旋转波片偏振仪波片方位误差研究

旋转波片Stokes偏振仪是最常用的测量光束偏振态的仪器。波片快轴方位误差是影响旋转波片Stokes偏振仪的主要误差源之一。为了研究波片方位偏差对测量精度的影响,提出了一种描述波片快轴方位误差向最终的偏振测量误差传递的数学模型,并引入协方差矩阵法表征偏振测量误差。根据这一模型,获得最优的偏振仪配置参数。在推导过程中,假设波片方位误差服从同一高斯分布。基于此误差模型,得到如下结论：(1)由波片方位误差引入的测量误差与光强测量次数N成反比;(2)测量误差独立于入射光强度,但是依赖于入射光偏振态(s₁, s₂, s₃)和波片的位相延迟量δ;(3)波片位相延迟量在(103.22°, 116.13°)范围内时波片方位误差引入的测量误差最小。最后,经过仿真实验证明,所得解析结果与仿真模拟结果相一致。     

Spectroscopic Mueller matrix polarimeter using four-channeled spectra

A Mueller matrix polarimeter acquired for four-channeled spectra is proposed. Both the polarizing and analyzing optics of this system consist of a linear polarizer and a high-order retarder. The polarizing elements can modulate the polarization states in the wavenumber space. By applying a Fourier transform method to a single-channeled spectrum, nine elements of the Mueller matrix can be deconvoluted without modifying the configuration of either the polarizing or analyzing optics. It is thus possible to determine the wavelength dependence of all the Mueller matrix elements from four-channeled spectra obtained using four different configurations for the polarizing and analyzing optics. The performance of this method is evaluated by measuring polarization properties, such as retardance, azimuthal angle, and linear diattenuation, from the obtained Mueller matrix in wavenumber space.     

15N chemical shift tensor magnitude and orientation in the molecular frame of uracil determined via MAS NMR

The potential of heteronuclear MAS NMR spectroscopy for the characterization of (15)N chemical shift (CS) tensors in multiply labeled systems has been illustrated, in one of the first studies of this type, by a measurement of the chemical shift tensor magnitude and orientation in the molecular frame for the two (15)N sites of uracil. Employing polycrystalline samples of (15)N(2) and 2-(13)C, (15)N(2)-labeled uracil, we have measured, via (15)N-(13)C REDOR and (15)N-(1)H dipolar-shift experiments, the polar and azimuthal angles (θ, psi) of orientation of the (15)N-(13)C and (15)N-(1)H dipolar vectors in the (15)N CS tensor frame. The (θ(NC), psi(NC)) angles are determined to be (92 +/- 10 degrees, 100 +/- 5 degrees ) and (132 +/- 3 degrees, 88 +/- 10 degrees ) for the N1 and N3 sites, respectively. Similarly, (θ(NH), psi(NH)) are found to be (15 +/- 5 degrees, -80 +/- 10 degrees ) and (15 +/- 5 degrees, 90 +/- 10 degrees ) for the N1 and N3 sites, respectively. These results obtained based only on MAS NMR measurements have been compared with the data reported in the literature.     

Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters

An imaging variable retardance polarimeter was developed and tested by Tyo and Turner [Proc. SPIE 3753, 214 (1999)]. The signal-to-noise ratio (SNR) in the reconstructed polarization images obtained with this system varied for the four Stokes parameters. The difference in SNR is determined to be due to differences in the Euclidean lengths of the rows of the synthesis matrix used to reconstruct the Stokes parameters from the measured intensity data. I equalize (and minimize) the lengths of the rows of this matrix by minimizing the condition number of the synthesis matrix, thereby maximizing the relative importance of each of the polarimeter measurements. The performance of the optimized system is demonstrated with simulated data, and the SNR is shown to increase from a worst case of -3.1 dB for the original settings to a worst case of +5.0 dB for the optimized system.     

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.     

Hybrid complete Mueller polarimeter based on phase modulators

Optical properties of matter as diattenuation, retardance and depolarization can be evaluated using polarimetric techniques. In this paper, the analysis and implementation of a complete Mueller polarimeter is presented. The system is constituted of a polarization state generator (PSG) and a polarization state analyzer (PSA), which are controlled and synchronized through a computer program. The PSG comprises a dual liquid crystal variable retarder system while the PSA is based on a two-photoelastic modulator setup. Using air and common polarizing optics as test samples for calibration at 633 nm, the hybrid instrument met a good precision when the Mueller matrices of those optical elements were measured.     

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.     

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.     

A three-spectrum method for accurate calibration of bi-plate zero-order retarder

A new spectroscopic method is proposed for the characterization of optical zero-order retarders. It is demonstrated that the retardance as well as the variation of the effective fast axis of a bi-plate zero-order quarter retarder （633 nm） can be obtained with high accuracy in a broadband wavelength range by taking spectra at only three independent angular orientations of the retarder. The calibration results excellently agree with theoretical models, indicating the new method could be used as a simple and reliable way for efficient self-spectral-calibration of optical zero-order retarders.     

Deuteron beam polarimetry at the nuclotron

The scheme of the deuteron beam polarization measurements at Nuclotron are presented. A deuteron beam polarimeter based on the spin-asymmetry measurements in the dp-elastic scattering at large angles in center-of-mass system has been constructed at the internal target station at the Nuclotron of JINR. This polarimeter is planned to use for the measurements of the vector and tensor components of deuteron beam polarizations at the energies 270–2000 MeV simultaneously. Details on the low energy polarimeters are also discussed.     

