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Skin expansion is a well-established technique in plastic surgery, and recent studies have highlighted its potential in promoting hair regeneration. This study aimed to explore how the mechanical and optical properties of skin change during a prolonged stretching process. A hybrid method was developed to assess, in vivo, the effects of an 8-day skin stretching protocol—previously used in hair regeneration research—on the dorsal skin of mice. This method combined mechanical and optical measurement systems. Tensile stress–strain curves were generated using a spring-based setup, while optical properties such as scattering and birefringence were analyzed with a polarimetry imaging system that incorporated the Mueller matrix (MM) and Mueller matrix polar decomposition (MMPD) methods. The results showed that Young's modulus increased from approximately 5 kPa on day 1 to 60–100 kPa by days 6–8, indicating collagen fiber straightening and increased stiffness. Optical analysis revealed greater anisotropy in both scattering and birefringence, as reflected by changes in MM elements and MMPD results. These changes suggest skin adaptation and regeneration, particularly within the first 24 h of stretching. Interestingly, alterations in optical properties closely mirrored changes in mechanical properties, pointing to a coordinated process of structural remodeling and functional adaptation in the skin. These findings offer valuable insights into skin remodeling and adaptation, which could guide future tissue engineering strategies. [ABSTRACT FROM AUTHOR]

Chiral thin films showing electronic and plasmonic circular dichroism (CD) are intensively explored for optoelectronic applications. The most studied chiral organic films are the composites exhibiting a helical geometry, which often causes entanglement of circular optical properties with unwanted linear optical effects (linearly polarized absorption or refraction). This entanglement limits tunability and often translates to a complex optical response. This paper describes chiral films based on dark conglomerate, sponge-like, liquid crystal films, which go beyond the usual helical type geometry, waiving the problem of linear contributions to chiroptical electronic and plasmonic properties. First, we show that purely organic films exhibit high electronic CD and circular birefringence, as studied in detail using Mueller matrix polarimetry. Analogous linear properties are two orders of magnitude lower, highlighting the benefits of using the bi-isotropic dark conglomerate liquid crystal for chiroptical purposes. Next, we show that the liquid crystal can act as a template to guide the assembly of chemically compatible gold nanoparticles into 3D spiral-like assemblies. The Mueller matrix polarimetry measurements confirm that these composites exhibit both electronic and plasmonic circular dichroisms, while nanoparticle presence is not compromising the beneficial optical properties of the matrix. [ABSTRACT FROM AUTHOR]

We report a two-layer Mueller matrix model of polarized light propagation through layered human skin. Our model is based on single scattering approximation and the fact that the main scatterers in the top layer are various types of cells and the scatterers beneath it consist of fibers. By modeling the first layer mainly with spherical particles inducing the characteristics represented by Mueller matrices of depolarization and diattenuation, the second layer mainly with cylindrical scatterers inducing the retardance caused by scattering and birefringence, and considering the effects of the first layer to the second one, and the equal weight of contributions from both layers to a scatterer, it is possible to separate polarization properties of the medium induced by light propagation and scattering processes. One advantage of our model is that its extension to multi-layer tissues is straightforward. Polarization effects of human nail fold are identified. [ABSTRACT FROM AUTHOR]

Nanostructures represent a frontier where meticulous attention to the control and assessment of structural dimensions becomes a linchpin for their seamless integration into diverse technological applications. However, determining the critical dimensions and optical properties of nanostructures with precision still remains a challenging task. In this study, by using an integrative and comprehensive methodical series of studies, the evolution of the depolarization factors in the anisotropic Bruggeman effective medium approximation (AB‐EMA) is investigated. It is found that these anisotropic factors are extremely sensitive to the changes in critical dimensions of the nanostructure platforms. In order to perform a systematic characterization of these parameters, spatially coherent, highly‐ordered slanted nanocolumns are fabricated from zirconia, silicon, titanium, and permalloy on silicon substrates with varying column lengths using glancing angle deposition (GLAD). In tandem, broad‐spectral range Mueller matrix spectroscopic ellipsometry data, spanning from the near‐infrared to the vacuum UV (0.72–6.5 eV), is analyzed with a best‐match model approach based on the anisotropic Bruggeman effective medium theory. The anisotropic optical properties, including complex dielectric function, birefringence, and dichroism, are thereby extracted. Most notably, the research unveils a generalized, material‐independent inverse relationship between depolarization factors and column length. It is envisioned that the presented scaling rules will permit accurate prediction of optical properties of nanocolumnar thin films improving their integration and optimization for optoelectronic and photonic device applications. As an outlook, the highly porous nature and extreme birefringence properties of the fabricated columnar metamaterial platforms are further explored in the detection of nanoparticles from the cross‐polarized integrated spectral color variations. [ABSTRACT FROM AUTHOR]

Underwater target information is submerged in background scattered light due to the scattering effect of suspended particles in turbid water. In order to improve the quality of target imaging in turbid water, this paper proposes a method for achieving clear underwater target imaging using the second Lorentz depolarization index based on a dual division of focal plane Mueller matrix imaging system. This method can directly quantify the attenuation of light in water, and then solve a clear image of the target. Experimental results on underwater targets of different materials (plastic, paper, metal) show that the method proposed can effectively remove background scattering light while enhancing image contrast, ultimately improving the imaging quality of targets in turbid water. [ABSTRACT FROM AUTHOR]

Determining the optical and electronic properties of strongly anisotropic materials with symmetries below orthorhombic remains challenging; generalized ellipsometry is a powerful technique in this regard. Here, we employ Mueller matrix spectroscopic and temperature-dependent ellipsometry to determine the frequency dependence of six components of the dielectric-function tensor of the two-dimensional charge-transfer salt α -(BEDT-TTF)2I3 across its metal–insulator transition. Our results offer valuable insights into temperature-dependent changes of the components of the spectroscopic dielectric-function tensor across the metal–insulator transition. This advanced method allows extension to other electronic transitions. [ABSTRACT FROM AUTHOR]

