Parallel Plate Interferometer with a Reflecting Mirror for Measuring Angular Displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10⁻⁸ rad.     

Measurement of thickness of a thin film by means of laser interference at many incident angles

An optical method for directly measuring the thickness of a thin transparent film has been proposed by means of multi-wave laser interference at many incident angles, and confirmed experimentally by means of equipment made on an experimental basis. Two methods are available: one can be used when an index of refraction of the film, a wavelength λ, and two successive angles of incidence at which the sinusoidal light intensity has minimum values, are known (Method I), and another can be used without an index of film refraction when three successive angles of incidence and a wavelength are known (Method II). The smallest measurable thickness is 1.43λ for Method I, and 2.5λ for Method II. The largest measurable thickness is about 100λ for both methods. The measurement error by means of numerical calculation is Δh/h−1.01×10⁻², and that obtained experimentally with an angular resolution of incident light of 0.3° is Δh/h7×10⁻² for Method I. The refractive index can also be measured by means of Method II.     

A new method for angular displacement measurement

We describe a new method for angular displacement measurements that is based on a Fabry-Perot interferometer. A measurement accuracy of 10-8 rad is obtained by use of the sinusoidal phase modulating interferometry. Another Fabry-Perot interferometer is used to obtain the key initial angle of incidence.     

KDP晶体折射率非均匀性检测系统

基于正交偏振干涉法,建立了KDP晶体折射率非均匀性的检测系统,并可实现晶体相位失谐角的间接检测.波前检测系统实现了测试光偏振态的精密控制与切换,采用波长调谐相移的方法去除了测试过程中参考面倾斜引入的误差,优化了抗振动相移算法,提高了波前测试的测量准确度及重复性.通过折射率非均匀性分析算法的设计,解决了晶体厚度变化引入的误差等.小口径晶体元件的测试结果表明系统的折射率非均匀性检测准确度(均方根值)优于10-6.     

Scanning monochromatic spatial low-coherence interferometer

A scanning spatial low-coherence interferometer (S-LCI), using an off-axis converging single wavelength laser beam as the probe, resembles a conventional or temporal low-coherence interferometer (T-LCI) in signal formation and data processing. However, the S-LCI is advantageous over a T-LCI with the combination of angle resolving and depth discrimination capabilities. The S-LCI is demonstrated by measuring the angle dependent phase shifts among the multiple reflections of a glass plate, with incident angles accurately scaled in the Fourier domain. The refractive index and geometric thickness of the glass plate are simultaneously produced in this one-step measurement.     

KDP晶体折射率非均匀性检测系统

基于正交偏振干涉法,建立了KDP晶体折射率非均匀性的检测系统,并可实现晶体相位失谐角的间接检测.波前检测系统实现了测试光偏振态的精密控制与切换,采用波长调谐相移的方法去除了测试过程中参考面倾斜引入的误差,优化了抗振动相移算法,提高了波前测试的测量准确度及重复性.通过折射率非均匀性分析算法的设计,解决了晶体厚度变化引入的误差等.小口径晶体元件的测试结果表明系统的折射率非均匀性检测准确度(均方根值)优于10~(-6).     

Suppression of Multiple-Beam Interference Noise in Testing an Optical-Parallel Plate by Wavelength-Scanning Interferometry

Measurements of optical parallel plates in a Fizeau interferometer lead to problems from multiple-beam interference noise unless the back surface of the plate has an additional treatment to prevent its reflection from reaching the detector. Such internal-reflection noise can be separated from the fundamental interference signal by its modulation frequency in a wavelength-scanning interferometer. However, to completely eliminate the noise, the air-gap distance between the testing and reference surfaces of the interferometer must be adjusted to a specific value, depending on the thickness and refractive index of the plate. This adjustment requires an undesirable change in the air gap, which is related to the phase modulation rate of the interferometer, and also requires additional information regarding the testing plate, which makes the measurement laborious. We show that if we add new symmetries to the sampling functions of the phase measuring algorithm, we can obtain significantly greater tolerance for the air-gap error. A new 19-sample algorithm allows a tolerance of ±23% while keeping the systematic errors at less than λ/200. The periodicity of the new algorithm and an integrating bucket technique also provide more options for the thickness of the testing plate, which guarantees an air-gap distance more independent of this thickness.     

Zygo interferometer for measuring refractive index of photorefractive bismuth silicon oxide (Bi12SiO20) crystal

An application of the Zygo system for measuring the refractive index of optical materials such as bismuth silicon oxide (BSO) having a higher value of the refractive index than that of glass is presented. The setting accuracy is found to be of the order of 1 μm in the Zygo phase measuring interferometer. The mean value of refractive index of BSO crystal measured by the interferometer for several samples of thickness in the range of 3–9 mm is 2.542 at a wavelength of 632.8 nm. The accuracy of measurement is ±0.002. It is possible to achieve an accuracy of ±0.0003 for a sample of thickness of 30 mm in the measurement of refractive index due to high setting accuracy of the Zygo system.     

Measurement of small angle based on a (1 0 0) silicon wafer and heterodyne interferometer

In this paper, a new optical material application and a heterodyne interferometer are proposed for measuring small angles. In the proposed interferometer, the optical material is a (1 0 0) silicon wafer applied to compose a new architecture of small angle sensor. The small angle measurement used the phase difference which is dependent on the incident angle at the silicon wafer surface to deduce the angular variation. The proposed architecture is simple and uses the common path method to compare test and reference signals; thus, small angles can be easily and accurately measured by estimating the phase difference. The experimental results demonstrate the feasibility of this method. The angular resolution and sensitivity levels superior to 7 × 10^?5° (1.3 × 10^?6 rad) and 150 (deg/deg), respectively, were attainable in a dynamic range of 0.45°.     

