A frequency domain method for the measurement of nonlinearity in heterodyne interferometry

This paper presents a method for the measurement of nonlinearity in heterodyne interferometry which utilizes the frequency spectrum of the output of the photodetector for the direct measurement of the magnitudes of the first and second harmonic nonlinearities. The underlying theory and the experimental technique are discussed. Results showing the application of this technique for the determination of the influence of the azimuthal alignments of the polarization beamsplitter, the analyzer and measurement retroreflector are presented. The applicability of the technique to the in situ optimization of an interferometer system is demonstrated. It is shown that using this technique an interferometer system can be optimized to reduce the first-harmonic nonlinearity to below 0.5 nm p-p and the second harmonic nonlinearity to 2 nm p-p. This method is contrasted with other methods and the advantages conferred by the elimination of an external reference and the phase measuring electronics are highlighted.     

分光镜对外差激光干涉仪非线性的影响

外差干涉仪的非线性误差不仅由激光源的椭圆偏振态或者非正交线偏振态引起,也由非理想的光学器件引起,其中分光镜是一个重要的误差源。除了通常熟知的偏振漏光,还分析偏振分光镜中可能存在的另一个误差,即偏振分光的正交性,介绍这种误差和其他各种原因(包括激光源的椭圆偏振态或者非正交线偏振态)对外差干涉仪非线性误差的影响,给出检测和区分两类不同频率混叠误差的方法。通过试验证实,偏振分光镜的漏光误差对外差干涉仪非线性的影响通常是可以被忽略不计的。试验研究还发现,与传统的理论假设相反,非偏振分光镜比偏振分光镜对外差干涉仪的非线性误差有着更严重的影响。     

Problems regarding linearity of data of a laser interferometer with a single-frequency laser

In this paper, the main causes of scale nonlinearity of a laser interferometer with a single-frequency laser and a quadrature fringe detection system are described. The primary causes of scale nonlinearity are quadrature phase shift error and imperfect optical elements in the interferometer and detection unit. A method for measuring this nonlinearity with an optical compensator is described. Nonlinearities arising from quadrature phase shift error, unequal amplitudes, and electronic offsets in the detection unit can be compensated by means of a PC program as described herein. By using a differential interferometer with a resolution of 0.3 nm, the nonlinearity compensation was experimentally verified, and by averaging the measured values for 20 s, a linearity better than ±0.5 nm was achieved.     

The fractional Talbot effect in differential x‐ray phase‐contrast imaging for extended and polychromatic x‐ray sources

The influence of different physical parameters, such as the source size and the energy spectrum, on the functional capability of a grating interferometer applied for phase‐contrast imaging is discussed using numerical simulations based on Fresnel diffraction theory. The presented simulation results explain why the interferometer could be well combined with polychromatic laboratory x‐ray sources in recent experiments. Furthermore, it is shown that the distance between the two gratings of the interferometer is not in general limited by the width of the photon energy spectrum. This implies that interferometers that give a further improved image quality for phase measurements can be designed, because the primary measurement signal for phase measurements can be increased by enlargement of this distance. Finally, the mathematical background and practical instructions for the quantitative evaluation of measurement data acquired with a polychromatic x‐ray source are given.     

On a novel approach to evaluate Schlieren interferograms of axisymmetric refractive index fields

In Schlieren interferometry one often encounters axisymmetric refractive index fields which principally violate the general assumption of interferometry, namely the two-dimensionality of the phase object. However, there exist numerical methods capable to evaluate axisymmetric refractive index fields using the fringe distribution of interferograms. This paper describes a novel approach for evaluating Schlieren interferograms of axisymmetric refractive index fields. The suggested algorithm exhibits higher accuracy without constrains for large beam separation (where the interferometer sensitivity is higher) when compared to methods given in the literature. The computational performance has been controlled and compared by using analytical test functions.     

Critical alignments in plane mirror interferometry

Each axis of a plane mirror interferometer has three associated measurement vectors: the interferometer beam, mirror normal, and axis of measurement. The transducer axis of a plane mirror interferometer target is the mirror normal. This contrasts with a retroflector for which the transducer axis is the interferometer beam. The classical cosine error in x-y plane mirror interferometry is removed by the orienting the mirror normals in the travel plane. The axes do not have to be orthogonal to eliminate cosine error.     