A polarimeter, fundamental for characterizing the polarization state of light, is critical for advancing optical measurement techniques by delivering precise polarization information. A compact and portable polarimeter holds particular importance in applications like remote sensing and medical diagnosis. However, existing methods for developing a compact polarimeter are difficult to achieve full Stokes vector detection for broadband operation, and the noise immunity is also very weak. These defects significantly constrain the versatility of polarimeters across diverse application scenarios. Herein, a metadevice with dual-layer subwavelength grating structure for full Stokes vector detection has been proposed, capable of simultaneously achieving broadband detection and noise suppression. The intensity of the four elliptical polarization states of the incident light can be captured by four regions on this metadevice, enabling the computation of the full polarization state information via Mueller matrix inversion. Additionally, a set of optimized retardance at 0.73 π and orientation angles at 43°, 80°, 111°, and 146° is provided to effectively suppress the noise. The results indicate that the recovery error remains below 5% across the 450–650 nm spectral range, showcasing a 1.5-fold enhancement in noise suppression capability compared to conventional structures. [ABSTRACT FROM AUTHOR]

Significance: Mueller matrix imaging (MMI) is a comprehensive form of polarization imaging useful for assessing structural changes. However, there is limited literature on the polarimetric properties of brain specimens, especially with multispectral analysis. Aim: We aim to employ multispectral MMI for an exhaustive polarimetric analysis of brain structures, providing a reference dataset for future studies and enhancing the understanding of brain anatomy for clinicians and researchers. Approach: A multispectral wide-field MMI system was used to measure six fresh lamb brain specimens. Multiple decomposition methods (forward polar, symmetric, and differential) and polarization invariants (indices of polarimetric purity and anisotropy coefficients) have been calculated to obtain a complete polarimetric description of the samples. A total of 16 labels based on major brain structures, including grey matter (GM) and white matter (WM), were identified. K-nearest neighbors classification was used to distinguish between GM and WM and validate the feasibility of MMI for WM identification. Results: As the wavelength increases, both depolarization and retardance increase, suggesting enhanced tissue penetration into deeper layers. Moreover, utilizing multiple wavelengths allowed us to track dynamic shifts in the optical axis of retardance within the brain tissue, providing insights into morphological changes in WM beneath the cortical surface. The use of multispectral data for classification outperformed all results obtained with single-wavelength data and provided over 95% accuracy for the test dataset. Conclusions: The consistency of these observations highlights the potential of multispectral wide-field MMI as a non-invasive and effective technique for investigating the brain's architecture. [ABSTRACT FROM AUTHOR]

Cirrus clouds have an extensive global coverage and their high altitude means they play a critical role in the atmospheric radiation balance. Hexagonal ice plates and columns are two of the most abundant species present in cirrus and yet there remains a poor understanding of how surface roughness affects the scattering of light from these particles. To advance current understanding, the scattering properties of hexagonal ice plates with varying surface roughness properties are simulated using the discrete dipole approximation and the parent beam tracer physical–optics method. The ice plates are chosen to have a volume-equivalent size parameter of 2 π r / λ = 60 , where r is the radius of the volume-equivalent sphere, and a refractive index n = 1.31 + 0 i at a wavelength λ = 0.532 µm. The surface roughness is varied in terms of a characteristic length scale and an amplitude. The particles are rotated into 96 orientations to obtain the quasi-orientation averaged scattering Mueller matrix and integrated single-scattering parameters. The study finds that the scattering is largely invariant with respect to the roughness length scale, meaning it can be characterised solely by the roughness amplitude. Increasing the amplitude is found to lead to a decrease in the asymmetry parameter. It is also shown that roughness with an amplitude much smaller than the wavelength has almost no effect on the scattering when compared with a pristine smooth plate. The parent beam tracer method shows good agreement with the discrete dipole approximation when the characteristic length scale of the roughness is several times larger than the wavelength, with a computation time reduced by a factor of approximately 500. [ABSTRACT FROM AUTHOR]

Antiferromagnetic Weyl semimetal Mn3Sn exhibiting strong magneto-optical Kerr effect (MOKE) due to non-zero Berry curvature is attractive for spintronic and photonic device applications. Despite many reports on the anisotropic anomalous Hall effect (AHE), so far, there have been few studies on its anisotropic optical properties. In this work, we experimentally characterized the anisotropic optical and magneto-optical (MO) properties of Mn3Sn(20)/MgO(110) and Mn3Sn(0001)/Al2O3(0001) epitaxial films using ellipsometry in the wavelength range from 300 to 1690 nm. By measuring the Mueller matrix of magnetized Mn3Sn, the anisotropic permittivity tensor is determined using the 4 × 4 transfer matrix method. Temperature dependent MOKE measurement confirmed the origin of the anisotropic MO effect to the non-zero Berry curvature of the chiral magnetic phase. The measured permittivity also agrees well with first-principles calculations. The anisotropic optical and MO properties determined in this work can be useful for Mn3Sn based spintronic device characterization and photonic device development. [ABSTRACT FROM AUTHOR]

In the current paper, we represent intrinsic fluorescence anisotropies as four-dimensional normalized Stokes vectors defined by the maximum excitation and emission in the fluorescence process with respect to linear, linear-45 and circular polarizations of light. Depending upon the transition moments for absorption/excitation and emission of fluorophores, eight types of these Stokes vectors can be realized from the Mueller fluorescence matrix of the system. These Stokes vectors probe the orientational distribution of fluorophores and predict the nature of optically active biological proteins, whether laevorotatory or dextrorotatory. The orthogonality relation between the Stokes vectors corresponding to the excitation and emission processes of fluorescence connects the molecular ground and excited states of biological and non-biological systems. [ABSTRACT FROM AUTHOR]

