用于测量小位移的偏振干涉仪外文翻译资料

Polarization Interferometer for Measuring Small Displacement

Xinqun Liu , Warwick Clegg , David Jenkins , and Bo Liu*

Centre for Research in Information Storage Technology, University of Plymouth, PL4 8AA, UK. *Data Storage Institute, 10 Kent Ridge Crescent, Singapore 119260

Abstract

A homodyne polarization laser interferometer is presented for high speed measurement of small displacements. No modulation technique is used, so the opto-mechanical set-up is relatively simple, The dual beam arrangement enables the displacement to be measured whilst the use of polarization interferometry enables the determination of the directional nature of the displacement. Another feature of this interferometer lies in the fact that it is also suitable for the measurement of head-media spacing of a hard disk drive. Combined with the electronics used at present, sub-nanometre resolution is achievable. Its measurement bandwidth is limited only by the sampling rate of the A/D board being used.

1. Introduction

Optical interferometry is a well established technique for precise and non-contact measurement. Various kinds of interferometry, such as heterodyne interferometry [ 1]- [3], sinusoidal phase modulating interferometry [4]-[5], and phase-shifting interferometry [6]-[7], have been developed to make high resolution measurement of small displacements. However, apart from the complexity of the system construction, these existing methods are generally feasible only for low speed measurement applications. When a high speed measurement is needed, it is difficult to find a suitable technique if the measurement accuracy requirement is high. The speed limitation in these displacement measurement interferometers is mainly due to the use of slow modulation or scanning techniques [8]. In this paper, we propose a homodyne polarization interferometer, which can be used for high speed measurement of small displacements with sub-nanometre resolution and accuracy.

2. Dual beam polarization interferometer

Our dual beam polarization interferometer for displacement measurement is as shown in Fig 1. Instead of using one or more acousto-optical modulators (AOM), this polarization interferometer configuration utilizes two orthogonally-polarized light beams to remove the directional ambiguity of the displacement. The main part of the interferometer utilises a polarizing beam splitter PBS 1, two quarter-wave plates QWl and QW2, two mirrors M1 and M2, and a non-polarizing beam splitter NPBSl as both a beam splitter and phase shifter.

Fig 1 Dual-beam polarization interferometer

The use of a polarizing beam splitter PBSl is to make the most use of the laser beam and prevent the returning beam from feeding back to the laser diode. Mirror M2 is driven by a piezoelectric translator PZT 1, which can be used to perform system calibration. Mirror M3 is used as a reference plane when single point displacement is measured. When the system is used to measure the relative displacement of two adjacent points, such as the vertical movement of the hard-disk read/write head relative to the disk surface, M3 is removed and the reference beam is coupled out by NPBS₁, to the second measurement point. Mirror M2 can also be micro-positioned manually to adjust the spacing of the two measurement points. A 670 nm wavelength laser diode is used as the light source. The laser beam passes through the polarizer and enters the polarizing beam splitter PBS 1. Then the s-polarized component is coupled out and reflected by mirror M1 and focused on the measurement point on the sample. The p- polarized component passes through and is focused onto the reference mirror or another measurement point. The returning beam enters the interferometric receiver, which is used to measure the intensity and phase difference between the two polarized beams. The interferometric receiver consists of a non-polarizing beam splitter NPBS2, two polarizing beam splitters PBS2 and PBS3, a quarter- wave plate QW3 and four photo-detectors. The detected voltage signals are amplified and equalized, then sampled in by the computer through a 12-bit A/D converter board. The sampling rate of the A/D converter will determine the measurement speed of the system. The A/D converter board with a sampling rate of 20MS/s is commercially available at present. The piezoelectric translators are also controlled by the computer through a 12-bit D/A converter board and a high voltage amplifier.