误差补偿技术在相位偏移干涉测量中的应用

在研究泰曼—格林相位偏移干涉仪测量原理基础上，分析了位移驱动器移相误差对五幅移相计算结果的影响，一阶线性误差和二阶非线性误差是相位偏移干涉测量技术中产生相位误差的主要因素；提出了五幅算法移相误差补偿技术，该方法直接从相位偏移干涉图中计算移相过程中存在的一阶及二阶移相误差，对五幅算法结果进行误差修正；采用玻璃平晶为测试对象，建立了泰曼一格林干涉仪移相误差补偿原理试验系统。试验结果表明在同时存在一阶移相误差及二阶移相误差情况下，采用提出的移相误差补偿方法可以将位移测量精度提高6倍，相当于采用氦氖激光器的倍程干涉仪中位移精度达到1．0nm。     

金刚石复合片与硬质合金的钎焊研究

通过聚晶金刚石复合片与YG8硬质合金的高频感应钎焊试验,研究了不同钎料钎剂搭配对高频感应钎焊接头抗剪强度、焊缝厚度的影响,并用扫描电镜和电子探针观察、分析了焊缝的微观结构。结果表明,690℃钎焊温度下含Mn的1号钎料和活性温度较高的QJ102钎剂是最佳搭配方案。探讨了聚晶金刚石复合片的特殊钎焊工艺,认为采用复焊方法可以大幅提高钎焊接头的抗剪强度。     

基于正弦相位调制的光纤干涉位移测量系统研究

针对全光纤干涉仪工作距离短、测量范围小等问题,提出了一种基于正弦相位调制的全光纤干涉系统,在参考臂通过电光调制器引入的调制参考光,与探头接收到的目标反射光产生干涉。根据锁相放大原理从干涉信号中提取出正交分量后,首先建立由正交分量构成的观测模型,通过卡尔曼滤波对正交分量的幅值和偏置进行迭代估计和修正,降低由相位延迟、调制深度漂移、寄生干扰等导致的幅值漂移和附加偏置;然后利用反正切法对反射光与参考光之间的相位差进行解调。开展了模拟干涉信号的相位解算仿真模拟和位移测量实验。仿真和实验验证了该算法解算相位的有效性。结果表明,该位移测量系统的工作距离可达到20 cm,测量精度为10 nm。     

Improved measurement characteristics in collimation testing using Lau interferometry and Fourier fringe analysis technique

We demonstrate an automated procedure for the detection of collimation position of an incoherent beam in Lau interferometry using Fourier fringe analysis technique. The experimental arrangement consists of a Lau based interferometer in which light from a source grating illuminates a set of two coarse gratings separated by self imaging distance. Direct phase measurement using Fourier Transform Method (FTM) has been used to obtain the slope map of the wavefront and hence the detection of collimation position is undertaken advantageously. The experimental arrangement is simple and interferometric noise is lower. Detailed uncertainty analysis has also been reported. The technique is fully automatic and provides good accuracy and high precision.     

Technique for the measurement of the amplitude and phase velocity of a slow space charge wave on a relativistic electron beam

A technique is described for the measurement of the axial electric field of a slow space charge wave. The measurement employs a double probe arranged to give an output proportional to the rate of change of magnetic flux linking the probe loop. This output may be related to the electric field of the wave. Two such probes used in an interferometer arrangement allow for the measurement of the phase velocity of the wave.     

Correction of Errors in Polarization Based Dynamic Phase Shifting Interferometers

Polarization based interferometers for single snap-shot measurements allow single frame, quantitative phase acquisition for vibration insensitive measurements of optical surfaces. Application of these polarization based phase sensors requires the test and reference beams of the interferometer to be orthogonally polarized. As with all polarization based interferometers, these systems can suffer from phase dependent errors resulting from systematic polarization aberrations. This type of measurement error presents a particular challenge because it varies in magnitude both spatially and temporally between each measurement. In this article, a general discussion of phase calculation error is presented. We then present an algorithm that is capable of mitigating phase-dependent measurement errors on-the-fly. The algorithm implementation is non-iterative providing sensor frame rate limited phase calculations. Finally, results are presented for both a high numerical aperture system, where the residual error is reduced to the shot noise limit, and a system with significant birefringence in the test arm.     

单频激光干涉系统的研制

单频激光干涉仪采用整体式的布局,提高了测量系统的稳定性和灵敏度,光程差放大技术,提高了系统的分辨率,利用偏振光移相和共模抑制的方法,对干涉仪的4路相互正交的信号进行差分处理,减小光强零漂以及环境变化对系统的影响,最终通过误差补偿修正处理,系统可以获得高质量的输出信号.     

