Stokes Parameters Research Articles

100G Self-Coherent PON Based on Pre-Amplified Stokes Vector Direct Detection

100G Self-Coherent PON Based on Pre-Amplified Stokes Vector Direct Detection

Color polarization imaging demosaicing based on stokes vector information complementation and fusion

Color polarization imaging demosaicing based on stokes vector information complementation and fusion

PixPol: An In-Water Multispectral Polarized Upwelling Radiance Distribution Camera System

Abstract PixPol is an in-water multispectral polarized upwelling radiance distribution fisheye camera system. Its imaging sensors utilize a pixel-level polarizer structure allowing for polarimetric retrieval from one image capture, offering an advantage compared to other in-water polarimetric fisheye camera systems that require information from multiple images. When submerged, PixPol images a scene from which the first three Stokes parameters are derived at an angular resolution of 1° within a field of view that encompasses all azimuthal angles up to an elevation of 43° from nadir. For all viewing angles, Stokes parameter I and the linear polarization parameters, Q/I and U/I, are retrieved with an interpixel uncertainty of ±5%, ±0.02%, and ±0.02%, respectively. From these parameters, an uncertainty of ±0.01 is attained for the degree of linear polarization and ±0.9° for the angle of linear polarization. A description of the camera system, its radiometric and polarization calibration, and the associated uncertainties are described. Example images of the distribution of downwelling polarized light in the sky just above the ocean’s surface and upwelling polarized light just below the surface are provided.

Full Stokes-vector Inversion of the Solar Mg ii h and k Lines

The polarization of the Mg ii h and k resonance lines is the result of the joint action of scattering processes and the magnetic field–induced Hanle, Zeeman, and magneto-optical effects, thus holding significant potential for the diagnostic of the magnetic field in the solar chromosphere. The Chromospheric LAyer Spectro-Polarimeter sounding-rocket experiment, carried out in 2019, successfully measured at each position along the 196″ spectrograph slit the wavelength variation of the four Stokes parameters in the spectral region of this doublet around 280 nm, both in an active-region plage and in a quiet region close to the limb. We consider some of these CLASP2 Stokes profiles and apply to them the recently developed HanleRT Tenerife Inversion Code, which assumes a one-dimensional model atmosphere for each spatial pixel under consideration (i.e., it neglects the effects of horizontal radiative transfer). We find that the nonmagnetic causes of symmetry breaking, due to the horizontal inhomogeneities and the gradients of the horizontal components of the macroscopic velocity in the solar atmosphere, have a significant impact on the linear polarization profiles. By introducing such nonmagnetic causes of symmetry breaking as parameters in our inversion code, we can successfully fit the Stokes profiles and provide an estimation of the magnetic field vector. For example, in the quiet region pixels, where no circular polarization signal is detected, we find that the magnetic field strength in the upper chromosphere varies between 1 and 20 G.

Fluorescence scattering under the Stokes–Mueller formalism determines the orientational distribution of fluorophores and the nature of optically active biological proteins

Abstract 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.

Generation of partially coherent full Poincaré beam arrays and their Stokes scintillations in turbulent media

A type of vector beam arrays, called partially coherent full Poincaré (PCFP) beam arrays, is introduced and experimentally synthesized using modal-vector-decomposition method. Our experimental system involves a digital micro-mirror device, which can generate such beam arrays with controllable spatial coherence and array structure in almost real-time, enabling to test the impact of atmospheric turbulence on them. Furthermore, we experimentally examine the scintillations of four Stokes parameters (denoted as S0, S1, S2, and S3) of PCFP beam arrays propagating through lab-simulated turbulence. The results indicate that the Stokes scintillations decrease as the number of beamlets increase or spatial coherence decreases. In contrast to S0 scintillation (intensity scintillation), S1, S2, or S3 scintillation is less affected by the turbulence under the same conditions. Our experimental results show that S2 and S3 scintillations could reduce by 67.2% and 52.4% compared to the intensity scintillation in strong turbulence. Our findings have potential applications in free-space optical communication when the Stokes parameter S2 or S3 is served as an information carrier.

Stokes-based analysis for the estimation of 3D dipolar emission

We provide a general description of the measurement capabilities of systems that probe the 3D state of polarization of light emitted by a dipole or a collection of dipoles. This analysis is based on a generalization of the Stokes parameters for 3D polarization, and its goal is to provide insight into what constitutes a good measurement system under specific circumstances, through the definition of appropriate merit functions. Three cases are considered: the general case of arbitrary states of 3D polarization, the special case of 3D linear full or partial polarization states, and the even more specific case of linear dipoles that wobble with rotational symmetry around a central direction. Note that the latter two cases are of interest in fluorescence microscopy. The analysis presented here is illustrated by applying it to two different approaches used commonly in orientation microscopy: PSF engineering and ratiometric measurements.

