Experimental validation of Mueller matrix differential decomposition

Polarimetric measurement of non-depolarizing optical systems

The use of polarization measurements has become more common in recent years, as it gives more information than pure intensity measurements. Polarimetric components such as fixed or variable retarders and polarizers must be included in optical systems to obtain the polarization parameters required, and in many cases the optical system also includes other components such as relay and/or imaging optical systems. In this work we present a simple and robust method for the polarimetric characterization of non-depolarizing polarization components and other optical elements in the system, which does not require a full polarimeter. Since there is no depolarization, we represent the components as pure retarders with diattenuation and find their parameters (transmittance for the polarization components, angle of orientation of the fast axis, and retardance), from which we can retrieve their Mueller matrix. Our results show that the proposed method is accurate when compared with results obtained with a Mueller matrix dual-rotating retarder polarimeter calibrated using the eigenvalue calibration method, considered in this work as the gold standard, and is comparatively easier than the latter to implement, particularly for imaging polarimeters.

Tailoring chiral optical properties by femtosecond laser direct writing in silica

An object that possesses chirality, that is, having its mirror image not overlayed on itself by rotation and translation, can provide a different optical response to a left- or right-handed circular polarized light. Chiral nanostructures may exhibit polarization-selective optical properties that can be controlled for micro-to-nano optical element engineering. An attractive way to induce such complex nanostructures in three-dimension in glass is femtosecond laser direct writing. However, the mechanism of femtosecond laser induced chirality remains to be unveiled due to complex physical and chemical processes occurring during the ultrashort light-matter interaction. Here, a phenomenological model is proposed and is built on two-layers phase shifters to account for this laser-induced optical chirality in an initially achiral material (silica glass). This model is based on the observation that femtosecond laser induced nanogratings own two principal contributions to its aggregate birefringent response: a form and a stress-related one. By refining this formalism, a multilayer approach is developed to imprint on demand optical rotation. Values up to +/-60° at 550 nm within an optimal 80 μm thickness in silica glass are possible, corresponding to the highest value in a glass to date. These results provide new insights of circular-optical control in micro-nano optical manufacturing and open new opportunities for photonics applications.

Optimization design and performance analysis of quaternion spatial pseudo-depolarizer

In this study, to improve the uniformity of transmission light intensity of depolarizer, we present an optimal design of the quaternion space pseudo-depolarizer consisting of four wedge crystals. By designing the optical axis and wedge angle of each crystals, the square distribution of the output spot is realized. The mathematical expression of the degree of depolarization is obtained using the light wave superposition method. Theoretical analysis shows that the new type of depolarizer can optimize the intensity distribution of the emergent light field when the depolarizer wedge angle is sufficiently large, and it can realize the perfect depolarization of monochromatic linear polarized light. A samples of the quartz crystal material are developed and tested using lasers of 405 nm and 670 nm wavelengths. The degree of depolarization is observed to be 99% for any azimuth angle, whereas the angle of field of view is −10°–10°.

Isolating individual polarization effects from the Mueller matrix: comparison of two non-decomposition techniques

The prevailing formalisms for isolating individual polarization effects from the experimental Mueller matrix M can be broadly divided into two categories; decomposition of M to derive the individual optical effects and directly associating the individual optical effects to specific elements of M (i.e., non-decomposition techniques). Mueller matrix transformation (MMT) and direct interpretation of Mueller matrix (DIMM) are two popular techniques of the latter category. In this study, these two non-decomposition techniques (i.e., MMT and DIMM) are compared in a detailed quantitative analysis comprising of tissues (n = 53) and phantom (n = 45) samples. In particular, two commonly investigated polarimetric variables (i.e., depolarization and retardance) were calculated from the experimentally measured M using both the non-decomposition (i.e., MMT and DIMM) techniques. The comparison carried out with scatter plots (integrated with the correlation coefficients), violin plots and Bland and Altman plots revealed better agreement of depolarization-related variables (as compared to the retardance) between the two non-decomposition techniques. The comparative analyses presented here would be beneficial for the interpretation of polarimetric variables and optical characterization of turbid media.

