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.     

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.     

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.     

1/4波片延迟量的相位调制椭偏测量法

利用椭偏测量术中的相位调制椭偏测量原理测量了1/4波片的延迟量。该方法预先对测量光束的偏振态进行调制,以生成随时间变化的光强信号,通过对信号中的谐变成分进行分析而获得待测波片的延迟量。测量了四个波片,其中三个波片的延迟量已经用电光调制法精确测量过,经对比测量的结果符合较好。观察到了和理论相符的云母波片延迟量的振荡现象。实验结果说明这种方法是一种有实际意义的方法。     

Wavelength dependence of the phase retardation of a quarter-wave plate

We describe an optical heterodyne polarization interferometer that can be efficiently used for the precision measurement of the change in the state of polarization of a light wave induced by polarizing optical devices. This technique is used to measure the change with wavelength of the phase retardation of a quarter-wave plate. A theoretical derivation is presented to permit computation of the wavelength dependence of the phase shift induced by a quarter-wave plate.     

Review of RGB photoelasticity

Automatic methods of photoelasticity have had a significant progress with the development of automatic acquisition and image processing methods. This article concerns RGB photoelasticity, which allows the determination of the photoelastic retardation using, usually, a single acquisition of the isochromatic fringes in white light by a colour camera. In particular, the article presents an overview of the main characteristics of RGB photoelasticity that is influence of the quarter-wave plate error, number of acquisitions, type of light source, determination of low and high fringe orders, methods for searching the retardation, scanning procedures, calibration on a material different from that under test, combined use of the RGB and phase shifting methods. A short section on the applications of RGB photoelasticity completes the article.     

利用傅里叶分析法测量光相位延迟器延迟量

为了精确测量光相位器的延迟量,提出了一种新的测量方法,并利用米勒矩阵理论分析了影响测量结果的因素。测量系统主要由起偏棱镜、标准四分之一波片、检偏棱镜、锁相放大器和微处理器构成。该方法利用最小二乘算法得到了最优傅里叶系数,利用锁相放大器的窄带滤波作用提高了信噪比,利用反馈环控制系统对步进电机的步进角进行了控制。误差分析表明这一方法的绝对误差小于0.29°,对四分之一石英波片相位延迟量进行了实验测试,结果表明其重复测量误差小于0.40°。     

四区域法消除偏振棱镜缺陷对波片相位延迟测量的影响

在起偏器-待测波片-检偏器系统基础卜提出一种四区域测量波片相位延迟量的方法.调整待测波片和检偏器的方位角,获得相应的四组光强值,通过线性运算得到待测波片的相位延迟量,完全消除了起偏器和检偏器不完全消光带来的误差.由于测量系统中不存在标准波片或其他相位调制元件,允许测量波长仅受偏振棱镜和探测器的限制,因此四区域法可适用于很大波长范围内的波片测量.以λ/4波片为例,理论分析了测量系统利用四区域测量法后的仪器误差为σφ≤士3.49065×10-3rad(约0.2°),精度比原算法提高约1个数量级.实验验证了四区域法能有效提高系统精度.     

Computer simulation of the zernike phase contrast in hard x-ray radiation using refractive lenses and zone plates

Computer simulation of an experiment on imaging transparent (phase) microobjects using the Zernike phase contrast method under hard X-ray radiation has been performed. The beam parameters typical for synchrotron radiation sources of the third generation were used in calculations. Both a refracting lens and a zone plate have been considered as a focusing element. The phase shifting quarter-wave plate is located at a spot of the point source image. The results of calculations have shown that the method can be successfully used for objects with the sizes greater than 0.1 μm along and 1 μm across the beam. It has been shown that the contrast is caused not only by increasing the intensity within the shadow of the objects, but also by decreasing the intensity in the area beyond the objects, which is necessary to retain the integral intensity.     

Multi-Wavelength Mueller Matrix Polarimeter

The retardation of two quarter-wave plates designed for a particular wavelength decreases or increases in accordance with the wavelength of input light beam. Compensating the shifted retardation at each measurement wavelength allows us to get Mueller matrices of samples at different wavelengths without exchanging the plates. Initial orientation errors of two plates and an analyzer, which remain constant through all wavelengths, are also taken into consideration. The availability and accuracy of this polarimeter is assessed by measurement of a quarter-wave plate designed for 632.8 nm wavelength. The results show that this system is very attractive to measure optical properties and dispersion in samples.     

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。     

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.     

Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error

The Fourier transform method, widely applied in photomechanics for the automated analysis of interferometric fringe patterns, has been recently extended to the photoelastic isochromatic fringe patterns analysis. Unfortunately, its use in photoelasticity involves some limitations that have not been completely highlighted in literature. This work deals with the influence of the quarter-wave plate tolerance on the evaluation of the retardation. Both theoretical and experimental analyses have shown that the quarter-wave plate error does not affect the retardation only if the principal stress directions in the model and in the carrier are aligned. In general, instead, the tolerance of the quarter-wave plates leads to an amplification of the retardation error due to the influence of the isoclinics with a subsequent restriction of the field in which the method can be applied. For instance, using common quarter-wave plates and tolerating a maximum retardation error of about 0.03 fringe order, than the Fourier transform method cannot be applied as a full-field technique but only in the model zones in which the misalignment between the principal stresses in the model and in the carrier is less than 15°.     

Effect of chromaticity on quarter-wave retarder performance

When a polarized polychromatic beam passes through a birefringent medium, the constituent spectral components suffer different change of state of polarization. As a result when the beam passes through an analyzer, the intensity of the resultant beam changes depending on the orientation of the analyzer, state of polarization of the input beam, spectral and spatial intensity distribution of the source and the polarizing properties of the birefringent medium. In the present study the intensity variation of the resulting beam passing through a quarter-wave retarder plate is observed theoretically with the variation of the azimuthal angle of the analyzer for monochromatic and polychromatic source of light. A simple experiment is conducted to observe the intensity variation for an incandescent lamp and HeNe laser as polychromatic and monochromatic source of light passing through a birefringent polymer-based quarter-wave retarder plate. The experimentally obtained values are compared with theoretical values and a good agreement is observed.     

1/4波片相位延迟分布的动态测量

通过密勒矩阵和斯托克斯参量法对一种1/4波片的相位延迟分布的测量模型进行了推导,并设计出一种空间分光移相器,取代一般测量系统中的检偏器,使得系统能于瞬间同时采集四幅具有90°移相步长的干涉图,避免了环境振动对测量的影响,从而可以对1/4波片的相位延迟分布进行动态在线测量.对一个实际标称波长632.8 nm的1/4波片进行了测量,结果显示其平均延迟量为149.36 nm,且接近75%部分其相位延迟误差在5 nm之内,显示出较好的延迟均匀性.     

Measurement of the linear electrooptic effect in poled polymer thin films with coplanar electrodes

The linear electrooptic (EO) effect of poled polymer thin film is measured in the coplanar-electrode structure. The optical geometry of the coplanar-electrode thin-film setup is analysed theoretically to find a relationship between the linear optical parameters and the EO modulation intensity. EO modulated intensity is measured as a function of the direction of incident light polarization relative to the macroscopic optic axis, also as a function of optical bias determined by quarter-wave plate. Comparison of experimental measurements with the theoretical analysis shows good agreement.     

Stokes parameters measurement of light over a wide wavelength range by judicious choice of azimuthal settings of quarter-wave plate and linear polarizer

The Stokes parameters (S_p, S₁, S₂, S₃) of light are measured at an arbitrary wavelength over a wide wavelength range. The Stokes parameters S₁ and S₂ are easily obtained. But the Stokes parameter S₃ at the arbitrary wavelength is affected by the phase difference error Δ₁ of the quarter-wave plate mismatch and the Stokes parameters S₁ or S₂. Therefore, in this paper, S₃ is obtained from both the intensity measurements by the circular polarizer rotating the quarter-wave plate by 0° and 90°. Then, S₃ is obtained by considering only Δ₁, but is not affected by S₁ and S₂. Also, though Δ₁ is not accounted for, S₃ is measured more accurately.     

Polarization eigenmodes of a QHQ retarder — some new features

A detailed analysis of the polarization eigenmodes of a QHQ retarder (a half-wave plate sandwiched between two identical quarter-wave plates) is presented. These are shown to be discontinuous as a function of the orientation of the half-wave plate, as a function of the wavelength of incident light and as a function of the retardation of the middle waveplate.     

Real-time phase-shift ing techniques for determining the photoelastic parameters: a theoretical comparison

Among data acquisition techniques in digital photoelasticity, the integrated phase shifting technique (IPST) can real-time analyze the photoelastic parameters at a video rate of the high speed CCD camera. In this paper, fourteen algorithms are described by different configurations of the rotating an analyzer at a constant rate and an output quarter-wave plate at another constant rate. The theoretical comparisons of the algorithms are given by the simulated phase distributions of the isochromatic and isoclinic parameters of the disk under two cases that the load keeps unchangeable or linearly increasing in exposure time of the camera. Then a guideline is given to alleviate the influence of the load changing with time on the IPST.