Polarized spectral bidirectional reflectance distribution function in visible band based on Cauchy’s empirical dispersion equation

The polarized bidirectional reflectance distribution function (pBRDF) can describe the changes between the Stokes vectors of incident and reflected light. The existing model can only describe the spatial distribution of the target’s polarization characteristics at a single wavelength, so further research is needed for the description of the target’s polarized spectral characteristics. In this paper, a modified three-component polarized spectral bidirectional reflectance distribution function (pSBRDF) is proposed, which combines Fresnel equation in the specular reflection component with Cauchy’s empirical dispersion equation, by introducing the wavelength variable and dispersion constants that do not change with wavelength. The degree of the linear polarization (DoLP) of two types of coated fabric samples was measured at three incident angles and 400 to 760 nm wavelength. The error of the model in describing the spectral and the spatial distribution of DoLP are controlled within 0.00743 and 0.0757 respectively, which proves the accuracy of the model. This research provides the model basis for analysis of the target’s polarization characteristics and the theoretical basis for the application of polarization detection.

Measuring linear birefringence via rotating-sample transmission Stokes spectropolarimetry

Linear birefringence is a fundamental property of optically anisotropic media, defined by the difference in refractive index experienced by light polarized along orthogonal directions. It is usually manifested in microscopically aligned molecular systems, where a preferential direction of light–matter interaction is created. For instance, the anisotropic structure of calcite crystal causes the famous double-refraction phenomenon. Another common example is commercial adhesive tapes, which are polymeric materials possessing birefringent properties due to their manufacturing processes. The intrinsic relation between birefringence and molecular alignment forges a new analytical route to study materials such as polymeric thin films. Therefore, the capacity of measuring linear birefringence and its fast axis is of paramount importance for the science of anisotropic molecular systems. In this contribution, a comprehensive approach to acquire linear birefringence using rotating-sample transmission Stokes spectropolarimetry is presented and applied to transparent adhesive tapes as a case study. The experimental setup comprises a thermal light source and a spectropolarimeter capable of determining wavelength distributions of Stokes parameters. The samples are carefully aligned in a rotating mount and subjected to a fixed broadband vertically polarized light beam. Then, the transmitted light is analyzed using a rotating retarder type of spectropolarimeter. Through systematic variation of the sample’s angular position, the Stokes parameters of transmitted light are measured for each transmitted wavelength as a function of the sample’s angular position. The linear retardance and fast axis direction relative to the tape’s long axis are then determined from the modulation of Stokes parameters over sample rotation. The model derivation, experimental procedure, and signal processing protocol are described in detail, and the approach is verified with a simple correlation between linear retardance and the number of stacked layers of tape.

Mapping the Longitudinal Magnetic Field in the Atmosphere of an Active Region Plage from the Inversion of the Near-ultraviolet CLASP2.1 Spectropolarimetric Data

We apply the HanleRT Tenerife Inversion Code to the spectropolarimetric observations obtained by the Chromospheric Layer Spectropolarimeter. This suborbital space experiment measured the variation with wavelength of the four Stokes parameters in the near-ultraviolet spectral region of the Mg ii h and k lines over a solar disk area containing part of an active region plage and the edge of a sunspot penumbra. We infer the stratification of the temperature, the electron density, the line-of-sight velocity, the microturbulent velocity, and the longitudinal component of the magnetic field from the observed intensity and circular polarization profiles. The inferred model atmosphere shows larger temperature and electron density in the plage and the superpenumbra regions than in the quiet regions. The shape of the plage region in terms of its brightness is similar to the pattern of the inferred longitudinal component of the magnetic field in the chromosphere, as well as to that of the overlying moss observed by the Atmospheric Imaging Assembly in the 171 Å band, which suggests a similar magnetic origin for the heating in both the plage and the moss region. Moreover, this heating is particularly significant in the regions with larger inferred magnetic flux. In contrast, in the superpenumbra, the regions with larger electron density and temperature are usually found in between these regions with larger magnetic flux, suggesting that the details of the heating mechanism in the chromosphere of the superpenumbra may be different from those in the plage, but with the magnetic field still playing a key role.

POLCAM: instant molecular orientation microscopy for the life sciences

Current methods for single-molecule orientation localization microscopy (SMOLM) require optical setups and algorithms that can be prohibitively slow and complex, limiting widespread adoption for biological applications. We present POLCAM, a simplified SMOLM method based on polarized detection using a polarization camera, which can be easily implemented on any wide-field fluorescence microscope. To make polarization cameras compatible with single-molecule detection, we developed theory to minimize field-of-view errors, used simulations to optimize experimental design and developed a fast algorithm based on Stokes parameter estimation that can operate over 1,000-fold faster than the state of the art, enabling near-instant determination of molecular anisotropy. To aid in the adoption of POLCAM, we developed open-source image analysis software and a website detailing hardware installation and software use. To illustrate the potential of POLCAM in the life sciences, we applied our method to study α-synuclein fibrils, the actin cytoskeleton of mammalian cells, fibroblast-like cells and the plasma membrane of live human T cells.