We take the electric field of the two orthogonally polarized beams to be:

E_p = A_p exp(i(omega;t)) (1) (1)

E_s = A_s exp(i(omega;t ɸ)) (2)

where omega; is the angular frequency of the radiation, A_p and A_s are the amplitudes of E_p and E_s respectively, and

ɸ=4pi;(d ∆d)/lambda; (3)

In equation (3), lambda; is the wavelength of the laser beam, d is the static optical path difference between the two polarized beams and ∆d is the displacement to be measured. The combined beam, E_p E_s, after passing through NPBS2 and QW3, and incident upon PBS2 and PBS3, is split into four orthogonal beams with a phase difference of pi;/2 between them. The wave intensities being received by the four photo-detectors (P_PD1 to P_PD4) are proportional to the square of the electric field and can be formulated by [9]:

P_PD1=K(b₁ – a₁ sin(4pi;(d ∆d)/lambda;) (4)

P_PD2=K(b₂ – a₂ sin(4pi;(d ∆d)/lambda;) (5)

P_PD1=K(b₃ – a₃ sin(4pi;(d ∆d)/lambda;) (6)

P_PD1=K(b₄ – a₄ sin(4pi;(d ∆d)/lambda;) (7)

where K is the photoelectric conversion factor of the photo-detector, b₁ to b₄ represent the DC components, and a₁ to a₄ represent the magnitudes of th

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用于测量小位移的偏振干涉仪

刘新群，沃里克·克莱格，戴维·詹金斯，刘博

普利茅斯大学信息存储技术研究中心，英国PL4 8AA 数据存储研究所，肯特港湾，新加坡119260

摘要

本文提出了一种零偏极化激光干涉仪用于微小位移的高速测量的方法。本方法不使用调制技术，因此光机械装置相对简单。双光束布置使得能够测量位移，而使用偏振干涉测量可以确定位移的方向性质。该干涉仪的另一个特征在于它也适用于测量硬盘驱动器的磁头-介质间距。结合目前使用的电子元件，可以实现亚纳米分辨率。其测量带宽仅受所使用的A / D板的采样率的限制。

1.介绍

光学干涉测量是用于精确和非接触测量的成熟技术。基于各种干涉测量技术，例如外差干涉测量^{[1] - [3]}，正弦相位调制干涉测量^{[4] - [5]}和相移干涉测量^{[6] - [7]}已经开发出用于进行微小位移的高分辨率测量。然而，除了系统构造的复杂性之外，这些现有的方法通常只适用于低速测量应用。当需要高速测量时，如果测量精度要求高，则难以找到合适的技术。 这些位移测量干涉仪的速度限制主要是由于采用慢速调制或扫描技术造成的^[8]。 在本文中，我们提出了一种零差偏振干涉仪，可以用于亚纳米分辨率精度的微小位移的高速测量。

2.双光束偏振干涉仪

用于位移测量的双光束偏振干涉仪如图1所示。代替使用一个或多个声光调制器（AOM），该偏振干涉仪配置利用两个正交偏振光束去除位移的定向模糊度。干涉仪的主要部分使用偏振分束器PBS 1，两个四分之一波片QW1和QW2，两个反射镜M1和M2以及非偏振分束器NPBS1作为分束器和移相器。

图1双光束偏振干涉仪

使用偏振分束器PBS1的目的是充分利用激光束并防止返回光束反馈到激光二极管。镜M2由压电转换器PZT 1驱动，可用于执行系统校准。当测量单点位移时，镜M3用作参考平面。当系统用于测量两个相邻点的相对位移，例如硬盘读/写头相对于磁盘表面的垂直移动时，M3被移除，参考光束由NPBS₁耦合到第二测量点。镜M2也可以手动调节，以调整两个测量点的间距。使用670nm波长的激光二极管作为光源。激光束通过偏振器并进入偏振分束器PBS 1后，然后将s偏振分量耦合出来并由反射镜M1反射并聚焦在样品上的测量点上。p偏振分量通过并聚焦到参考反射镜或另一测量点上。返回光束进入干涉测量接收机，用于测量两个偏振光束之间的强度和相位差。干涉测量接收机包括非偏振分束器NPBS2，两个偏振分束器PBS2和PBS3，四分之一波片QW3和四个光电检测器。检测到的电压信号被放大和均衡，然后由计算机通过12位A / D转换器板进行采样。A / D转换器的采样率将决定系统的测量速度。采样率为20MS / s的A / D转换板目前是市售的。压电转换器也由计算机通过12位D / A转换器板和高压放大器控制。