Self-spectral calibration of a compound zero-order waveplate at blind rotation angles

A blind-angle calibration method is introduced for self-spectral calibration of a compound zero-order waveplate. By rotating the waveplate at blind detection angles, the wavelength-dependent retardance and the orientation of the effective fast axis can be determined through iterative least-squares calculations of the spectra measured by a multi-channel spectrometer. Excellent agreement between the experimental values and the theoretical values is achieved, indicating that the new method can be used as a reliable way to calibrate compound zero-order wave plates. Using the new method, there is no need to rotate the waveplate at specific detection angles. A high-precision waveplate holder or complex adjustment procedure is not required.     

Mueller matrix polarimetry for improved liver fibrosis diagnosis

An experimental Mueller matrix polarimeter is used to quantify human liver fibrosis by measuring retardance and depolarization of thin biopsies. The former parameter is sensitive to fibrillar collagen, the latter is specifically sensitive to fibrillar collagen around blood vessels, which is not significant for liver fibrosis diagnosis. By using depolarization like a filter, retardance distribution enables distinguishing between disease stages and limits the high degree of observer discrepancy.     

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 .     

双菱体λ/4消色差相位延迟器的设计

根据菲涅尔全内反射相变理论,给出了双菱体λ/4消色差器的结构设计、性能分析和测量方法.由有效通光孔径和光线追迹设计出BK7玻璃在波长532 nm时相位延迟λ/4的双菱体的结构,用作532 nm至1 064 nm波长范围的标准λ/4相位延迟器.理论分析了入射角变化和波长变化对双菱体相位延迟的影响,当入射角变化限制在±4.3°以内时,其影响得到补偿;波长从532 nm到1 064 nm产生的误差为－0.65°.采用椭偏法中的消光技术,分别实测了双菱体在532 nm和1 064 nm波长下的相位延迟为：90.08±0.14°和88.99±0.1°,可知两不同波长产生的相位延迟误差为－1.09°.     

Tuneable Sagnac comb filter including two wave retarders

In this paper we study theoretically and experimentally a wavelength-tuneable Sagnac birefringence filter. The device is a Sagnac interferometer including a symmetric fibre coupler and a length of high-birefringence fibre in the loop. A wave retarder is inserted at each end of the birefringent fibre for absolute wavelength tuning. We show theoretically that wavelength tuning through wave plate orientation ensuring constant amplitude of the filtering function is possible only if a minimum of two wave retarders are included in the setup. The position of the transmission peaks then varies linearly with the angle of one of the retarders and can be adjusted over one entire channel spacing. This happens only when a quarter-wave retarder and a half-wave retarder are used, if the former is oriented at 45° with respect to the fibre birefringence axes, while the orientation of the latter serves as the adjustment parameter. The theoretical predictions are confirmed by the experimental results.     

Optimized Mueller polarimeter with liquid crystals

We demonstrate a Mueller polarimeter in which the polarization-state generator and analyzer are both composed of a linear polarizer and two liquid-crystal variable retarders. The polarimeter is designed to optimize the accuracy of the final results by minimization of the condition numbers of the modulation and analysis matrices. The polarimeter calibration, a difficult task by conventional procedures, is achieved easily by use of the eigenvalue method of Compain et al. [Appl. Opt. 38, 3490 (1999)]. The overall polarimeter performance is tested with a linear polarizer at various angles and a compensator at various retardations.     

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.     

Orientation of TOAC amino-acid spin labels in alpha-helices and beta-strands

The orientation of alpha-helices or beta-strands, e.g., in membranes, can be determined from EPR order parameters of (2,2,6,6-tetramethyl-piperidine-1-oxy-4-amino-4-carboxylic acid) TOAC amino-acid spin labels incorporated in the polypeptide backbone. This requires knowledge of the inclination of the nitroxide axes, relative to the alpha-helix or beta-strand axis. Crystal structures of TOAC-containing peptides are used to derive the spin-label orientation relative to refined alpha-poly-l-alanine and beta-poly-l-alanine structures. The spin-label z-axes of the two mirror-image TOAC twist-boat conformers are inclined at 13+/-2 degrees and 65+/-3 degrees , respectively, to the alpha-helix axis, or at 25+/-3 degrees and 32+/-3 degrees to the beta-strand axis.     

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.     

Photon transmission technique for studying multiple phase transitions in a liquid crystal

A photon transmission technique was used to monitor the multiple phase transitions in a 4-butoxyphenyl4(')-declyoxybenzoate (BOPDOB) liquid crystal. Drastic decreases in the transmitted photon intensity (I) were attributed to the sequential phase transitions in BOPDOB upon cooling. In this paper, it is assumed that the order parameter rho is proportional to the transmitted photon intensity. The isotropic-nematic and nematic-smectic-A transitions were observed and found to be of first order. It was observed that the smectic-A-smectic-C and smectic-C-smectic-G transitions are second order. It was found that for the smectic-A-smectic-C transition, critical exponent crosses over from beta=0.513+/-0.006, which is consistent with mean-field theory, to beta=0.35+/-0.009, which is consistent with heliumlike behavior, as the Ginzburg criterion predicts. The critical exponent for the smectic-C-smectic-G transition was found to be beta=0.703+/-0.001. Transition temperatures were established at each phase transitions and found to be 84.92 degrees C, 74.85 degrees C, 52.96 degrees C, and 33.03 degrees C for isotropic-nematic, nematic-smectic-A, smectic-A-smectic-C and, smectic-C-smectic-G transitions, respectively.