaged in diffuse light and backscattering geometry by using a Mueller imaging polarimeter. The tumoral parts at the early stage of cancer are found to be less depolarizing than the healthy ones. This trend clearly shows that polarimetric imaging may provide useful contrasts for optical biopsy. Moreover, both types of tissues are less depolarizing when the incident polarization is linear rather than circular. However, to really optimize an optical biopsy technique based on polarimetric imaging a realistic model is needed for polarized light scattering by tissues. Our approach to this goal is based on numerical Monte-Carlo simulations of polarized light propagation in biological tissues modeled as suspensions of monodisperse spherical scatterers representing the cell nuclei. The numerical simulations were validated by comparison with measurements on aqueous polystyrene sphere suspensions, which are commonly used as tissue phantoms. Such systems exhibit lower depolarization for incident linear polarization in the Rayleigh scattering regime, i.e. when the sphere diameters are smaller than the wavelength, which is obviously not the case for cell nuclei. In contrast, our results show that this behaviour can also be seen for "large" scatterers provided the optical index contrast between the spheres and the surrounding medium is small enough, as it is likely to be the case in biological tissues.

Experimental validation of the symmetric decomposition of Mueller matrices.

We experimentally assess the validity of the symmetric decomposition of Mueller matrices [R. Ossikovski, J. Opt. Soc. Am A 26, 1109-1118 (2009)] into a sequence of five factors consisting of a diagonal depolarizer between two retarder and diattenuator pairs. The raw data were Mueller images of combinations of polarization components which were individually measured and then assembled in different combinations. The possibility to recover all the elements is discussed, including the experimentally relevant cases of "degenerate" depolarizers, with two equal eigenvalues, which were not explicitly considered in the general theory.

Scattered light measurements on textured crystalline silicon substrates using an angle-resolved Mueller matrix polarimeter.

Dry plasma etching is a promising technique for crystalline silicon surface texturing aimed at improving solar cell efficiencies by reducing incident light reflection and backscattering at the cell front surface. In this work we present a new optical characterization technique for textured surfaces based on a Mueller polarimeter coupled with a high numerical aperture microscope operated either in real or in angular spaces. This tool provides both the specularly reflected and the angle-resolved backscattered intensities in a very efficient manner, due to the absence of moving parts. Three different silicon samples were etched in a standard reactor with SF(6)/O(2) plasmas at various RF powers, resulting in different textures that were characterized by scanning electron microscopy, standard reflectometry, and by our tool. The three techniques yielded consistent results. However, reflectometry could not take into account the backscattered light from highly textured surfaces, leading to significant underestimation of the overall amount of the reflected light. In contrast, our tool has demonstrated the potential to measure both reflected and backscattered light quickly and efficiently for all samples, paving the way for a new characterization technique for textured solar cells both at the development and at the production stage.

Angle resolved Mueller polarimetry with a high numerical aperture and characterization of transparent biaxial samples.

We present a polarimetric instrument suitable for the simultaneous measurement of angle resolved normalized Mueller matrices for polar angles ranging from 0 degrees to 60 degrees and all azimuths. The polarimetric modulation and analysis are performed by means of an optimized polarization state generator and analyzer based on nematic liquid crystals. A high numerical aperture (0.95) microscope objective is used in double pass to illuminate the sample, with its rear focal plane imaged on a low noise CCD. This polarimeter can be used either in reflection, with the sample set in the objective front focal plane, or in transmission, for thin transparent samples. This latter configuration, which involves an additional spherical mirror with its center of curvature at the objective front focus, is described in detail. This instrument was used to accurately determine the directions of the optic axes and the angular dependence of the retardation of a biaxial polyethylene terephthalate (PET) plastic substrate in spite of the strong depolarization essentially due to the source 10 nm spectral width or the limitation in angular resolution due to the pixels distribution of the CCD combined with the sample large retardation.

Experimental evidence for naturally occurring nondiagonal depolarizers.

We report on two Stokes nondiagonalizable Mueller matrices experimentally observed in a biological and in an organic sample. These matrices are examples of naturally occurring nondiagonal depolarizers whose unique property is to preserve the degree of polarization of all but one totally polarized light state. The description of the experimental matrices within the theory of Bragg scattering on cholesteric liquid crystals, as well as their interpretation in physical and structural terms, are likewise addressed.

Adapted polarization state contrast image.

We propose a general method to maximize the polarimetric contrast between an object and its background using a predetermined illumination polarization state. After a first estimation of the polarimetric properties of the scene by classical Mueller imaging, we evaluate the incident polarized field that induces scattered polarization states by the object and background, as opposite as possible on the Poincar e sphere. With a detection method optimized for a 2-channel imaging system, Monte Carlo simulations of low flux coherent imaging are performed with various objects and backgrounds having different properties of retardance, dichroism and depolarization. With respect to classical Mueller imaging, possibly associated to the polar decomposition, our results show a noticeable increase in the Bhattacharyya distance used as our contrast parameter.

Experimental implementation and properties of Stokes nondiagonalizable depolarizing Mueller matrices.

We report on the experimental realization of a family of depolarizing Mueller matrices that are Stokes nondiagonalizable. We likewise demonstrate a unique characteristic property of Stokes nondiagonalizable matrices consisting in the preservation of the degree of polarization of a single totally polarized input and illustrate it on our experimental example.