基于径向偏振光的波片参数测量方法

Parameter Measurement of Wave Plate Based on Radially Polarized Beams

提出了一种利用径向偏振光同时测量波片相位延迟量和快轴方位角的方法。水平线偏振光通过涡旋半波片后生成径向偏振光,然后用径向偏振光照射被测波片。由于径向偏振光具有空间非均匀分布的偏振特性,对单次检偏后采集的光强分布依次进行Radon变换和最小二乘拟合,可得到强度调制曲线。最后对强度调制曲线进行傅里叶分析,就可计算得到被测波片的相位延迟量和快轴方位角。实验结果表明,当波片的快轴与水平方向的夹角为45°时,消色差1/4波片和808nm零级1/4波片的相位延迟量和快轴方位角的测量标准差小于0.03°。该方法测量装置简单,测量过程无需转动器件,测量快速方便且测量精度高。

Objective Wave plates are critical components in several fields,including precision measurement,singularity optics,and optical communication.A wave plate's phase retardation and fast axis azimuth are two key parameters.The precise measurement of these two parameters is of great significance for the use of a wave plate.The methods including photoelastic modulation method,laser frequency division method,rotating device method,heterodyne interference method,and finite element simulation method are used to measure the two parameters.These methods are effective;however,they are not without drawbacks.Vector beams have a spatially inhomogeneous polarized distribution compared to common linearly and circularly polarized beams.The polarization state of radially polarized vector beams,for example,is distributed along the radial direction at any point in the cross-section.Furthermore,all linear polarization states can simultaneously be very useful for measuring the parameters of a wave plate,and as a result,vector beams are gaining popularity in the field of polarimetry.Methods First,the measurement principle of the proposed method based on the Muller matrix and Stokes vector is described in Fig.1.Second,formulas for calculating the measured wave plate's phase retardation and fast axis azimuth are developed.Finally,the effects of the vortex retarder(VR)zero-degree fast axis error,charge-coupled device(CCD)noise,and other factors on measurement accuracy are investigated.The experimental setup is constructed based on the measurement principle.The light source in the experiment is a white-light emitting diode,which is transformed into a collimated uniform red light field of 633 nm after passing through a plane-convex lens and a bandpass filter.When the red light passes through the horizontal linear polarizer and the vortex retarder,it produces a radially polarized beam.The radially polarized beam is then passed through a measured wave plate and a vertical linear polarizer.Finally,the intensity distribution is captured by a CCD.The intensity distribution image in Fig.3(a)shows an hourglass distribution.Since the edges and center of the intensity distribution are typically poorly modulated,the ring area of interest region is intercepted from the image in Fig.3(a),as illustrated in Fig.3(b).The Radon transform is adopted to obtain the intensity curve I′(θ)varying along with the azimuthθ.To reduce the influence of noise from CCD on the measurement results,the intensity curve I′(θ)is fitted by the least-square fitting method to obtain the intensity curve I(θ).By using Fourier analysis of the normalized intensity curve I(θ),the phase retardation and fast axis azimuth of the wave plate can be measured.Results and Discussions The error analysis shows that a minor error in the vortex retarder's zero-degree fast axis can affect phase retardation measurements;however,it has little effect on the measurement results of fast axis azimuth.Using the nominal fast axis direction of the measured wave plate as a reference,the nominal fast axis azimuth(NFAA)is defined as the angle between the nominal fast axis direction and the horizontal direction.From the error analysis,we can see that measurement results for the phase retardation tend to be inaccurate if measuring a wave plate with phase retardation of 0°or a multiple of 180°.Furthermore,for the same reason,phase retardation measurement results are sensitive to errors when the NFAA of the wave plate is 0°or a multiple of 180°.Before inserting the wave plate to be measured,an experiment is performed without any sample to calculate the deviation of VR's zero-degree fast axis,which can greatly improve measurement accuracy.An achromatic quarter-wave plate is measured in the experiment.The experimental results show that it has the highest measurement accuracy when the NFAA of the measured achromatic quarter-wave plate is in the range near 45°and 135°,but the measured value fluctuates greatly when the NFAA is near 0°,90°,and 180°.When the NFAA of the measured achromatic quarter-wave plate is in the range of 30°-60°and 120°-150°,the measured average value and standard deviation of the phase retardation are 87.30°and 0.26°,respectively.The average value and standard deviation of the deviation between the measured value and the nominal value of the fast axis azimuth are 3.20°and 0.68°,respectively.To further confirm the accuracy and stability of the measurement scheme,the NFAA is set as 45°,and it is measured 10 times.The measured average value and standard deviation of the phase retardation are 87.33°and 0.01°,respectively,and those of the fast axis azimuth is 48.01°and 0.01°,respectively.To further verify the practical value of this measurement method,a zero-order quarter-wave plate at 808 nm is also measured.When the NFAA of the measured zero-order quarter-wave plate is in the range of 30°-60°and 120°-150°,the measured average value and standard deviation of the phase retardation are 116.60°and 0.59°,respectively.Moreover,the average value and standard deviation of the deviation between the measured value and the nominal value of the fast axis azimuth are 0.85°and 0.26°,respectively.Multiple measurements are performed when the NFAA is 45°.The measured average value and standard deviation of phase retardation are 117.04°and 0.03°,respectively,and the measured mean value and standard deviation of fast axis azimuth are 45.64°and 0.01°,respectively.Conclusions This paper proposes a method for simultaneously measuring phase retardation and fast axis azimuth of a wave plate using a radially polarized vector beam.In this method,the phase retardation and fast axis azimuth of the measured wave plate can be calculated by Fourier analysis of the intensity modulation curve obtained by the Radon transform and least-square fitting of the recorded light intensity with a snapshot baesd on the spatially variant polarized distribution characteristics of radially polarized beams.The theoretical analysis shows that when the phase retardation of the measured wave plate is 0°or a multiple of 180°or the angle between the fast axis direction of the measured wave plate and the horizontal direction is 0°or a multiple of 90°,the measurement results are sensitive to errors.Two wave plates are measured in the experiment.The experimental results demonstrate that when the angle between the fast axis and the horizontal direction of the evaluated wave plate is in the range of 30°-60°and 120°-150°,particularly near 45°,the parameters of the wave plate can be measured by a single snapshot,and the measurement results have good accuracy and stability.The advantages of this method are as follows:first,the error source is reduced since the measuring device is simple;second,the measurement is rapid and convenient since only a single imaging is used in the measurement process and there is no need to rotate the device;and finally,the fast axis distribution error of the vortex retarder is calibrated,and the influence of noise of the CCD camera on the measurement results is reduced by the least-square fitting.However,some aspects require further investigation,such as the measurement of the measured wave plate's global birefringence distribution and the effects of the linear polarizer's extinction ratio and the uniformity of the light source on measurement results.