Principal Axis Angle Research Articles

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development. In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle (α) reduces the strength of the generalized shear stress and shear strain curves. Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient (b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.

Quantum imaging of biological organisms through spatial and polarization entanglement.

Quantum imaging holds potential benefits over classical imaging but has faced challenges such as poor signal-to-noise ratios, low resolvable pixel counts, difficulty in imaging biological organisms, and inability to quantify full birefringence properties. Here, we introduce quantum imaging by coincidence from entanglement (ICE), using spatially and polarization-entangled photon pairs to overcome these challenges. With spatial entanglement, ICE offers higher signal-to-noise ratios, greater resolvable pixel counts, and the ability to image biological organisms. With polarization entanglement, ICE provides quantitative quantum birefringence imaging capability, where both the phase retardation and the principal refractive index axis angle of an object can be remotely and instantly quantified without changing the polarization states of the photons incident on the object. Furthermore, ICE enables 25 times greater suppression of stray light than classical imaging. ICE has the potential to pave the way for quantum imaging in diverse fields, such as life sciences and remote sensing.

Effects of graphene layer addition on sensitivity of surface plasmon resonance sensor for immunoglobulin M detection

A novel technique is proposed for detecting immunoglobulin M (IgM) using differential Mueller matrix polarimetry and a surface plasmon resonance (SPR) sensor enhanced through the addition of multiple (1–10) thin layers of graphene on the sensing surface. Simulations are first performed to optimize the structure of the SPR device. The feasibility of the proposed sensor is then demonstrated by measuring the principal fast axis angle (α) of linear birefringence (LB) of human IgM serum aqueous solution samples with known concentrations in the range of 0–250 ng/ml. The results shows that α increases linearly over the considered concentration range. However, α reduces with an increasing number of graphene layers. The finest resolution of 7.8 ng/ml is obtained from the sensor incorporating three graphene layers.

Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics

This paper focuses on the development of three newly formed representations of dual attitude and their respective kinematics equations - Dual Classical Rodrigues Parameters, Dual Modified Rodrigues Parameters, Dual Principal Axis and Principal Angle (Dual Principal Rotation Vector). These three formulations are developed by building off of the theories and concepts used with Dual Quaternions and utilizing numerous attitude identities for quaternions to create new identities using dual quaternions and dual attitudes while detailing the process used throughout the derivation. The accompanying dual kinematic equations using these dual attitude parameters are also generated using their respective dual attitude coordinate systems. Furthermore, the new dual attitude representations with their respective, distinct kinematic equations and identities are validated against a simulated 6-DOF rigid body spacecraft control problem to verify equivalency across equations using the dual quaternion as a baseline.

Single-Layer-Graphene-Coated and Gold-Film-Based Surface Plasmon Resonance Prism Coupler Sensor for Immunoglobulin G Detection.

A graphene-based surface plasmon resonance (SPR) prism coupler sensor is proposed for the rapid detection of immunoglobulin G (IgG) antibodies. The feasibility of the proposed sensor is demonstrated by measuring the IgG concentration in phantom mouse and human serum solutions over the range of 0–250 ng/mL. The results show that the circular dichroism and principal fast axis angle of linear birefringence increase in line with increases in IgG concentration over the considered range. Moreover, the proposed device has a resolution of 5–10 ng/mL and a response time of less than three minutes. In general, the sensor provides a promising approach for IgG detection and has significant potential for rapid infectious viral disease testing applications.

Streamwise variations of turbulence statistics up to maximum drag reduction state in turbulent boundary layer flow due to surfactant injection

We investigate streamwise variations of turbulence statistics in the wide range of drag reduction (DR) up to the maximum drag reduction (MDR; DR ≥ 60%) state for the turbulent boundary layer flow due to surfactant injection. One-component laser-Doppler velocimetry (LDV) measurements show that the DR is drastically varied from the low drag reduction (LDR) to the high drag reduction (HDR) regions and is saturated in the MDR region, and such variation is sensitive to the free-stream velocity and dependent on the process of diffusion of injected surfactant solution. Both two-component LDV measurements and particle image velocimetry (PIV) measurements clarify that the mean velocity in wall units agrees with the so-called Virk’s ultimate profile in the MDR region, where both wall-normal turbulence intensity and the Reynolds shear stress with outer scaling are considerably suppressed compared to those in the LDR and HDR regions, while the maximum of streamwise turbulence intensity is comparable with that of water. Such behavior is independent of flow types such as internal and external flows and kinds of additives such as polymer and surfactant. The principal axis angle in joint probability density function of streamwise and wall-normal velocity fluctuations near the wall is the most promising index as the amount of DR based on the LDR, HDR, and MDR. The PIV measurements also show that the sheet-like structures in the HDR and MDR regions expand to around the maximum location of streamwise turbulence intensity, at which spanwise length scales are evaluated.