Demonstration of a terahertz multi-spectral 3×3 Mueller matrix polarimetry system for 2D and 3D imaging

Mueller matrix polarimetry (MMP) has been demonstrated and recognized as an effective approach to attaining imaging enhancement as well as revealing polarization properties of an imaged sample. Generally, a minimum of 16 combinations of intensity-only measurements involving both linear and circular polarizations are required to completely and accurately determine the 4 × 4 Mueller matrix (MM) and comprehensively describe the polarization properties of the sample. However, broadband circular polarizations (CP) are rather difficult to obtain for design and fabrication limitations in the terahertz region, which poses a challenge to the acquisition of the 4 × 4 MM. In this circumstance, the 3 × 3 MM degradation using only linear polarizations (LP) is preferred and sufficient for characterization of non-depolarizing samples. In this paper, a multi-spectral 3 × 3 MMP system based on the THz time-domain spectroscopy (THz-TDS) is established from 0.1 to 1 THz. The system demonstrated is capable of fulfilling the accurate determination of the 3 × 3 MM. The Mueller matrix polar decomposition (MMPD), modified to be compatible with the MM degradation, is employed to explore the fine details and properties of the sample. By signal post-processing techniques, the MM elements in the time domain are retrieved, and the time dimension reflecting the depth information facilitates the 3D reconstruction of the sample. This work provides a prototype for 3D imaging of biological samples at higher frequencies in the future.

Optical Technologies for the Improvement of Skin Cancer Diagnosis: A Review

The worldwide incidence of skin cancer has risen rapidly in the last decades, becoming one in three cancers nowadays. Currently, a person has a 4% chance of developing melanoma, the most aggressive form of skin cancer, which causes the greatest number of deaths. In the context of increasing incidence and mortality, skin cancer bears a heavy health and economic burden. Nevertheless, the 5-year survival rate for people with skin cancer significantly improves if the disease is detected and treated early. Accordingly, large research efforts have been devoted to achieve early detection and better understanding of the disease, with the aim of reversing the progressive trend of rising incidence and mortality, especially regarding melanoma. This paper reviews a variety of the optical modalities that have been used in the last years in order to improve non-invasive diagnosis of skin cancer, including confocal microscopy, multispectral imaging, three-dimensional topography, optical coherence tomography, polarimetry, self-mixing interferometry, and machine learning algorithms. The basics of each of these technologies together with the most relevant achievements obtained are described, as well as some of the obstacles still to be resolved and milestones to be met.

Mueller polarimetric imaging for surgical and diagnostic applications: a review

Polarization is a fundamental property of light and a powerful sensing tool that has been applied to many areas. A Mueller matrix is a complete mathematical description of the polarization characteristics of objects that interact with light, and is known as a transfer function of Stokes vectors which characterise the state of polarization of light. Mueller polarimetric imaging measures Mueller matrices over a field of view and thus allows for visualising the polarization characteristics of the objects. It has emerged as a promising technique in recent years for tissue imaging, improving image contrast and providing a unique perspective to reveal additional information that cannot be resolved by other optical imaging modalities. This review introduces the basis of the Stokes-Mueller formulism, interpretation methods of Mueller matrices into fundamental polarization properties, polarization properties of biological tissues, and considerations in the construction of Mueller polarimetric imaging devices for surgical and diagnostic applications, including primary configurations, optimization procedures, calibration methods as well as the instrument polarization properties of several widely-used biomedical optical devices. The paper also reviews recent progress in Mueller polarimetric endoscopes and fibre Mueller polarimeters, followed by the future outlook in applying the technique to surgery and diagnostics. Tissue polarization properties convey morphological, micro-structural and compositional information of tissue with great potential for label free characterization of tissue pathological changes. Recent progress in tissue polarimetric imaging and polarization resolved endoscopy paved the way for translation of polarimetric imaging to surgery and tissue diagnosis.

Stokes-Mueller matrix polarimetry technique for circular dichroism/birefringence sensing with scattering effects

A surface plasmon resonance (SPR)-enhanced method is proposed for measuring the circular dichroism (CD), circular birefringence (CB), and degree of polarization (DOP) of turbid media using a Stokes–Mueller matrix polarimetry technique. The validity of the analytical model is confirmed by means of numerical simulations. The simulation results show that the proposed detection method enables the CD and CB properties to be measured with a resolution of 10 ? 4 refractive index unit (RIU) and 10 ? 5 ?? RIU , respectively, for refractive indices in the range of 1.3 to 1.4. The practical feasibility of the proposed method is demonstrated by detecting the CB/CD/DOP properties of glucose–chlorophyllin compound samples containing polystyrene microspheres. It is shown that the extracted CB value decreases linearly with the glucose concentration, while the extracted CD value increases linearly with the chlorophyllin concentration. However, the DOP is insensitive to both the glucose concentration and the chlorophyllin concentration. Consequently, the potential of the proposed SPR-enhanced Stokes–Mueller matrix polarimetry method for high-resolution CB/CD/DOP detection is confirmed. Notably, in contrast to conventional SPR techniques designed to detect relative refractive index changes, the SPR technique proposed in the present study allows absolute measurements of the optical properties (CB/CD/DOP) to be obtained.