Many species of beetles from the family Scarabaeidae reflect light with near-circular polarization. In some cases, spectral narrow-band polarization phenomena result in a distinct color with a metallic shine. In other cases, broad-band features are seen, and these beetles have a silvery or goldish appearance. These features in the cuticles originate from helicoidal structures, so-called circular Bragg structures and also referred to as Bouligand structures. In this communication, Protaetia mirifica, exhibiting near-circular polarization properties in dual spectral regions, centered approximately at the wavelengths of 474 and 770 nm, is investigated in considerable detail using Mueller matrix spectroscopic ellipsometry (MMSE). From interference oscillations in the MMSE spectra, the pitch profile of the helicoidal structures in the beetle cuticle is extracted and further used in electromagnetic modeling of the cuticle structure, including the determination of epicuticle and exocuticle thicknesses (280 nm and 8.1 µm, respectively) and anisotropic optical properties. These findings are confirmed by scanning electron microscopy. The analysis shows that the uppermost 4 µm of the cuticle has a nearly constant pitch of 310 nm, which abruptly jumps to 440 nm and then gradually increases up to 575 nm. Sum decompositions of MMSE spectra reveal that the beetle cuticle reflects like a circular polarizer or like a dielectric mirror, depending on the spectral region. [ABSTRACT FROM AUTHOR]

This paper proposes a full-automatic high-efficiency Mueller matrix microscopic imaging (MMMI) system based on the tissue microarray (TMA) for cancer inspection for the first time. By performing a polar decomposition on the sample's Mueller matrix (MM) obtained by a transmissive MMMI system we established, the linear phase retardance equivalent waveplate fast-axis azimuth and the linear phase retardance are obtained for distinguishing the cancerous tissues from the normal ones based on the differences in their polarization characteristics, where three analyses methods including statistical analysis, the gray-level co-occurrence matrix analysis (GLCM) and the Tamura image processing method (TIPM) are used. Previous MMMI medical diagnostics typically utilized discrete slices for inspection under a high-magnification objective (20×–50×) with a small field of view, while we use the TMA under a low-magnification objective (5×) with a large field of view. Experimental results indicate that MMMI based on TMA can effectively analyze the pathological variations in biological tissues, inspect cancerous cervical tissues, and thus contribute to the diagnosis of postoperative cancer biopsies. Such an inspection method, using a large number of samples within a TMA, is beneficial for obtaining consistent findings and good reproducibility. [ABSTRACT FROM AUTHOR]

Titanium dioxide (TiO2) thin films prepared by the sol–gel technique have been shown to be optically isotropic and, unlike the films obtained by competitive methods, do not exhibit measurable birefringence. A series of submicrometer-thin titanium dioxide films were prepared using the sol–gel technique and then thermally annealed at different temperatures. The samples were analyzed by spectroscopic ellipsometry using the Mueller matrix formalism, X-ray diffractometry and scanning electron microscopy. The conversion of amorphous titanium dioxide to polycrystalline anatase occurred at 400 °C or higher. Crystallites of a few percent of the film thickness were observed. Nevertheless, the crystallization process did not trigger the appearance of birefringence. These observations demonstrate that high-quality planar optical waveguides can be successfully fabricated on flexible substrates, in particular those composed of efficient polymers that can withstand the aforementioned temperatures. [ABSTRACT FROM AUTHOR]

Motivation Imaging Mueller polarimetry has already proved its potential for biomedicine, remote sensing, and metrology. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms. First, one must check the physical realizability of the experimental Mueller matrices in order to filter out non-physical data, i.e. to test the positive semi-definiteness of the 4 × 4 Hermitian coherency matrix calculated from the elements of corresponding Mueller matrix pixel-wise. For this purpose, we compared the execution time for the calculations of (i) eigenvalues, (ii) Cholesky decomposition, (iii) Sylvester's criterion, and (iv) coefficients of the characteristic polynomial (two different approaches) of the Hermitian coherency matrix, all calculated for the experimental Mueller matrix images (600 pixels × 700 pixels) of mouse uterine cervix. The calculations were performed using C++ and Julia programming languages. Results Our results showed the superiority of the algorithm (iv) based on the simplification via Pauli matrices over other algorithms for our dataset. The sequential implementation of latter algorithm on a single core already satisfies the requirements of real-time polarimetric imaging. This can be further amplified by the proposed parallelization (e.g. we achieve a 5-fold speed up on six cores). Availability and implementation The source codes of the algorithms and experimental data are available at https://github.com/pogudingleb/mueller_matrices. [ABSTRACT FROM AUTHOR]

To provide ongoing continuity for the ocean, cloud, and aerosol science data records, NASA will launch the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission on 8 February 2024. The Ocean Color Instrument (OCI) is the primary sensor onboard PACE and will provide ocean color science data to continue the data sets collected by heritage sensors MODIS, SeaWiFS, and VIIRS, but with increased spectral coverage and improved accuracy. The OCI is a grating spectrometer with hyperspectral coverage from the ultraviolet (about 315 nm) to near-infrared (about 900 nm), with additional filtered channels in the short-wave infrared (940 nm–2260 nm). A rigorous ground test program was conducted to calibrate the instrument and ensure that the calibration can be transferred to on-orbit operations in order to achieve the high levels of accuracy demanded by the science community. Some calibration parameters, such as polarization sensitivity, can only be measured during pre-launch testing. Tests were performed to measure the Mueller matrix components necessary to correct polarized scenes encountered on orbit. Measurements covered all spectral bands and a series of telescope scan angles encompassing the expected on-orbit scan range. The sensitivity (linear diattenuation) was measured above 340 nm to be below 0.6%, except at wavelengths, and was characterized as better than 0.1%. Below 340 nm, the sensitivity can be much higher, but this is not expected to affect the science data significantly. These results indicate that any polarized scenes encountered on orbit can be corrected with a high degree of confidence. [ABSTRACT FROM AUTHOR]

This paper delves into the depolarization phenomenon of materials using the integral equation method and Mueller matrix method. In the integral equation method, it is observed that depolarization trends with roughness are similar at different wavelengths, but numerical differences exist. The results are well-supported by both theory and experiments. Specifically, at 1064 nm wavelength, materials exhibit smaller depolarization peaks, smoother trends, and right-shifted peaks compared to 633 nm. Additionally, the polarization characteristics of materials may change with varying incident polarization states. The Mueller matrix method investigates the depolarization trend with varying incident angles and different roughness levels. It reveals a gradual increase in depolarization with the incident angle until 60°, followed by a rapid rise, reaching a peak around 80°. Moreover, materials with higher absorption coefficients exhibit stronger depolarization effects. Overall, this research uncovers the impact of absorption and scattering on the polarization properties of materials, providing valuable insights for future studies in polarization recognition. [ABSTRACT FROM AUTHOR]