Optical characterization of porcine articular cartilage using a polarimetry technique with differential Mueller matrix formulism.

A method is proposed for characterizing the optical properties of articular cartilage sliced from a pig's thighbone using a Stokes-Mueller polarimetry technique. The principal axis angle, phase retardance, optical rotation angle, circular diattenuation, diattenuation axis angle, linear diattenuation, and depolarization index properties of the cartilage sample are all decoupled in the proposed analytical model. Consequently, the accuracy and robustness of the extracted results are improved. The glucose concentration, collagen distribution, and scattering properties of samples from various depths of the articular cartilage are systematically explored via an inspection of the related parameters. The results show that the glucose concentration and scattering effect are both enhanced in the superficial region of the cartilage. By contrast, the collagen density increases with an increasing sample depth.

Polarisation‐sensitive sub‐terahertz‐wave detector implementing antenna‐integrated zero‐bias Schottky barrier diode

A polarisation-sensitive sub-terahertz-wave detector has been developed by integrating an InP/InGaAsP Schottky barrier diode and a modified bowtie antenna. The fabricated quasi-optical module could detect signals at frequencies ranging from 30 GHz to 1 THz. The measured sensitivities were 1080 V/W at 250 GHz, 250 V/W at 400 GHz and 86 V/W at 600 GHz for a zero-bias condition. The principal polarisation axis angle for signal detection was confirmed to be stable within ±1.5° in a frequency ranging from 80 to 600 GHz, while the degree of polarisation was more than 95%.

Angle between principal axis triples

SUMMARY The principal axis angle ξ0, or Kagan angle, is a measure of the difference between the orientations of two seismic moment tensors. It is the smallest angle needed to rotate the principal axes of one moment tensor to the corresponding principal axes of the other. This paper is a conceptual review of the main features of ξ0. We give a concise formula for calculating ξ0, but our main goal is to illustrate the behaviour of ξ0 geometrically. When the first of two moment tensors is fixed, the angle ξ0 between them becomes a function on the unit ball. The level surfaces of ξ0 can then be depicted in the unit ball, and they give insights into ξ0 that are not obvious from calculations alone. We also include a derivation of the known probability density of ξ0. The density is proportional to the area of a certain surface . The easily seen variation of with t then explains the rather peculiar shape of . Because the curve is highly non-uniform, its shape needs to be considered when analysing distributions of empirical ξ0 values. We recall an example of Willemann which shows that ξ0 may not always be the most appropriate measure of separation for moment tensor orientations, and we offer an alternative measure.

Concurrent measurement of linear birefringence and dichroism in ferrofluids using rotating-wave-plate Stokes polarimeter

In this study, an optical scheme based on Stokes–Mueller Formalism and rotating-wave-plate Stokes polarimeter is successfully developed for obtaining concurrent measurements of the linear birefringence and dichroism. For a quarter-wave plate sample, the measured values of the principal axis angle and retardance are found to have average absolute and normalized errors of 0.0859° and 0.76%, respectively, while the measured dichroism of the quarter-wave plate has an average value of 0.0203. When analyzing ferrofluid film samples with concentrations ranging from 2 to 6%, it was found that for a given concentration of ferrofluid, retardance increases with applied magnetic fields and tends to saturate at high levels. Additionally, under the condition of the same magnetic field, the experimental results show that retardance is proportional to the concentration; the higher concentration will result in more retardance and absorption. Consequently, the derived algorithm for concurrent measurements of the linear birefringence and dichroism is feasible, and the relation between the concentration and magneto-optical effect was successfully investigated.

Characterization on five effective parameters of anisotropic optical material using Stokes parameters—Demonstration by a fiber-type polarimeter

An analytical technique based on the Mueller matrix method and the Stokes parameters is proposed for extracting five effective parameters on the principal axis angle, phase retardance, diattenuation axis angle, diattenuation and optical rotation angle of anisotropic optical materials. The linear birefringence (LB) / circular birefringence (CB) properties and linear diattenuation (LD) properties are decoupled within the analytical model. The analytical method is then integrated with a genetic algorithm to extract the optical properties of samples with linear birefringence property using a fiber-based polarimeter. The result demonstrates the feasibility of analytical model in characterizing five effective parameters of anisotropic optical material. Also, it confirms that the proposed fiber-based polarimeter provides a simple alternative to existing fiber-based probes for parameter measurement in the near field or the remote environment. A low birefringence fiber-based polarimeter based on effective parameters and genetic algorithm without using a fiber polarization controller is first proposed confirmatively.

