Simultaneous measurement of optical rotation angle and retardance

In this study, an optical scheme based on Stokes-Mueller Formalism and rotating wave-plate Stokes polarimeter is successfully developed to simultaneously measure optical rotation angle and retardance. The average relative errors in the measured rotation angle and retardance of a half-wave plate which are solved by nonlinear equations of detected Stokes parameters are determined to be just 0.74% (1.16% for a perfect half-wave plate with retardance of 180°) and 0.40% respectively. The average relative error in the measured rotation angles of glucose solutions with concentrations ranging from 0 to 1.2 g/dl is determined to be 4.53% (2.98% under calibration with sample cell). From the inspection of simultaneous measurement of rotation angle and retardance in a glucose solution followed by a half-wave plate, the average relative error in the measured rotation angles of glucose solutions is determined to be 4.23% (1.81% under calibration with sample cell). The correlation coefficient between the measured rotation angle and the glucose concentration is found to be 0.99966, while the standard deviation is just 0.00357°, and the average relative error in the measured retardance of a half-wave plate is determined to be just 0.47%. Consequently, the derived algorithm for simultaneously measuring rotation angle and retardance is feasible, and the developed system is evaluated with a precision of 10% approximately in rotation angle and a high precision of 0.0032% in retardance measurement.     

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.     

The new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence

We present a new circular heterodyne interferometer with electro-optic modulation for measurement of the optical linear birefringence. It enables the measurement of not only the phase retardation but also the principal angle. The measurement procedure is carried out in two steps. In the first step of measurements, we use the electro-optic modulated circular heterodyne interferometer and the phase-lock technique to precisely measure the principal axis angle. After rotating the analyzer in the setup, the phase retardation is determined also by the phase-lock technique. The compact configuration requires only a photodetector and two simple phase-lock extractions to determine the principal axis angle and the phase retardation. The validity of the proposed design is demonstrated by measurement of the principal axis angle and phase retardation of a quarter-wave plate sample. The root-mean-square resolutions for the principal axis angle and phase retardation are found to be 0.0396° and 0.0796°, respectively, with corresponding dynamic ranges of 0–180° and 0–180°.     

A new electro-optic modulated circular heterodyne interferometer for measuring the rotation angle in a chiral medium

A new optical polarimeter capable of measuring the rotation angle in a chiral medium is developed successfully, and is an extension of previously developed simultaneous or sequential measurement system of the principal axis and retardance in linearly birefringent materials. The polarimeter for measuring the rotation angle is based on an electro-optic modulated circular heterodyne interferometer and using phase-lock technique to measure the rotation angle directly and precisely. The validity of the proposed design is demonstrated by the measurement of rotation angle in a half-wave plate and the glucose sample. The average relative error in rotation angle level of 0.00284° has been obtained for a half-wave plate. A correlation coefficient value of 0.9999975 is determined; it indicates a highly linear relationship between the reference values and the measured rotation angles. Moreover, a standard deviation in rotation angle level of 0.005275° has been obtained for glucose solutions with concentrations ranging from 0 to 1.2 g/dl in 0.2 g/dl increments, with a correlation coefficient value of 0.99915 between the reference and the measured values. This setup is compact in configuration, and is easy in calibration. The linearity and resolution characteristics of this system are comparable to those previous studies adopting phase-sensitive techniques.     

Determination of high-purity polarization state of X-rays

We report on the measurement of the highest purity of polarization of X-rays to date. The measurements are performed by combining a brilliant undulator source with an X-ray polarimeter. The polarimeter is composed of a polarizer and an analyzer, each based on four reflections at channel-cut crystals with a Bragg angle very close to 45°. Experiments were performed at three different X-ray energies, using different Bragg reflections: Si(400) at 6457.0 eV, Si(444) at 11,183.8 eV, and Si(800) at 12,914.0 eV. At 6 keV a polarization purity of 1.5 × 10^− 9 is achieved. This is an improvement by more than two orders of magnitude as compared to previously reported values. The polarization purity decreases slightly for shorter X-ray wavelengths. The sensitivity of the polarimeter is discussed with respect to a proposed experiment that aims at the detection of the birefringence of vacuum induced by super-strong laser fields.     

Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights

This paper presents an experimental technique for measuring the optical rotation, depolarization, and phase retardance of optical samples. In the proposed approach, the optical properties of the sample are derived using a Stokes–Mueller matrix formalism in conjunction with linearly and circularly polarized probe lights. For a compound sample comprising a half-wave plate positioned in front of glucose solutions with concentrations ranging from 0 to 1.2 g/dl, the average normalized error in the measured rotation angle is determined to be 3.11% when using a linearly polarized light. The average surviving linear and circular polarization fractions of the glucose solutions are determined to be 1.0252 and 0.9945. The average normalized error in the measured retardance of the half-wave plate is 3.45%. When measuring a compound sample comprising a half-wave plate positioned in front of the scattered glucose solutions with turbidities from 0% to 50% by the addition of milk, experimental results show that the induced rotation angle increased as the turbidity increased, whereas both surviving linear and circular polarization fractions decreased as the turbidity increased. The effect of the turbidity on rotation angle is more significant than that on both surviving linear and circular polarization fractions. The average normalized error in the measured retardance of the half-wave plate is 1.43%. Consequently, a simplified geometry of the polarimeter is proposed to independently estimate the rotation angle, surviving linear and circular polarization fractions, and retardance from the derived viable algorithm.     

Simplified method for polarization-sensitive optical coherence tomography

We report a method for extracting the birefringence properties of biological samples with micrometer-scale resolution in three dimensions, using a new form of polarization-sensitive optical coherence tomography. The method measures net retardance, net fast axis, and total reflectivity as a function of depth into the sample. Polarization sensing is accomplished by illumination of the sample with at least three separate polarization states during consecutive acquisitions of the same pixel, A scan, or B scan. The method can be implemented by use of non-polarization-maintaining fiber and a single detector. In a calibration test of the system, net retardance was measured with an average error of 7.5 degrees (standard deviation 2.2 degrees ) over the retardance range 0 degrees to 180 degrees , and a fast axis with average error of 4.8 degrees over the range 0 degrees to 180 degrees .     

The application of a rotating-wave-plate stokes polarimeter for measurement of the optical rotation angle

An optical scheme based on Stokes-Mueller formalism and rotating-wave-plate Stokes polarimeter is successfully developed to measure the optical rotation angle in a chiral medium. The average relative error in the measured rotation angle of a half-wave plate is determined to be 1.16%. The average relative error in the measured rotation angles of glucose solutions with concentrations ranging from 0 to 1.2 g/dl is determined to be 3.78%. The correlation coefficient between the measured rotation angle and the glucose concentration is found to be 0.99950, while the standard deviation is just 0.00376°. From the inspection of measured rotation angle in the sol-gel materials containing C₁₇H₁₇ClO₆ with concentrations ranging from 0 to 0.0665 g/ml, the average relative error in the measured rotation angles is determined to be 3.63%. Consequently, the derived algorithm for measuring the rotation angle of a chiral medium is feasible, and the developed system is evaluated with a precision of 5.4% approximately in rotation angle measurement.     

Error analysis and Stokes parameter measurement of rotating quarter-wave plate polarimeter

In this paper, we present a simple Stokes parameter measurement method for a rotating quarter-wave plate polarimeter.This method is used to construct a model to describe the principle of how the magnitudes of errors influence the deviation of the output light Stokes parameter, on the basis of accuracy analysis of the retardance error of the quarter-wave plate,the misalignment of the analyzing polarizer, and the phase shift of the measured signals, which will help us to determine the magnitudes of these errors and then to acquire the correct results of Stokes parameters. The method is validated by the experiments on left-handed circularly polarized and linear horizontal polarization beams. With the improved method, the maximum measurement deviations of Stokes parameters for these two different polarized states are reduced from 2.72%to 2.68%, and from 3.83% to 1.06% respectively. Our results demonstrate that the proposed method can be used as a promising approach to Stokes parameter measurement for a rotating quarter-wave plate polarimeter.     