Significance: Most biological fibrous tissues have anisotropic optical characteristics, which originate from scattering by their fibrous microstructures and birefringence of biological macromolecules. The orientation-related anisotropic interpretation is of great value in biological tissue characterization and pathological diagnosis. Aim: We focus on intrinsic birefringence and form birefringence in biological tissue samples. By observing and comparing the forward Mueller matrix of typical samples, we can understand the interpretation ability of orientation-related polarization parameters and further distinguish the sources and trends of anisotropy in tissues. Approach: For glass fiber, silk fiber, skeletal muscle, and tendon, we construct a forward measuring device to obtain the Mueller matrix image and calculate the anisotropic parameters related to orientation. The statistical analysis method based on polar coordinates can effectively analyze the difference in anisotropic parameters. Results: For those birefringent fibers, the statistical distribution of fast-axis values derived from Mueller matrix polar decomposition was found to exhibit bimodal characteristics, which is a key point in distinguishing the single-layer birefringent fiber sample from a layered, multioriented fibrous sample. The application conditions and interference factors of anisotropic orientation parameters are analyzed. Based on the parameters extracted from the orientation bimodal distribution, we can evaluate the relative change trend of intrinsic birefringence and form birefringence in anisotropic samples. Conclusions: The cross-vertical bimodal distribution of the fast axis of anisotropic fibers is beneficial to accurately analyze the anisotropic changes in biological tissues. The results imply the potential of anisotropic orientation analysis for applications in pathological diagnosis. [ABSTRACT FROM AUTHOR]

Significance: Breast cancer ranks second in the world in terms of the number of women diagnosed. Effective methods for its early-stage detection are critical for facilitating timely intervention and lowering the mortality rate. Aim: Polarimetry provides much useful information on the structural properties of breast cancer tissue samples and is a valuable diagnostic tool. The present study classifies human breast tissue samples as healthy or cancerous utilizing a surfaceilluminated backscatter polarization imaging technique. Approach: The viability of the proposed approach is demonstrated using 95 breast tissue samples, including 35 healthy samples, 20 benign cancer samples, 20 grade- 2 malignant samples, and 20 grade-3 malignant samples. Results: The observation results reveal that element m23 in the Mueller matrix of the healthy samples has a deeper color and greater intensity than that in the breast cancer samples. Conversely, element m32 shows a lighter color and reduced intensity. Finally, element m44 has a darker color in the healthy samples than in the cancer samples. The analysis of variance test results and frequency distribution histograms confirm that elements m23, m32, and m44 provide an effective means of detecting and classifying human breast tissue samples. Conclusions: Overall, the results indicate that surface-illuminated backscatter polarization imaging has significant potential as an assistive tool for breast cancer diagnosis and classification. [ABSTRACT FROM AUTHOR]

Significance: Quantitative optical polarimetry has received considerable recent attention owing to its potential for being an efficient diagnosis and characterizing tool with potential applications in biomedical research and various other disciplines. In this regard, it is crucial to validate various Mueller matrix (MM) decomposition methods, which are utilized to extract and quantify the intrinsic individual polarization anisotropy properties of various complex optical media. Aim: To quantitatively compare the performance of both polar and differential MM decomposition methods for probing the structural and morphological changes in complex optical media through analyzing their intrinsic individual polarization parameters, which are extracted using the respective decomposition algorithms. We also intend to utilize the decomposition-derived anisotropy parameters to distinguish among the cervical tissues with different grades of cervical intraepithelial neoplasia (CIN) and to characterize the healing efficiency of an organic crystal. Approach: Polarization MM of the cervical tissues with different grades of CIN and the different stages of the self-healing crystal are recorded with a home-built MM imaging setup in the transmission detection geometry with a spatial resolution of ≈400 nm. The measured MMs are then processed with both the polar and differential MM decomposition methods to extract the individual polarization parameters of the respective samples. The derived polarization parameters are further analyzed to validate and compare the performance of both the MM decomposition methods for probing and characterizing the structural changes in the respective investigated optical media through their decomposition-derived intrinsic individual polarization properties. Results: Pronounced differences in the decomposed-derived polarization anisotropy parameters are observed for cervical tissue sections with different grades of CIN. While a significant increase in the depolarization parameter ðΔÞ is obtained with the increment of CIN stages for both the polar [Δ = 0.32 for CIN grade one (CIN-I) and Δ = 0.53 for CIN grade two (CIN-II))] and differential (Δ = 0.35 for CIN-I and Δ = 0.56 for CIN-II) decomposition methods, a trend reversal is seen for the linear diattenuation parameter ðdLÞ, indicating the structural distortion in the cervical morphology due to the CIN disease. More importantly, with the differential decomposition algorithm, the magnitude of the derived dL parameter decreases from 0.26 to 0.19 with the progression of CIN, which was not being probed by the polar decomposition method. Conclusion: Our results demonstrate that the differential decomposition of MM holds certain advantages over the polar decomposition method to characterize and probe the structural changes in the cervical tissues with different grades of CIN. Although the quantified individual polarization parameters obtained through both the MM decomposition methods can be used as useful metrics to characterize various optical media, in case of complex turbid media such as biological tissues, incorporation of the differential decomposition technique may yield more efficient information. Also, the study highlights the utilization of MM polarimetry with an appropriate decomposition technique as an efficient diagnostic and characterizing tool in the realm of biomedical clinical research, and various other disciplines. [ABSTRACT FROM AUTHOR]