Measurement of linear birefringence using a rotating-wave-plate Stokes polarimeter

In this study, a compact polarimeter is developed to measure the linear birefringence property of optical materials. The principal axis angle and the retardance are obtained by a simple signal-processing algorithm, which is derived via Stokes parameters extractions when using an incident light linearly polarized at 45°. There exists an absolute error of 0.0296° on average in the principal axis angle measurement and a relative error of 2.54% in the retardance measurement of a quarter-wave-plate sample with its principal axis ranging from −40° to 40°. The standard deviations for the principal axis angle and retardance measurements are determined to be 0.015° and 0.018°, respectively, while one standard deviation to the average value of the principal axis angle and retardance, respectively, are just 0.066% and 0.020% with high repeatability, and corresponding dynamic ranges of −45° to 45° and −180° to 180°, respectively. Consequently, the developed polarimeter has a potential in linear birefringence measurement, especially in the retardance measurement.

Using polarimeter and Stokes parameters for measuring linear birefringence and diattenuation properties of optical samples

A technique is proposed for measuring the linear birefringence and linear diattenuation of an optical sample using a polarimeter. In the proposed approach, the principal axis angle (α), phase retardance (β), diattenuation axis angle (θd ), and diattenuation (D ) are derived using an analytical model based on the Mueller matrix formulation and the Stokes parameters. The dynamic measurement ranges of the four parameters are shown to be α = 0~180°, β = 0~180°, θd = 0~180°, and D = 0~1, respectively. Thus, full-range measurements are possible for all parameters other than β. In this study, the proposed methodology does not require the principal birefringence axes and diattenuation axes to be aligned. In addition, the linear birefringence and linear diattenuation properties are decoupled within the analytical model, and thus the birefringence properties of the sample can be solved directly without any prior knowledge of the diattenuation parameters.

Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters

A technique is proposed for measuring the linear birefringence and linear diattenuation of an optical sample using a polarimeter. In the proposed approach, the principal axis angle (alpha), phase retardance (beta), diattenuation axis angle (thetad), and diattenuation (D) are derived using an analytical model based on the Mueller matrix formulation and the Stokes parameters. The dynamic measurement ranges of the four parameters are shown to be alpha = 0 approximately 180 degrees, beta = 0 approximately 180 degrees, theta(d) = 0 approximately 180 degrees, and D = 0 approximately 1, respectively. Thus, full-range measurements are possible for all parameters other than beta. In this study, the proposed methodology does not require the principal birefringence axes and diattenuation axes to be aligned. In addition, the linear birefringence and linear diattenuation properties are decoupled within the analytical model, and thus the birefringence properties of the sample can be solved directly without any prior knowledge of the diattenuation parameters. Also, the characteristic parameters in the baked polarizer with linear birefringence are successfully extracted from an optically equivalent model and proved by the respective simulation and experiment introduced in this study.

Glucose concentration measurement using an electro-optically modulated circular polariscope

This paper develops an electro-optically modulated circular polariscope based on a phase-lock technique for measuring the optical rotation angle of a glucose solution such that its concentration can be proportionally extracted. The validity of the proposed design is demonstrated by measuring the optical rotation angle of a half-wave plate as its principal axis angle is rotated through in increments of . The corresponding correlation coefficient is found to be 0.999996. Hence, it is inferred that the measurement system has a good linear response. When applied to the measurement of glucose samples with concentrations ranging from 0–1.2 g dl−1, the correlation coefficient between the measured rotation angle and the glucose concentration is determined to be 0.998599, while the corresponding standard deviation is . The current system is capable of measuring glucose concentration as low as 0.2 g dl−1. Furthermore, the dynamic measurement range of the polarization rotation angle extends from to . Compared to other optical measurement systems presented in the literature, the current system has the advantages of a simpler structure, fewer optical elements, a tunable heterodyne frequency and a simple signal processing scheme. Overall, the proposed system provides a highly-precise, straightforward, non-invasive means of obtaining glucose concentration measurements.

Simultaneous Separation Measurement of Principal Thermal Conductivities and Principal Axis Angle of Pyrolytic Graphite Sheet for Two-Dimensional Anisotropic Material Using Integrated Multi-Temperature Probe Method

We measured the principal thermal conductivities and the principal axis angle of a 0.1-mm-thick pyrolytic graphite sheet (PGS), by the integrated multi-temperature probe method. To determine its principal thermal conductivities, a sample is heated using a point heat source places on the sample surface and the transient temperature changes of nine points with radii of r1 = 2.5, r2 = 5.0, and r3 = 7.5 mm on three axes with β= 120° are measured by the integrated multi-temperature probe method. The two measured principal thermal conductivities are λp1 = 746 W/(m·K) and λp2 = 925 W/(m·K). The geometrical mean of the two measured principal thermal conductivities of PGS is λ= (λp1·λp2)1/2 = 831 W/(m·K). The relative errors in this measurement are 7.1% for λp1 and 8.7% for λp2. The calculated anisotropic factor ξ, which is the ratio of λp2 to λp1, is 1.24. The measured data of PGS showed a strong anisotropy of thermal conductivity. This suggests that there is a possibility for PGS to become a standard two-dimensional anisotropic material.

