Real-time measurement of retardation of eighth-wave plate independent of fast-axis direction

A real-time measurement method for the retardation of an eighth-wave plate is proposed. The collimated laser beam is split using a Glan Taylor polarizer with two side escape windows. The reflected sub-beam is detected using a detector, whereas the transmitted sub-beam passes through the quarter-wave plate and the eighth-wave plate of interest. Then, it is reflected by the mirror and passes reversely through the eighth-and quarter-wave plates. Finally, it is analyzed using the Glan Taylor polarizer and detected using another detector. With two detection signals, the retardation is resolved and found to be independent of the fast-axis direction, initial intensity, and circuit parameters. In the experiment, a crystal quartz sample is measured at different fast-axis angles. The standard deviation of the retardation is 0.9 o . The usefulness of the method is verified.     

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.     

Real-time measurement of the fast axis angle of a quarter-wave plate based on simultaneous phase shifting technique

Real-time measurement of the fast axis angle of a quarter-wave plate based on simultaneous phase shifting technique is presented. The simultaneous phase shifting function is realized by an orthogonal grating, a diaphragm, an analyzer array, and a 4-quadrant detector. The intensities of the light beams from the four analyzers with different azimuths are measured simultaneously. The fast axis angle of the quarter-wave plate is obtained through the four light intensity values. In this method, rotating elements are not required, so real-time measurement is achieved.     

Method for measuring retardation of a quarter-wave plate based on normalized secondary harmonic component

A method for measuring retardation of a quarter-wave plate based on normalized secondary harmonic component is proposed, and the measuring principle is analyzed. The optical measuring system is composed of a laser, a polarizer, a phase modulator, the quarter-wave plate to be measured, an analyzer and a detector. The azimuths of the transmission axes of the polarizer and the analyzer with respect to the modulating axis of the phase modulator are +45°, 0°, respectively. The retardation of the quarter-wave plate is calculated precisely using the normalized secondary harmonic components prior to and after 22.5° rotation of the quarter-wave plate. In this method, the major axis position of the quarter-wave plate is not required to be known in advance, and the measured retardation is independent of the intensity fluctuation of the light source. The feasibility of the method is verified by the experiments.     

基于旋转波片的斯托克斯参量检测与精度分析

用于偏振光学遥感器定标的参考光源,其偏振态的检测精度会直接影响偏振光学遥感器的定标精度,进而影响目标特性的反演水平。选用870 nm波段的水平线偏振光作为被测试的定标参考光源,通过旋转1/4波片(quarter-wave plate, QWP)对其光强进行调制。调制光强可表达为波片快轴旋转角度的傅里叶级数,采用傅里叶变换法反演出级数的系数,根据该系数即可计算出被测试光源的Stokes参量。给出10次测量各参量及偏振度的平均值、标准偏差、合成不确定度以及测量平均值与理论值的相对偏差。为提高测试精度,通过对波片快轴初始定位角度偏差Δα、延迟量偏差Δδ与检偏器透光轴角度偏差Δβ进行分析,提出了偏差修正模型。该模型通过Stokes参量检测偏差随Δδ和Δβ的变化趋势及实际偏差值,确定Δδ和Δβ的大小。结合模拟出的波片快轴初始定位角度偏差Δα,对实验装置加以调整,再次对光源的偏振态进行检测。结果表明,基于该修正模型测得光源的各Stokes参量与理论值最大偏差从未经修正的3.77%降低至1.41%。证实了基于本实验的原理、装置、测量方法及所提出的偏差修正模型可有效提高定标参考光源偏振态检测的精度。     

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.     

Simple method for simultaneous determination of the phase retardation and fast axis of a wave plate

A simple method for simultaneous determination of the phase retardation and fast axis of a wave plate is presented. In this method, double light path compare system is adopted to achieve better accuracy. In the main optical path, laser beam passes successively through a polarizer, a wave plate to be measured, an analyzer, and then is incident on a detector. In the reference optical path, another detector is used to monitor the fluctuation of the light source. With rotation of the wave plate, the maximum and minimum output light intensity, rotation angle of the wave plate are detected in the main light path; corresponding light intensity are simultaneously detected in the reference light path. Based on the light intensity and the rotation angle, the phase retardation and fast axis of the wave plate can be determined simultaneously. The main advantage of this method is its simplicity of apparatus, easy operation, low cost, and high accuracy. We believe that the method reported in this paper should be a useful approach to measure a wave plate without requiring any complex and expensive components.     

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.     