Significance: Current treatment for stage III colorectal cancer (CRC) patients involves surgery that may not be sufficient in many cases, requiring additional adjuvant systemic therapy. Identification of this latter cohort that is likely to recur following surgery is key to better personalized therapy selection, but there is a lack of proper quantitative assessment tools for potential clinical adoption. Aim: The purpose of this study is to employ Mueller matrix (MM) polarized light microscopy in combination with supervised machine learning (ML) to quantitatively analyze the prognostic value of peri-tumoral collagen in CRC in relation to 5-year local recurrence (LR). Approach: A simple MM microscope setup was used to image surgical resection samples acquired from stage III CRC patients. Various potential biomarkers of LR were derived from MM elements via decomposition and transformation operations. These were used as features by different supervised ML models to distinguish samples from patients that locally recurred 5 years later from those that did not. Results: Using the top five most prognostic polarimetric biomarkers ranked by their relevant feature importances, the best-performing XGBoost model achieved a patient-level accuracy of 86%. When the patient pool was further stratified, 96% accuracy was achieved within a tumor-stage-III sub-cohort. Conclusions: ML-aided polarimetric analysis of collagenous stroma may provide prognostic value toward improving the clinical management of CRC patients. [ABSTRACT FROM AUTHOR]

Significance: Knowledge of fiber microstructure and orientation in the brain is critical for many applications. Polarized light imaging (PLI) has been shown to have potential for better understanding neural fiber microstructure and directionality due to the anisotropy in myelin sheaths surrounding nerve fibers of the brain. Continuing to advance backscattering based PLI systems could provide a valuable avenue for in vivo neural imaging. Aim: To assess the potential of backscattering PLI systems, the ability to resolve crossing fibers, and the sensitivity to fiber inclination and curvature are considered across different imaging wavelengths. Approach: Investigation of these areas of relative uncertainty is undergone through imaging potential phantoms alongside analogous regions of interest in fixed ferret brain samples with a five-wavelength backscattering Mueller matrix polarimeter. Results: Promising phantoms are discovered for which the retardance, diattenuation and depolarization mappings are derived from the Mueller matrix and studied to assess the sensitivity of this polarimeter configuration to fiber orientations and tissue structures. Conclusions: Rich avenues for future study include further classifying this polarimeter's sensitivity to fiber inclination and fiber direction to accurately produce microstructural maps of neural tissue. [ABSTRACT FROM AUTHOR]

Active illumination light becomes strongly reflective interference light after specular reflection. It causes saturation in some areas of the image during target detection, resulting in the inability to recognize detailed target feature information. This greatly limits the application of active illumination detection. Based on the Mueller matrix analysis of the difference in polarization characteristics between the background specular reflected light and the target reflected light, we propose a reflection suppression method based on orthogonal polarization imaging. The method employs a polarization modulation strategy in a bidirectional manner between the light source and the detector. First, the polarization information difference is amplified by active polarized illumination between the background specular reflected light and the target reflected light. Then, the target recovery is achieved by suppressing the background specular reflected light through the polarized orthogonal imaging method. Meanwhile, this method can also be used for moving target detection. The experimental results show that the reflection suppression method of orthogonal polarization imaging can effectively suppress the interference of specular reflection on the target image. Additionally, it can reduce the problems of missed and false detection that occurs in moving target detection and improve the active illumination detection effect. [ABSTRACT FROM AUTHOR]

The transformation of the states of polarization of electromagnetic waves through their interaction with polarimetrically linear media can be represented by the associated Mueller matrices. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as the distance from the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed. [ABSTRACT FROM AUTHOR]

This work presents a complete Mueller matrix imaging polarimeter that uses three liquid-crystal retarders and a pixelated polarization camera. The polarimeter is characterized and optimized with a standard correction procedure here adapted to be performed fully in-situ, without any additional element, based on considering the polarization camera as the reference. The accuracy limit caused by the extinction ratio in the camera micro-polarizers is analyzed. Finally, the imaging polarimeter is tested experimentally by analyzing well-known samples for structured light applications such as patterned retarders, a patterned polarizer, and a liquid-crystal depolarizer. The work is presented in a tutorial style useful to reproduce the procedure by non-experts in polarimetry. [ABSTRACT FROM AUTHOR]

For a wide range of applications, a fast, non-destructive, remote, and sensitive identification of samples with predefined characteristics is preferred instead of their full characterization. In this work, we report on the experimental implementation of a nonlocal quantum measurement scheme, which allows for differentiation among samples out of a predefined set of transparent and birefringent objects in a distant optical channel. The measurement is enabled by application of polarization-entangled photon pairs and is based on remote state preparation. On an example set of more than 80 objects characterized by different Mueller matrices, we show that only two coincidence measurements are already sufficient for successful discrimination. The number of measurements needed for sample differentiation is significantly decreased compared to a comprehensive polarimetric analysis. Our results demonstrate the potential of this polarization detection method for polarimetric applications in biomedical diagnostics, remote sensing, and other classification/detection tasks. [ABSTRACT FROM AUTHOR]

Strain engineering has been extensively explored to modulate the various intrinsic properties of flexible inorganic semiconductor films. However, experimental characterization of tensile and compressive strain-induced modulation of optoelectronic properties and their differences has not been easily implemented in flexible inorganic semiconductor films. Herein, the strain-dependent structural, optical, and optoelectronic properties of flexible ZnO films under pre-tensile and pre-compressive strains are systemically investigated by a Mueller matrix ellipsometry-based quantitative characterization method combined with x-ray diffraction and first-principle calculation. With extended prestress-driven deposition processing under bi-direction bending modes, pre-tensile and pre-compressive strains with symmetric magnitudes can be achieved in flexible ZnO films, which allows precise observation of the strain-driven asymmetric modulation of optoelectronic properties. When the applied prestrain varies approximately equally from 0% (baseline) to −0.99% (compression) and 1.07% (tensility), respectively, the relative changes for the c-axis lattice constant are 0.0133 and 0.0104 Å, respectively. Meanwhile, the dependence factors of the bandgap energy on the pre-compression and pre-tensile strains were determined as −0.0099 and −0.0156 eV/%, respectively, and the complex refractive index also presents an asymmetric varying trend. With the help of the strain–stress analysis and the first-principle calculation, the intriguing asymmetric strain-optical modulation effect could be attributed to the biaxial strain mechanism and the difference in the deformation potential between the two prestrain modes. These systematic investigation consequences are thus promising as a basis for the booming applications of the flexible inorganic semiconductor ensemble. [ABSTRACT FROM AUTHOR]