POLARIZATION-CORRELATION MAPPING OF MICROSCOPIC IMAGES OF BIOLOGICAL TISSUES OF DIFFERENT MORPHOLOGICAL STRUCTURE

The results of polarization-correlation mapping of the fourth parameter of the two-point Stokes vector of microscopic images of histological sections of biological tissues with different architectonics of the optically anisotropic polycrystalline component are presented. The coordinate distributions of randomly generated values representing the modulus of the fourth parameter of the polarization-correlation vector from microscopic images of histological sections of fibrillar tissues (such as skin dermis) and parenchymal tissues (like spleen) have been replicated. The statistical analysis results of algorithmically generated coordinate distributions of random values representing the modulus of the fourth parameter of the polarization-correlation vector from microscopic images of histological sections of biological tissues with varying morphological structures are provided.

Hybrid Anapole Induced Chirality in Metasurfaces.

The interaction between light and matter, particularly chirality, plays a pivotal role in modern science and technology. Typically, metasurfaces achieve chiro-optical effects by coupling electric and magnetic dipoles in specific orientations. In this work, the design and optimization of an asymmetric H-shaped metasurface is explored to induce hybrid anapole (HA) for optical activity. When the symmetry of the metasurface structure is disrupted, the design can simultaneously excite first-order and pseudo high-order HA under illumination with a specific circular polarization, both occurring within the same spectral regime. This results in high reflection for one circular polarization and a significant reduction in reflection for the orthogonal polarization, thereby exhibiting exceptional chiro-optical activity. Moreover, the HA-based chiral metasurface demonstrates strong polarization control capabilities, as verified by Stokes parameter analysis, revealing high birefringence and a pronounced dependence on the incident polarization angle. These results provide valuable insights for the design and optimization of HA metasurfaces for advanced optical applications and polarization control, paving the way for new developments in chiral nanophotonics.

Accurate Inspection and Super-Resolution Reconstruction for Additive Manufactured Defects Based on Stokes Vector Method and Deep Learning

Defects in additive manufacturing processes are closely related to the mechanical and physical properties of the components. However, the extreme conditions of high temperatures, intense light, and powder during the manufacturing process present significant challenges for defect detection. Additionally, the high reflectivity of metallic components can cause pixels in image sensors to become overexposed, resulting in the loss of many defect signals. Thus, this paper mainly focuses on proposing an accurate inspection and super-resolution reconstruction method for additive manufactured defects based on Stokes vector and deep learning, where the Stokes vectors, polarization degree, and polarization angles of the inspected defects are effectively utilized to suppress the high reflectivity of metallic surfaces, enhance the contrast of defect regions, and highlight the boundaries of defects. Furthermore, a modified SRGAN model designated SRGAN-H is presented by employing an additional convolutional layer and activation functions, including Harswish and Tanh, to accelerate the convergence of the SRGAN-H network and improve the reconstruction of the additive manufactured defect region. The experiment results demonstrated that the SRGAN-H model outperformed SRGAN and traditional SR reconstruction algorithms in terms of the images of Stokes vectors, polarization degree, and polarization angles. For the scratch and hole test sets, the PSNR values were 33.405 and 31.159, respectively, and the SSIM values were 0.890 and 0.896, respectively. These results reflect the effectiveness of the SRGAN-H model in super-resolution reconstruction of scratch and hole images. For the scratch and hole images chosen in this study, the PSNR values of SRGAN-H for single image super-resolution reconstruction ranged from 31.86786 to 43.82374, higher than the results obtained by the pre-improvement SRGAN algorithm.

Optical phase image encryption using stokes parameters and singular value decomposition

Abstract In this paper, we propose an optical asymmetric phase image encryption method in which the vectorial light field is used to encode the data. In transverse plane, the vectorial light field has spatially varying polarization distributions where we are allowed to have a greater number of degrees of freedom. In this scheme, the input image is first phase encoded and then modulated by a phase encrypting key, synthesized from the speckles obtained by the scattering of Hermite–Gaussian beams. The modulated image is further processed using fractional Fourier transform with a specific order (α). A pixel scrambling operator is utilized to increase the randomness to further enhance the security and singular value decomposition approach is employed to add the nonlinearity in the encryption process. Now, the stokes parameters, i.e. S 1 and S 2 are calculated using the light intensities correspond to different polarizations. S 1 is used as the encrypted image for transmission and S 2 is reserved as one of the private decryption keys. The robustness of the proposed technique is tested against various existing attacks, such as known plaintext attack, chosen plaintext attack, and contamination attacks. Numerically simulated results validate the effectiveness and efficiency of the proposed method.