Spectral variation of the birefringence,group birefringence and retardance of a gypsum plate measured using the interference of polarized light

Polarized white light interferometry is used to characterize the wavelength dependence of the birefringence, group birefringence and retardance of a gypsum crystal. Two different calculation schemes are used to extract values of the birefringence across the whole visible spectrum. In the spectral range 435 nm–642 nm, the variation of the gypsum birefringence is fitted to the two terms Cauchy formula and to a fourth order dispersion function. The gypsum birefringence is found to be inversely proportional with wavelength. The experimental method used gives a relative error in finding the gypsum birefringence of an order of 6×10^?4. The wavelength dependence of gypsum group birefringence is also calculated with a relative error of order 5×10^?4. In the same spectral range, the retardance changes by 28π and the gypsum plate introduced halfwave retardance 15 times.     

光学玻璃应力双折射叠加

为解决在光学玻璃应力双折射测量中遇到的双折射叠加问题,利用光学等效原理,使用一个线性双折射模型和一个旋转器来代替叠加模型。对叠加的情况做了分析和计算,得到了叠加后的特征延迟、主应力方向和旋转角随两个应力模型主应力方向夹角变化的曲线。理论分析表明,应力双折射叠加不是应力双折射的简单相加,而是与叠加模型各自的应力双折射值和主应力方向的夹角有关。实验结果与理论计算相吻合。应力双折射叠加对实际光学玻璃测试造成不良影响,使测量精度降低,特别是有透光支撑机构或折射液容器的情况下,应力双折射叠加的影响不可忽略。     

Simultaneous measurement of retardation and fast axis angle of eighth-wave plate in real time

A simultaneous measurement method for the retardation and the fast axis angle of the eighth-wave plate in real time is proposed. The beam emitted from the laser passes through the circular polarizer and the eighth-wave plate to be measured successively, and then is split by the Dammann grating to form three sub-beams. They are analyzed by an analyzer array and detected by a detector array. Three detection signals are obtained simultaneously to calculate the retardation and the fast axis angle in real time. In experiments, a crystal quartz sample is measured at different fast axis angles. The average and standard deviation of its retardation respectively are 40.9°and 0.5°. The maximum measurement deviation of the fast axis angle is 2.1°. The usefulness of the method is verified.     

An instrument for measuring low optical rotation angle

This paper develops a linear heterodyne interferometer based on phase-locked extraction for measuring low optical rotation angle. The validity of the proposed design is demonstrated by measuring a half-wave plate. The average relative error in the measured rotation angle of the half-wave plate is determined as just 0.74%. When applied to the measurement of glucose solutions with concentrations ranging from 0 to 1.2 g/dl, the average relative error in the measured rotation angle of glucose solutions is determined to be 1.46%. The correlation coefficient between the measured rotation angle and the glucose concentration is determined to be 0.999991, while the standard deviation is just 0.00051°. The current system is capable of measuring glucose concentration as low as 0.01 g/dl with an error of 6.67% in the rotation angle measurement. Overall, the experimental results demonstrate the ability of the proposed system to obtain highly accurate measurement of the optical rotation angle.     

Polarimetric characterization of ultra-high molecular weight polyethylene (UHMWPE) for bone substitute biomaterials

In this work the UHMWPE is characterized for their optical properties with Mueller matrix polarimeter. The transmittance birefringence, retardance, polarizance, linear and circular polarization and absorbance of polarized light at different wavelengths ranging 400-800 nm are measured. The presented Mueller matrix elements along with depth resolve polarization decrease in intensity with the change in the wavelength. Linear retardance increases compared to circular through highly scattering polyethylene. High refractive index and low mean free path; and close bonding of particles of material rotates the incoming photons and circular polarization which is dominant as compared to the linear one. Therefore the average intensity increases with both the optical depth and the scattered concentration in UHMWPE, which would accordingly decrease the apparent degree of polarization.The extracted results in terms of linear and circular retardances prove that UHMWPE is compatible, strong, and compact. This research work provides an optical characterization technique for bone substitute biomaterial in the health care industry.     