Polarization imaging and sensing techniques have shown great potential for biomedical and clinical applications. As a novel optical biosensing technology, Mueller matrix polarimetry can provide abundant microstructural information of tissue samples. However, polarimetric aberrations, which lead to inaccurate characterization of polarization properties, can be induced by uneven biomedical sample surfaces while measuring Mueller matrices with complex spatial illuminations. In this study, we analyze the detailed features of complex spatial illumination-induced aberrations by measuring the backscattering Mueller matrices of experimental phantom and tissue samples. We obtain the aberrations under different spatial illumination schemes in Mueller matrix imaging. Furthermore, we give the corresponding suggestions for selecting appropriate illumination schemes to extract specific polarization properties, and then provide strategies to alleviate polarimetric aberrations by adjusting the incident and detection angles in Mueller matrix imaging. The optimized scheme gives critical criteria for the spatial illumination scheme selection of non-collinear backscattering Mueller matrix measurements, which can be helpful for the further development of quantitative tissue polarimetric imaging and biosensing. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Polarization imaging is a label-free and non-invasive technique that is sensitive to microstructure and suitable for probing the microstructure of living tissues. However, obtaining deep-layer information from tissues has been a challenge for optical techniques. In this work, we used tissue optical clearing (TOC) to increase optical penetration depth and characterize the layered structures of tissue samples. Different tissue phantoms were constructed to examine changes in the polarization features of the layered structure during the TOC process. We found that depolarization and anisotropy parameters were able to distinguish between single-layer and double-layer phantoms, reflecting microstructural information from each layer. We observed changes in polarization parameter images during the TOC process and, by analyzing different regions of the images, explained the sensitivity of these parameters to double-layer structures and analyzed the influence of oblique incident illumination. Finally, we conducted TOC experiments on living skin samples, leveraging the experience gained from phantom experiments to identify the double-layer structure of the skin and extract features related to layered structures. The results show that the combination of backscattering polarization imaging and tissue optical clearing provides a powerful tool for the characterization of layered samples. [ABSTRACT FROM AUTHOR]

The presented results concern the diagnostic application of vector-parameter polarization mapping and polarization-interference phase scanning applied to layered azimuths and ellipticity polarization maps obtained with the help of digital holographic reproduction for phase-inhomogeneous tissue layers in the female reproductive system. The differential diagnosis of the pathological changes in optically anisotropic polycrystalline tissue components, specifically "benign (fibroids) and precancerous (endometriosis)," was investigated. All studies within the representative groups of the histological samples were conducted using circularly polarized laser radiation, ensuring azimuthal invariance and polarization measurement reliability. Integral and layered maps and polarization azimuths and ellipticity random variable distribution histograms were obtained from the microscopic images of histological sections from the female reproductive system tumors. Systematized tables present statistical moments which characterize azimuths and ellipticity polarization maps for fibroids and endometriosis tissues. It is shown that the statistical parameters (diagnostic markers) are the most sensitive to benign and precancerous changes in the female reproductive system tissues. The results of information analysis, including the accuracy determination of the diagnostic vector- parameter polarization and polarization-interference methods for detecting and differentiating the samples of fibroids and precancerous endometriosis tissues in the female reproductive system, are presented. [ABSTRACT FROM AUTHOR]

Wide‐bandgap CsPbCl3 perovskite has fueled studies on applications in a variety of newly developing optoelectronic devices, including solar cells, lasers, light‐emitting diodes, and photodetectors. Most of them are now focused on film fabrication and device performance optimization, technology transfer of these proof‐of‐concept devices to the market will necessitate optimization of the device structure to minimize the optical loss and fabrication cost. While device model‐based electro‐optics simulations are considered a powerful method to attain the purpose, during which accurate optical constants are preconditions. Herein, for the first time, the optical constants of CsPbCl3 film through Mueller matrix spectroscopic ellipsometry (SE) are reported. Taking optoelectronic devices in vertical structure as a demonstration, simulations on the distributions of 2D electromagnetic field and photo‐generated electron field are arranged, successfully demonstrating the profile of the photons and electrons inside the devices. The evolution trend of device performance in the experiments matched with the simulations, for device performance is closely related to the photons and photo‐generated electrons. Benefitting from the simulations and experiments, general design criteria of the CsPbCl3‐based optoelectronic and photonic devices are posed, inevitably accelerating their development and commercialization. [ABSTRACT FROM AUTHOR]

Mueller polarimetry has proven to be a powerful optical technique to complement medical doctors in their conventional histology analysis. In this work, various degenerative and malignant human skin lesions were evaluated ex vivo using imaging Mueller polarimetry. The Mueller matrix images of thin sections of biopsies were recorded and the differential decomposition of Mueller matrices was applied pixel-wise to extract the polarization fingerprint of the specimens under study. To improve the classification accuracy, a deep learning model was created. The results indicate the sensitivity of polarimetry to different skin lesions and healthy skin zones and their differentiation, while using standard histological analysis as a ground truth. In particular, the deep learning model was found sufficiently accurate to detect and differentiate between all eight classes in the data set. Special attention was paid to the overfitting problem and the reduction of the loss function of the model. Our approach is an effort in establishing digital histology for clinical applications by complementing medical doctors in their diagnostic decisions. [ABSTRACT FROM AUTHOR]

This study delves into the polarization properties of various hair colors using several techniques, including polarization ray tracing, full Stokes, and Mueller matrix imaging. Our analysis involved studying hair in both indoor and outdoor settings under varying lighting conditions. Our results demonstrate a strong correlation between hair color and the degree of linear polarization. Specifically, light-colored hair, such as white and blond, exhibits high albedo and low DoLP. In contrast, dark hair, like black and brown hair, has low albedo and high DoLP. Our research also revealed that a single hair strand displays high diattenuation near specular reflections but high depolarization in areas with diffuse reflections. Additionally, we investigated the wavelength dependency of the polarization properties by comparing the Mueller matrix under illumination at 450 nm and 589 nm. Our investigation demonstrates the impact of hair shade and color on polarization properties and the Umov effect. [ABSTRACT FROM AUTHOR]