Single-shot polarization detection with a highly scattering system

Polarization detection plays a significant role in optics. However, the current detection methods usually involve mechanically rotating components, multiple measurement steps, complicated optical design, and precise microfabrication process. To address this issue, we propose a single-shot method to detect the polarization state of light based on a highly scattering system, which is constituted by a spatial light modulator and a highly scattering medium. When the incident light beam shaped by a superimposed wavefront is incident on a highly scattering medium, the foci represented the six components at horizontal, vertical, diagonal, antidiagonal, right circularly polarized, and left circularly polarized directions will appear behind the highly scattering medium simultaneously. By measuring the intensities of these six foci, all the Stokes parameters can be extracted. Taking advantage of the measured Stokes parameters, the orientation angle of major axis, the ellipticity, and the handedness of the polarization ellipse of incident light beam can be determined. Various light beams with different polarization states are detected to demonstrate the viability of the method. The experimental results and theoretical values are in a good agreement. Compared to the existing methods, this approach is fast, free of complicated fabrication, and independent of mechanical movement. The proposed method is expected to promote the development of real-time and broadband polarimetry.

Metasurface-based broadband full Stokes polarimeter with optimized simulation design

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 0.73π 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.

Systematical and universal calibration scheme for division-of-aperture polarimetric camera

Division-of-aperture polarimetric (DoAP) camera has been widely used to obtain polarization images of scene owing to its feature in simultaneous acquisition of polarization information, real-time measurement and compact system. However, practical applications of DoAP imaging inevitably involve calibrating the camera from several aspects, which is very essential but the related reports are relatively lacking in current research. In this paper, we proposed a systematical and universal calibration scheme for the DoAP camera, which includes the lens distortion correction, the image registration, the polarization channel calibration and the Stokes parameters modification. Accordingly, a software for calibration and imaging processing, which consists of four modules, is designed to collectively facilitate the efficient and accurate execution of all calibration steps. In order to achieve real-time polarimetric imaging, the lens distortion correction and the image registration were done by means of lookup tables. Experimental results by using a full-Stokes DoAP camera we fabricated indicate that, via the lens distortion correction and the image registration, the alignment error between two images with a mean absolute error (MAE) less than 0.16 pixels can be obtained, resulting in the aligned images having an average increase of 64.53 % for the structural similarity index (SSIM) and that of 84.97 % for the peak signal to noise ratio (PSNR), respectively; and further via the polarization channel calibration and the Stokes parameters modification, the MAE of 0.0146 for the degree of polarization (DoP) and that of 0.3544° for the angle of polarization (AoP) are obtained, respectively. This proposed calibration scheme for DoAP camera is systematic, automatic and robust, which is benefit of improving the polarization detection accuracy, enhancing the camera calibration efficiency and thus promoting its polarimetric imaging performance.

Efficient completely polarization-encoded binocular structured light 3D measurement method for metallic objects

In practical 3D measurement applications, stereo vision assisted with phase shift patterns is intensively studied and widely used for its high precision and excellent noise resilience. While aiming to improve matching efficiency, excessive projection patterns or unreliable algorithms may be introduced as a side effect. We propose a completely polarization-encoded phase shift (CPPS) method to overcome the above challenges. In our method, the Stokes parameter S1 of the polarization patterns is encoded. Compared to the traditional fringe patterns, our method can reduce the number of projected patterns to improve the measurement efficiency. Therefore, the exact constraints can be realized without additional patterns. Experimental results show that the CPPS method reduces the matching time by 76.6% while reducing the number of fringe patterns by half.

Mueller matrix symmetry for both reciprocal and nonreciprocal metamaterials

Mueller matrices relate the Stokes parameters of the incident and emerging light, providing useful information about the radiative properties and other characteristics of the medium. Determining all elements of the 4 × 4 Mueller matrix requires complete polarimetry, which is often challenging to perform. Partial polarimetry, on the other hand, uses simpler optical components in generating and/or analyzing states of polarization, thereby measuring only a subset of the Mueller matrix. However, it may determine the full Mueller matrix under specific symmetry conditions. The present study develops a symmetry classification scheme to categorize the Mueller matrix of materials. It is shown that the symmetry of the Mueller matrix is directly determined from the information of symmetries of the sample's optical properties. Numerical calculations of various measurement scenarios, structures, and materials (with or without Lorentz reciprocity) are carried out to validate the methodology. This study offers an insightful understanding of Mueller matrix symmetry and practical guidance for simplified ellipsometry measurements.