适合于微细加工的外差探测技术及应用

本文详细地讨论了外差干涉仪的两个主要问题,即干涉仪的横向定位问题和非线性误差分析及其误差补偿问题.首先,提出了一种新颖的解析方法实现干涉仪亚微米级的高精度定位.该方法首先建立了测量光束扫过台阶边缘时测量相位渐变数学模型,并讨论了它与激光束分布的关系.文章利用以上数学模型对测量相位数据进行了详细地分析,实现了在一般激光束径时,干涉仪的定位精度为亚微米量级.另一方面,文章详细地分析了共光路干涉仪三个主要误差源.分析结果表明:由Wollaston棱镜引起的误差主要是二阶误差,而由激光束的椭圆偏振化引起的误差为一阶误差.同时我们发现:金属反射镜的方位误差可以使线偏振光经反射后变为椭圆偏振光,该椭圆偏振光具有不正交性和不相等偏心度,文章首次详细地分析了这种不正交性和不相等偏心度与反射镜方位误差的关系及其由此产生的非线性误差.最后,文章分析了干涉仪的误差补偿措施以提高整个干涉仪的测量精度.     

Quasi-quadrature interferometer for plasma density radial profile measurements

A cw Mach Zehnder multichannel interferometer has been developed to measure time-dependent fractional fringe shifts with an accuracy of one-fortieth fringe. The design is quasi-quadrature in that known phase shifts, introduced in the reference beam, are time multiplexed with the normal reference beam. This technique requires only one detector per interferometer channel as compared to two detectors for most quadrature designs. The quadrature information makes the sense of density changes unambiguous, it automatically calibrates the instrument during the plasma event, and it makes fringe shift measurements virtually independent of fringe contrast fluctuations caused by plasma refractive and/or absorptive effects. The interferometer optical design is novel in that the electro-optic crystal used to introduce the 90 degrees phase shifts is located in the common 2-mm-diam HeNe entrance beam to the interferometer, by exploiting polarization techniques, rather than in the expanded 1-2-cm reference beam itself. This arrangement greatly reduces the size, cost, and high-voltage requirements for the phase modulating crystal.     

用空间载频法测量玻璃平板的厚度均匀性

设计了一种基于迈克耳逊干涉光路的相位测量系统,将单臂作为检测端完成了对玻璃平板厚度均匀性的直接测量和分析。该系统由CCD采集干涉图样,利用傅里叶变换条纹分析术和相位解包裹技术提取干涉图中所包含的待测相位信息;对于傅里叶变换法中频谱旁瓣中心无法准确定位的问题,采用三角变换法去载频,从而不需要准确地得知频谱旁瓣的中心位置就可以计算出相位结果,消除了人为估算和垂轴方向上的微小载频分量给测量结果带来的误差。实验测量了多块玻璃平板的厚度均匀性。测量结果显示：使用像元大小为4.65 μm×4.65 μm的CCD相机,测量玻璃平板两表面在长度方向和宽度方向上的厚度均匀性的理论精度分别达到0.93%和0.92%,表明本系统基本满足玻璃平板厚度均匀性测量的要求,且对干涉图频谱旁瓣的定位精度和载频的方向精度要求较低。     

双频激光干涉仪中的数字相位计设计

基于Altera公司FPGA芯片,提出了一种基于双频激光干涉仪系统中数字相位计的实现方法。该相位计用于测量系统中被测信号和参考信号之间的相位差角度,间接测量激光干涉仪的光程差信息。被测信号经过光电接收器以及A/D模数转换成数字信号送到FPGA芯片中,与FPGA内建的查找表参考信号做正交相关法解调运算,得到一组X-Y值,再利用CORDIC算法计算arctan函数获取相位差,最后计算出干涉仪的光程差,算法的全过程使用FPGA硬件实现。实验结果表明,该相位计使双频激光干涉仪的相位差测量精度在0.01°以内。     

激光双谱线功率的不一致性与拍波干涉仪对准精度的关系

双谱线功率一致性是拍波干涉测长方案对激光光源提出的特殊要求。本文从拍波干涉仪对准方法的实际出发,在分析双谱线拍波干涉仪输出信号的基础上,研究了双谱线功率不一致与拍波干涉仪对准精度的关系,提出了基本对准盲区和盲区扩大量的新概念,建立了描述盲区扩大量与双谱线相对功率差之间关系的解析表达式。为设计拍波干涉仪的激光稳定环路和提高拍波干涉仪的对准精度提供了理论分析工具。     

水下声信号的激光干涉测量

为准确测量水下目标的发声频率,在光学暗室下建立了基于激光干涉法探测水下目标的实验系统。当水下声源引起水表面波动时,用激光照射水面,携带声波信息的水面散射光与参考光干涉,利用精密光学测量装置探测光程差的改变,通过数据采集和处理系统从干涉信号的频谱分析图中解调出水下声信号的频率信息。干涉信号的频谱分析图中存在以水下声信号频率为中心的频带,频带宽度与自然水表面波引起的多普勒频移有关。实验结果表明,水下发声目标引起水表面波动的振幅在纳米级,系统可以实时探测出4～15kHz的水下声信号,且测量标准偏差7Hz。该系统可满足水下目标识别技术的实时性、准确性等要求。