We present an advanced optical method to measure the phase function of circular intensity differential scattering (CIDS), i.e., the normalized Mueller matrix element -S14/S11, from individual single flowing through aerosol particles. Here, a 32-anode photomultiplier tube and its associated electronics, combined with an elliptical reflector, were used to record the scattering phase functions, when a particle were illuminated by a left-handed and a right-handed circular polarization laser beam around the focus of the reflector successively. The new design does not need lock-in amplifier, polarization modulator, and rotating goniometer as the traditional setup. It can reach a particle detection ability with a maximum rate of 50,000 particle/sec. CIDS phase functions from tryptophan particles, polystyrene latex microspheres, aggregates of Escherichia coli, Bacillus subtilis spores, Yersinia rohdei, and bacteriophage MS2 were measured, the results showed that this method has the ability to rapidly discriminate between single bioaerosol and non-bioaerosol particles. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A method and system for diagnosing subsurface scars of two-component biological structures has been developed based on the measurement and analysis of orientation and phase images of the Mueller matrices of optically thin samples. The diagnostic method is complemented by a classification analysis of informative features of Mueller matrix images. The diagnostic system has expanded functionality due to the introduction of a decision support subsystem. Fuzzy models of decision-making support were derived and the reliability of diagnosis of cervical oncology using the developed system was evaluated. [ABSTRACT FROM AUTHOR]

Optical anisotropy offers a heightened degree of flexibility in shaping optical properties and designing cutting-edge devices. Quasi-one-dimensional Ta2NiS5, with giant optical anisotropy, has been used in the development of new lasers and sensors. In this research endeavor, we successfully acquired the complete dielectric tensor of Ta2NiS5, utilizing the advanced technique of Mueller matrix spectroscopic ellipsometry, enabling a rigorous quantitative assessment of its optical anisotropy. The results indicate that Ta2NiS5 demonstrates giant birefringence and dichroism, with Δnmax = 1.54 and Δkmax = 1.80. This pursuit also delves into the fundamental underpinnings of this optical anisotropy, drawing upon a fusion of first-principles calculations and critical points analysis. The anisotropy of Ta2NiS5 arises from differences in optical transitions in different directions and is shown to be due to van Hove singularities without exciton effects. Its giant optical anisotropy is expected to be useful in the design of novel optical devices, and the revelation of the physical mechanism facilitates the modulation of its optical properties. [ABSTRACT FROM AUTHOR]

With the advantages of a large field of view, portability, and cost-effectiveness, lensless imaging has been applied widely nowadays. However, as a powerful tool for complete polarimetric characterization of microstructural and optical properties of a medium, Mueller matrix imaging has not yet been integrated in lensless imaging scheme. Here we propose a lensless inline polarization holographic system for high-speed and high-resolution Mueller matrix imaging. Liquid crystal variable retarders are introduced to realize high-speed response and avoid vibrations and positioning errors. We apply the blind deconvolution for depolarized imaging reconstruction and the back-propagation approach for polarization hologram reconstruction, respectively. The polarimetric imaging ability and resolution performance of the proposed technique are demonstrated. Furthermore, Mueller matrix images and certain quantitative polarimetric parameters of biological samples are calculated. The proposed method can be easily implemented and integrated in various lensless imaging techniques for on-chip polarimetric imaging. [ABSTRACT FROM AUTHOR]

Depending on processing methods and conditions, cellulose nanocrystal (CNC) films exhibit linear birefringence or selective Bragg reflection. The latter means reflection of light with left‐handed circular polarization (LCP) due to CNC in a helicoidal microstructure of the same handedness. Herein, glass‐supported CNC/polyethylene glycol (CNC/PEG) composite films with PEG concentrations in the range of 0–30% w/w with selective Bragg reflection at wavelengths from 440 to 550 nm are prepared. A modular device comprised of a dip‐coated birefringent CNC‐glass sample sandwiched between two CNC/PEG‐glass samples shows different responses to light with LCP and to light with right‐handed circular polarization (RCP). The device suppresses selective Bragg reflection from the rear (front) CNC/PEG sample for incident light with LCP (RCP), even when the birefringent film does not meet the condition for a halfwave plate. This behavior resembles the performance of optical diodes for circular polarization. Polarization properties of composite films and optical diodes in terms of degree of polarization and ellipticity are discussed within the Stokes–Mueller formalism. Electromagnetic simulations of Mueller matrices reveal the equivalence of modular and in‐tandem film approaches of optical diodes. [ABSTRACT FROM AUTHOR]

In this paper, Mueller polarimetry is applied to study the three groups of common barley leaf samples (Hordeum vulgare) in the visible spectrum (λ = 632.8 nm): Chlorina mutant, Chlorina etiolated mutant and Cesaer varieties. These samples differed in internal leaf structure from genetic mutation or by illumination during growth. Our main concern is to discriminate and characterize these three groups of leaf samples by depolarization metrics: degree of polarization (DoP), average degree of polarization (Average DoP), depolarization index (DI(M)), and Q(M) and R(M) metrics. The results obtained show that all depolarization metrics are sensitive to the sample's polarization properties. The most effective observable is the Q(M) metric in both forward and backward scattering. The DoP metric showed presence of depolarization anisotropy, which is significantly different for forward and backward scattering for all three groups of samples. Dichroism is observed for both forward and backward scattering, with lower dichroism in forward scattering. [ABSTRACT FROM AUTHOR]

The quality of the measured signature is influenced not only by the instrument's precision but also by the selected measurement configuration. In optical scatterometry, the purpose of measurement configuration optimization (MCO) is to select an optimal or suboptimal combination of measurement conditions, such as the angles of incidence, azimuth, polarization and wavelength, to achieve higher measurement accuracy. This analysis not only requires an effective optimization strategy but is also time-consuming. In this work, we propose a general MCO method that incorporates error propagation theory and condition-number-based error estimation technique, by which the MCO problem can be formulated as an optimization problem for the condition number of the coefficient matrix in the linear estimation of parameter deviations. The method is demonstrated on a multi-wavelength Mueller matrix scatterometry measuring a Si grating. With the help of the neural-network-based surrogate model, the feasibility of the method is verified by making a comparison with Latin hypercube sampling. Fitting results of the measured and calculated Mueller matrix spectra obtained at the selected optimal measurement configuration show a good agreement. The proposed method is promising to provide an alternate solution to globally evaluate the MCO problem in optical scatterometry and other measurement scenarios. [ABSTRACT FROM AUTHOR]