Forward scattering of polarized light from a turbid slab: theory and Monte Carlo simulations

It is proved that if reciprocity and mirror symmetry hold for single scattering by a particle, they also hold for multiple scattering in turbid slab media. Monte Carlo simulations generate a reduced effective Mueller matrix for forward scattering, which satisfies reciprocity and mirror symmetry, but satisfies only reciprocity if the medium contains chiral components. The scattering matrix was factorized by using the Lu-Chipman polar decomposition, which affords the polarization parameters as a function of the radial distance from the center. The depolarization coefficients decrease with increasing distance, whereas the scattering-induced linear diattenuation and retardance become larger in the middle-distance range. The optical rotation for a chiral medium increases with increasing distance.

Physically meaningful depolarization metric based on the differential Mueller matrix

We present a novel depolarization metric for Mueller matrices based on the differential Mueller formalism. The proposed metric relies on the statistical interpretation of the differential Mueller matrix. We show that the differential depolarization index successfully quantifies depolarization even when applied to specific types of Mueller matrices for which some widely used depolarization metrics yield erroneous results. Moreover, the fact that the presented metric is directly linked to the variances and covariances of the elementary anisotropic properties of the sample makes it a valuable tool to quantify depolarization on a physically meaningful basis.

Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment

Polarized light point measurements and wide-field imaging have been studied for many years in an effort to develop accurate and information-rich tissue diagnostic methods. However, the extensive depolarization of polarized light in thick biological tissues has limited the success of these investigations. Recently, advances in technology and conceptual understanding have led to a significant resurgence of research activity in the promising field of bulk tissue polarimetry. In particular, with the advent of improved measurement, analysis, and interpretation methods, including Mueller matrix decomposition, new diagnostic avenues, such as quantification of microstructural anisotropy in bulk tissues, have been enabled. Further, novel technologies have improved the speed and the accuracy of polarimetric instruments for ex vivo and in vivo diagnostics. In this paper, we review some of the recent progress in tissue polarimetry, provide illustrative application examples, and offer an outlook to the future of polarized light imaging in bulk biological tissues.

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.

Two wavelength Mueller matrix reconstruction of blood plasma films polycrystalline structure in diagnostics of breast cancer

The model of a Mueller matrix description of mechanisms of optical anisotropy typical for polycrystalline films of blood plasma--optical activity, birefringence, as well as linear and circular dichroism--is suggested. On this basis, the algorithms of reconstruction of parameters distribution (polarization plane rotations, phase shifts, coefficients of linear and circular dichroism) of the indicated types of anisotropy were found for different spectrally selective ranges. Within the statistical analysis of such distributions, the objective criteria of differentiation of films of blood plasma taken from healthy women and breast cancer patients were determined. From the point of view of probative medicine, the operational characteristics (sensitivity, specificity and accuracy) of the method of Mueller matrix reconstruction of optical anisotropy parameters were found, and its efficiency in diagnostics of breast cancer was demonstrated.

Polarimetric study of birefringent turbid media with three-dimensional optic axis orientation

Recent approaches to the analysis of biological samples with three-dimensional linear birefringence orientation require numerical methods to estimate the best fit parameters from experimental measures. We present a novel analytical method for characterizing the intrinsic retardance and the three-dimensional optic axis orientation of uniform and uniaxial turbid media. It is based on a model that exploits the recently proposed differential generalized Jones calculus, remarkably suppressing the need for numerical procedures. The method is applied to the analysis of samples modeled with polarized sensitive Monte Carlo. The results corroborate its capacity to successfully characterize 3D linear birefringence in a straightforward way.

Physical model of differential Mueller matrix for depolarizing uniform media

In this article, we address the question of significance of the parameters of differential Mueller matrix formalism. We show how the concept of mean value and uncertainty of the optical properties recently introduced to depict this differential matrix can be related to the random fluctuations of these optical properties. From the layered-medium interpretation introduced by Jones [J. Opt. Soc. Am. 38, 671 (1948)] and extended to Mueller-Jones matrix by Azzam [J. Opt. Soc. Am. 68, 1756 (1978)], a generalization to depolarizing Mueller matrices is proposed. Based on the random Mueller-Jones matrix approach, the obtained parameterization perfectly fits the previous results from the literature. Necessary conditions of positivity on specific coefficients imposed in order to have physical Mueller matrix are introduced in a natural way and not inferred a posteriori. Interpretations of the underlying physical processes are also presented. An illustrative experimental example is provided from literature data.

Differential matrix physically admissible for depolarizing media: the case of diagonal matrices

In this Letter, we address the question of the physical validity of a depolarizing differential matrix. A parameterization of the diagonal terms of these depolarizing differential matrices is proposed. It ensures that the generators associated with diagonal depolarization terms lead to physical Mueller matrices. The validity of this parameterization is discussed. A condition is derived and related to the spatial extension of inhomogeneities with respect to the optical path length as proposed by Ossikovski [Opt. Lett. 36, 2330 (2011)].