基于电光补偿测量的光相位延迟拓展测量法

在激光电光调制补偿测量光相位延迟量过程中,加入交流调制电压形成倍频接收信号,获得消光的精确定位,能提高测量精确度。通过调制信号形状变化与相关参量之依赖关系,可拓展测量范围,解决在某些点附近无法测量波片相位的"盲区"问题。根据接收到的调制光信号形状变化趋势与待测波片样品方位、延迟量、旋转方向等条件的联系,在待测波片快轴选定后,通过波片旋转影响信号形状变化规律的观测,可敏锐地甄别在半波点或全波长点附近波片的正负偏差特性,从而解决了一般偏振干涉补偿测量相位无法解决的测量盲区问题。不改变测量系统结构也不需添加任何器件,适应于最小延迟偏差≥λ/360的情况。     

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°.     

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.     

A phase quadrature interferometer for measuring the small optical rotation angle of a chiral medium

The passage of a linearly polarized beam through a chiral material and a phase retarder will induce a phase difference between the s and p polarizations of the beam. In this study, a phase quadrature interferometer is designed to measure the phase difference variation proportional to the optical rotation. The proportionality constant (or measurement sensitivity) can be greatly enhanced by setting the retardation of the phase retarder close to 0° or 180°. The experimental results demonstrate that with our system we can obtain a measurement resolution for the rotational angle of better than 3.5° × 10⁻⁴. This method has several advantages such as a simple optical setup, easier operation in real time, and low cost. In addition, due to the common-path arrangement, surrounding noise can be eliminated.     

Alternative method for measuring the phase retardation and fast axis of a wave plate

Optical Review - An alternative method is proposed for simultaneously measuring the phase retardation and fast axis angle of a wave plate by utilizing a radially polarized symmetric light beam. A...     

Real-time adjustment of optical transmitter by laser beam parameter measurement based on two linear array CCD scanning imaging

In this paper, we present a real-time measurement and adjustment method, based on scanning imaging, for optical transmitter which emits 90° × 2° linear laser beam. This novel optical arrangement consists of an area array CCD and two linear array CCDs. According to the relationship between the positions, angles of transmitter optical components and the beam parameters of emergent laser, the system can help us to decide the real-time adjustment of optical transmitter by measuring the related beam parameters. In order to improve the measurement speed, avoid occlusion and ensure simultaneous measurement, the two linear array CCDs are placed at near field, far field and separated by a definite angle to acquire the beam intensity distribution through suitable nonlinear correction during the process of scanning. After a complete scanning, the beam parameters and the spot image are acquired by continuous measurement. The proof-of-principle experiments showed that the measurement results were in agreement with the analysis. The presented method was applied to direct fast adjustment for higher quality on the assembly of the optical transmitter. The presented procedure is highly advantageous for diverse laser beam emitted from the optical transmitter, such as elliptic, linear and so on.     

Temperature measurement of air convection using a Schlieren system

In this work, we have developed a procedure for full-field measurement of temperature of a fluid flow by using the schlieren technique. The basic idea is to relate the intensity level of each pixel in a schlieren image to the corresponding knife-edge position measured at the exit focal plane of the system. The method is applied in the measurement of temperature fields of the air convection caused by a heated rectangular metal plate (7.3 cm×12 cm). Our tests are carried out at plate temperatures of 50 °C and 80 °C. To validate the proposed method, the schlieren temperature results are compared to those obtained by a thermocouple. Thermocouple data are obtained along two mutually perpendicular directions (one direction along the optical axis, z-direction, and other direction along the x-axis, which is perpendicular to the optical axis) at points located on a 9×9 grid with a variable spacing. The thermocouple measurements were integrated along the z-axis in order to be compared with the measurements obtained by the schlieren technique. The results from the two methods show good agreement between them.     

Method for rapid measuring retardation of a quarter-wave plate based on simultaneous phase shifting technique

A method for rapid measuring retardation of a quarter-wave plate based on simultaneous phase shifting technique is presented. The simultaneous phase shifting function is realized by an orthogonal grating, a diaphragm, an analyzer array, and a 4-quadrant detector. The intensities of the light beams from the four analyzers with different azimuths are measured simultaneously. The retardation of the quarter-wave plate is obtained through the four light intensity values. In this method, the major axis position of the quarter-wave plate need not be determined in advance. In addition, the measured result is free of the intensity fluctuation of light source. The feasibility of the method is verified by the experiments.     

波片复合旋光器研究

利用矩阵光学方法，分析了波片复合旋光器的理论基础，给出了二元和三元复合波片旋光器的条件及其旋光角的大小的数学表达式，并根据此理论作了典型设计。结果表明，旋光角的大小与各波片的延迟量和它们的快轴同X轴的夹角有关。     

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.     

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.     

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.