This document is an editorial from the journal Photonics, titled "Advanced Polarimetry and Polarimetric Imaging." It discusses the importance of polarization in light waves and its applications in various fields such as object detection, biomedical imaging, and remote sensing. The editorial highlights a special issue of the journal that focuses on advanced polarimeters and polarimetric imaging. It mentions the fourteen papers that were accepted for publication in this special issue, covering topics such as polarization measurements, metasurfaces and metamaterials, polarimetric imaging in scattering environments, and polarization lidar. The editorial concludes by emphasizing the progress and potential of polarization technology in various applications. [Extracted from the article]

The peri-tumoural stroma has been explored as a useful source of prognostic information in colorectal cancer. Using Mueller matrix (MM) polarized light microscopy for quantification of unstained histology slides, the current study assesses the prognostic potential of polarimetric characteristics of peri-tumoural collagenous stroma architecture in 38 human stage III colorectal cancer (CRC) patient samples. Specifically, Mueller matrix transformation and polar decomposition parameters were tested for association with 5-year patient local recurrence outcomes. The results show that some of these polarimetric parameters were significantly different (p value < 0.05) for the recurrence versus the no-recurrence patient cohorts (Mann–Whitney U test). MM parameters may thus be prognostically valuable towards improving clinical management/treatment stratification in CRC patients. [ABSTRACT FROM AUTHOR]

Chiral materials with strong linear anisotropies are difficult to accurately characterize with circular dichroism (CD) because of artifactual contributions to their spectra from linear dichroism (LD) and birefringence (LB). Historically, researchers have used a second‐order Taylor series expansion on the Mueller matrix to model the LDLB interaction effects on the spectra in conventional materials, but this approach may no longer be sufficient to account for the artifactual CD signals in emergent materials. In this work, we present an expression to model the measured CD using a third‐order expansion, which introduces "pairwise interference" terms that, unlike the LDLB terms, cannot be averaged out of the signal. We find that the third‐order pairwise interference terms can make noticeable contributions to the simulated CD spectra. Using numerical simulations of the measured CD across a broad range of linear and chiral anisotropy parameters, the LDLB interactions are most prominent in samples that have strong linear anisotropies (LD, LB) but negligible chiral anisotropies, where the measured CD strays from the chirality‐induced CD by factors greater than 103. Additionally, the pairwise interactions are most significant in systems with moderate‐to‐strong chiral and linear anisotropies, where the measured CD is inflated twofold, a figure that grows as linear anisotropies approach their maximum. In summary, media with moderate‐to‐strong linear anisotropy are in great danger of having their CD altered by these effects in subtle manners. This work highlights the significance of considering distortions in CD measurements through higher‐order pairwise interference effects in highly anisotropic nanomaterials. [ABSTRACT FROM AUTHOR]

We used a partial Mueller matrix polarimeter to measure the corneal anisotropic properties at three pupil sizes (dilated, natural, and constricted). The geometrical parameters of first order isochromes were described by quadrilaterals. These parameters are statistically significantly different between the three pupil sizes. The pupillary size changes do not influence the azimuth angle distribution α. The retardation R and birefringence distributions show asymmetry in the nasal–temporal cross-section. There are differences between pupil sizes for both nasal and temporal parts of the cornea for these distributions. Iridial light scattering and diffraction might be the reason for these differences. [ABSTRACT FROM AUTHOR]

This work presents a novel approach for investigating symmetry‐breaking processes during crystallization using Mueller matrix polarimetry. By applying this method to the cooling process of NaClO3 solutions, we demonstrate its ability to capture not only the initial and final stages of crystallization but also the intermediate steps and dynamics of the process. This technique provides more comprehensive information and insights into the symmetry‐breaking mechanisms involved in crystal formation. Overall, this study highlights the potential of Mueller matrix polarimetry for in situ statistical measurements of the optical rotation and for monitoring the evolution of enantiomeric excesses. [ABSTRACT FROM AUTHOR]

We studied the impact of two different thawing mechanisms on the microstructure of defrosted cryopreserved 3D tissue models using transmission Mueller microscopy and a statistical analysis of polarimetric images of thin histological sections of defrosted tissue models. The cryopreserved 3D tissue models were thawed by using either a 37 °C water bath or radio-frequency inductive heating with the magnetic nanoparticles embedded into the 3D tissue model during the preparation process. Polarimetric measurements were conducted at 700 nm and the acquired Mueller matrices of the samples were post-processed using the differential decomposition and the statistical analysis of the maps of the azimuth of the optic axis. Our results indicate the sensitivity of polarimetry to the changes in thawed tissue morphology compared to that of reference non-frozen tissue. Thus, Mueller microscopy can be used as a fast complementary technique to the currently accepted gold standard methods for the assessment of the cryopreserved tissue microstructure after thawing. [ABSTRACT FROM AUTHOR]

A 3 × 3 Mueller matrix polarimeter, as one of the primary polarization measurement tools, has attracted intensive interest in various fields of polarization optics. In this paper, from a novel viewpoint with more mathematical analysis of the basic configuration and the working performance of a 3 × 3 Mueller matrix polarimeter, we systematically study the relationship between Mueller matrix measurement errors with the configuration and characteristics of polarizers in the polarimeter. We figure out that, mathematically, there is an optimal orientation angle configuration (0°, 60°, and 120°) of polarizers, which inherently ensures a minimal relative measurement error in general. Moreover, we interpret the internal source of such a robust error resistance under this optimized configuration mathematically for the first time. Simulation and practical experiments show the effectiveness of our mathematical analyses, and compared to the frequently used orientation angle configuration, the average relative error is reduced by up to 32% under such an optimized configuration. [ABSTRACT FROM AUTHOR]