我们将两个正交偏振光束的电场取为：

E_p = A_p exp(i(omega;t)) (1) (1)

E_s = A_s exp(i(omega;t ɸ)) (2)

其中omega;是辐射的角频率，Ap和As分别是Ep和Es的振幅，

ɸ=4pi;(d ∆d)/lambda; (3)

在等式（3）中，lambda;是激光束的波长，d是两个偏振光束之间的静态光程差，∆ d是要测量的位移。组合光束E_p E_s经过NPBS2和QW3，入射到PBS2和PBS3上后，被分成四个正交光束，它们之间的相位差为pi;/ 2。由四个光电检测器（P_PD1至P_PD4）接收的波强与电场的平方成比例，可表示为^[9]：

P_PD1=K(b₁ – a₁ sin(4pi;(d ∆d)/lambda;) (4)

P_PD2=K(b₂ – a₂ sin(4pi;(d ∆d)/lambda;) (5)

P_PD1=K(b₃ – a₃ sin(4pi;(d ∆d)/lambda;) (6)

P_PD1=K(b₄ – a₄ sin(4pi;(d ∆d)/lambda;) (7)

其中K是光电检测器的光电转换因子，b₁至b₄表示DC分量，a₁至a₄表示AC分量的大小。 通过简单的信号调理和处理，获得正交信号（P_PD2-P_PD1 b₂ / b₁）和（P_PD4-P_PD3 b₃/ b₄）。 这两个信号由计算机通过A / D转换器板的两个通道进行采样。 然后通过相位评估和展开确定位移∆d ^[10]。

3.实验结果

为了测试该干涉仪的能力和有效性，已经进行了几个实验。我们使用另一个压电转换器PZT2作为样本。12位D / A转换器用于控制应用于PZT2的0 - 1V电压输出。我们首先进行实验来测试系统的一般噪声水平或系统测量误差。在该实验中，PZT1和PZT2均保持静止。A / D转换器的采样率设置为50KHz。测量结果如图2所示。

（a）9000份抽样数据

（b）图（a）的局部视图

图2 系统测量误差和一般噪声电平

从图2，我们可以看到系统测量误差由低频和高频分量组成。从图2（a）中可以看出低频噪声。这可能是由背景振动，热漂移气流干扰等引起的。这些噪声水平的大小可以高于1nm。在快速变化的位移测量情况下，通过简单的信号处理可以消除这种低频噪声。高频噪声来自激光二极管，光电检测器和系统的电子元件。该噪声电平的大小约为0.3nm，这可从图2（b）中看出。我们现在进行进一步的实验，我们使用PZT2将样品以从约4.75pm到1nm的不同的幅度的锯波形移动测量连续较小的位移，结果如图1图3〜 7所示。

位移振幅约约为4.79mu;m的测量结果

位移振幅约约为30mu;m的测量结果

位移振幅约约为8.5mu;m的测量结果

位移振幅约约为3.5mu;m的测量结果

位移振幅约约为0.8mu;m的测量结果

从上述实验结果可以看出，测量不同大小的位移均可以获得相当满意的精度。

4.实验结果

本文提出的零偏极化激光干涉仪可用于精确测量小位移，特别适用于高速位移的测量。 理论上，12位A / D转换器可提供高于lambda;/4096的测量分辨率。然而，由于系统噪声，特别是电噪声，其目前配置中的系统具有约0.5nm的一般测量分辨率。通过仔细改进系统的电子和机械技术，测量分辨率将进一步提高。这种双光束干涉仪特别适用于表征硬盘驱动器的磁头间距^[11]。还可以通过选择更高的采样率AD板来提高系统的测量带宽。

参考文献

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