The use of polarization modulation and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement

A novel common-path polarization modulation and amplitude-sensitive optical heterodyne polarimeter is setup in order to characterize a phase retardation plate (PRP) in real time. The phase retardation ΔΦ and fast-axis angle β of the linear birefringence parameters (LBP) of a PRP are measured simultaneously. Meanwhile, the dynamic ranges of 0° < ΔΦ < 180° and 0° < β < 180° are demonstrated experimentally. In order to measure LBP in real time, a polarization modulation is introduced by continuously rotating the tested PRP such that ΔΦ and β are able to be obtained in terms of the ratio of the amplitudes of S polarization and the ratio of P polarization of the heterodyne signals, respectively. Consequently, this novel method, which combines optical heterodyne interferometry with a polarization modulation technique, not only improves the detection sensitivity, but also provides a real time capability to measure LBP. In addition, the error in the LBP measurement is derived and analyzed.     

Analysis of 2-D motion tracking in ultrasound with dual transducers

We study displacement and strain measurement error of dual transducers (two linear arrays, aligned orthogonally and coplanar). Displacements along the beam of each transducer are used to obtain measurements in two-dimensions. Simulations (5 MHz) and experiments (10 MHz) are compared to measurements with a single linear array, with and without angular compounding. Translation simulations demonstrate factors of 1.07 larger and 8.0 smaller biases in the axial and lateral directions respectively, for dual transducers compared to angular compounding. As the angle between dual transducers decreases from 90° to 40°, for 1% compression simulations, the lateral RMS error ranges from 2.1 to 3.9 μm compared to 9 μm with angular compounding. Simulation of dual transducer misalignment of 1 mm and 2° result in errors of less than 9 μm. Experiments demonstrate factors of 3.0 and 5.2 lower biases for dual transducers in the axial and lateral directions respectively compared to angular compounding.     

The Local-Sampling Phase Shifting Technique for Precise Two-Dimensional Birefringence Measurement

A precise method for measurement of two-dimensional birefringence distribution is described and discussed. This method can determine the relative retardation and the azimuthal angle of the fast axis in an optical component. In order to detect relative retardation with high resolution, a local-sampling phase shifting technique is proposed. This method can measure 256 × 256 values of the birefringent phase difference and azimuthal angle in a short time with ± 0.02 deg (0.03 nm) of retardation accuracy.     

High-Sensitivity Two-Dimensional Observation of Thermal Birefringence Compensation in Laser-Diode Pumped Nd: Glass Laser Rods

We measured the two-dimensional birefringence compensation in laser-diode (LD) pumped Nd:glass (HAP4) laser rods with a high-sensitivity polarimeter. The compensation was performed by inserting a 90° quartz rotator between two identical LD pumped Nd:glass rods with conductive cooling. A considerable reduction of birefringence loss from 9.8% to less than 0.9% after compensation was observed.     

Theoretical analysis of the effect of coating polarization on the second harmonic generation of an Nd:YVO4/KTP laser

Jones calculus is used to analyze the effect of the polarization characteristics of the output mirror coating of a V-shaped Nd:YVO4/KTP laser on the second harmonic generation. The reflection-induced phase retardance (RIPR) of the coating can quench the second harmonic generation. When the optical axis of Nd:YVO4 makes a π/4 angle with the incident plane of the output mirror and the fast axis of KTP in the incident plane, the RIPR induced reduction of coupling factor of the second harmonic generation is less than 1% if the phase retardance is smaller than 25°. If the polarization direction of the fundamental wave coincides with the eigen-polarization directions of the incident plane, the effect of the reflection-induced phase retardance on the conversing efficiency can be avoided.     

Self-assembled monolayers on magnesium alloy surfaces from carboxylate ions

Self-assembled monolayers (SAMs) of carboxylate salts (C_n−1H_2n−1COONa, n = 12, 16, 18) were successfully formed on Mg alloy substrate in ethanol solution and characterized by the contact angle measurement, ATR-FTIR, ellipsometry and XPS. The SAMs were regularly and densely anchored to the Mg alloy substrate via monodentate bonding with the tilting angles of about 40°, 33° and 27° for C12, C16 and C18 monolayers, respectively. Electrochemical impedance spectroscopy (EIS) proved the corrosion protection of SAMs for Mg alloy substrate with protective efficiency (PE) of even up to 98.5%.