Concurrent measurement of linear and circular birefringence using rotating-wave-plate Stokes polarimeter

A novel technique is presented for obtaining concurrent measurements of the linear and circular birefringence properties of an optical sample by using a rotating-wave-plate Stokes polarimeter to extract the 2x2 central elements of the corresponding Mueller matrix via two linearly polarized probe lights. For a compound sample comprising a half-wave plate in series with a quarter-wave plate, the measured values of the principal angle and retardance of the quarter-wave plate are found to have average normalized errors of 0.56% and 1.16%, respectively, while the measured value of the rotation angle of the half-wave plate has an error of just 0.39%. When analyzing glucose solutions with concentrations ranging from 0-1.2 g/dl positioned in front of a half-wave plate, the average normalized errors in the principal axis angle and retardance measurements of the half-wave plate are 0.69% and 2.65%, respectively, while the error in the rotation angle measurements of the glucose solutions is 2.13%. The correlation coefficient between the measured rotation angle and the concentration of the glucose solution is determined to be 0.99985, while the standard deviation is just 0.0022 deg. Overall the experimental results demonstrate the ability of the proposed system to obtain highly accurate measurements of the linear and circular birefringence properties of an optical sample and to decouple the relationship between the principal axis angle and the rotation angle.

High dynamic range measurement of linear birefringence with an electro-optic modulated circular polariscope

This paper presents a common-path electro-optic modulated circular polariscope capable of performing the sequential measurements of the principal axis and retardance of the linearly birefringent media with high accuracy by means of two phase-locked extractions, and with a high dynamic range obtained by the design of optical configuration and the derivation of an easy algorithm. There exist an absolute error of 0.10° on average in the principal axis measurement of 36 times within the range of 0°–180°, and a relative error of 1.10% in the retardance measurement of a λ/2-wave plate by this method. Consequently, the standard deviations for the principal axis angle and retardance measurements are determined to be 0.0033° and 0.086°, respectively, triple standard deviations to the average values of principal axis angle and retardance are just 0.10% and 0.14% with high repeatability, respectively, and corresponding dynamic ranges of 0°–180°.

Optical anisotropy measurements of TRISO nuclear fuel particle cross-sections: The method

The analysis of two-modulator generalized ellipsometry microscope (2-MGEM) data to extract information on the optical anisotropy of coated particle fuel layers is discussed. Using a high resolution modification to the 2-MGEM, it is possible to obtain generalized ellipsometry images of coating layer cross-sections with a pixel size of 2.5 μm and an optical resolution of ∼4 μm. The most important parameter that can be extracted from these ellipsometry images is the diattenuation, which can be directly related to the optical anisotropy factor (OAF or OPTAF) used in previous characterization studies of tristructural isotropic (TRISO) coated particles. Because high resolution images can be obtained, the data for each coating layer contains >6000 points, allowing considerable statistical analysis. This analysis has revealed that the diattenuation of the inner pyrocarbon (IPyC) and outer pyrocarbon (OPyC) coatings varies significantly throughout the layer. The 2-MGEM data can also be used to determine the principal axis angle of the pyrocarbon layers, which is nearly perpendicular to the TRISO radius (i.e., growth direction) and corresponds to the average orientation of the graphene planes.

The optical linear birefringence measurement using a Zeeman laser

In the paper we present a new optical system that uses a transverse Zeeman dual-frequency laser in conjunction with plane polariscope for simultaneously measuring both the principal axis angle and the retardance of the optical linearly birefringent materials. The Zeeman laser produces a standard heterodyne signal as a polarizer is set in front of a photodetector. Owing to the use of a Zeeman laser and design of optical configuration, the measurement system has the advantages of compact structure, low non-linearity, high stability, and good portability. By using the amplitudes of a reference signal and of two measuring signals, a simply derived algorithm can obtain the principal axis angle and the retardance directly and easily. The dynamic range of the principal axis angle measurement is limited in the range from 0° to 90° and that of the retardance measurement is extended to be 180° successfully. According to the measurement results, the average absolute errors of the principal axis angle and the retardance measurements for a quarter-wave plate with its principal axis angle set at 90° are determined to be 1.47° and 2.85%, respectively. The absolute error of the retardance measurement is within the uncertainty range of 5% or more for commercial quarter-wave plates.