A high-precision optical metrology system for determining the thickness of birefringent wave plates

This study develops a non-destructive measurement system for determining the thickness and refractive indices of birefringent optical wave plates. Compared to previous methods presented in the literature, the proposed metrology system provides the ability to measure the thickness of the birefringent optical plate in high-precision. The results show that for a commercially available birefringent optical wave plate with refractive indices of n_e=1.5518, n₀=1.5427 and a thickness of 452.1428 μm, the experimentally determined value for the error in the wave plate thickness measurement is just 0.046 μm. The measurement resolution of the proposed system exceeds that of the interferometer hardware itself. The proposed method provides a simple yet highly accurate means of measuring the principal optical parameters of birefringent glass wave plates.     

Novel optical film sensor design based on p-polarized reflectance

A new scheme of optical film sensor is presented. The sensor is based on p-polarized reflectance, consisting of a sensing coated substrate, is easily optimized for maximum sensitivity in different applications. The resolutions of refractive index n_f, extinction coefficient k_f and thickness h_f of the sensitive films are predicted to be 10⁻⁷, 10⁻⁵ and 10⁻³ nm, respectively. Experimentally, we selected the sol–gel derived SnO₂ films as gas-sensitive films and conducted preliminary gas-sensing test. The results indicate that novel optical film sensor scheme has higher sensitivity, and the detection sensitivity is available to 10⁻¹ ppm on the condition of optimum optical parameters and incident angle.     

一种基于相位测量的角漂移自适应结构表面等离子体共振气体折射率测量系统

提出了一种可抑制角漂移的表面等离子体传感器结构,并结合相位测量设计了相应的气体折射率测量系统。分析表明激光入射角、金膜厚度以及反射光p、s分量的相位差与气体折射率之间的固有非线性是影响相位响应度与折射率测量精度的主要因素。计算表明所提出的自适应结构将角漂移引起的误差降低了一个数量级并很大程度提高了测量灵敏度。同时分析设计了金膜厚度参数,并评估了反射光p、s分量的相位差与气体折射率之间固有非线性带来的误差。应用于空气折射率的测量比对实验显示其测量精度达到了10-6量级。     

Relative beam misalignment errors in high accuracy displacement interferometers: calculation and detection

We consider the effects of misalignment in a two-beam interferometer resulting from lateral displacement as well as angular misalignment of the beams. Furthermore, a technique to determine such misalignments is discussed and examples of measurement strategies and expected performance are given. It is found that, when the waist of the beam used to illuminate the interferometer is larger than 0.7 mm (∼1000λ), such an approach allows alignment to be made resulting in a relative interferometric error smaller than 1×10⁻¹⁰ provided that the diffraction effect is fully accounted for.     

法布里-珀罗板正弦相位调制型高精度角位移测量

提出了一种基于法布里-珀罗板和正弦相位调制干涉术的角位移测量新方法。采用CCD探测法布里-珀罗板两透射光束光斑的中心距,通过运算得到了入射光的初始角,解决了采用法布里-珀罗板干涉法测量角位移需确定入射光初始角的问题。采用正弦相位调制干涉术通过测干涉信号的相位来测量物体的角位移,增强了对杂散光的抗干扰能力,减少测量误差,提高了测量精度。理论模拟和实验结果表明本方法可以实现精度为10^-8rad数量级的高精度角位移测量。     

Modified Michelson interferometer for probing refractive index of birefringent crystal CSBN50

Based on the modified Michelson interferometer and phase analysis method, a high-accuracy method for probing the refractive index (RI) of transparent medium is proposed. The validated test was performed on a birefringent crystal CSBN50 with the estimated accuracy being up to 10⁻⁴. The ordinary and extraordinary refractive indices of CSBN50 at 632.8 nm are determined as n₀=2.32853±0.00016 and n_e=2.27664±0.00016, respectively.     

Digitally processed, phase-reading fibre gyroscope

We present a simple digital processing method that provides a significant improvement for the performance of a phase-reading open-loop fibre-optic gyroscope. The phase-reading gyroscope measures the angular speed in terms of a phase difference between the two counter-propagating beams in the Sagnac interferometer. Instead of electronic phase meters we use a very simple PC-based digital process which computes the Sagnac phase. With this method we measure rotation rates down to 100°h⁻¹. The errors of this scheme are studied for different signal-to-noise ratios and the number of bits of the analog-to-digital converter.     

A new lateral shearing interferometer for precision surface measurement

A new lateral shearing interferometer is proposed for precision surface measurement. In this shearing interferometer, a novel shear generator made of a single birefringence crystal plate is utilized. The shear adjustment is realized through the change of angle at which tested wavefront is incident into the crystal plate. By changing the orientation of the principal section of the plate, the generator can adjust the shearing direction. With the incident beam being circularly polarized, the generator can equalize the intensities of two shearing beams to make a good contrast interference pattern. The interferometer is simple and compact in terms of mechanism and has a complete common optical path structure. Phase shifting can be realized conveniently. The interferometer is insensitive to external vibrations and environmental disturbances, and hence has good stability and reliability with high measurement accuracy. To examine the performance of the proposed interferometer, experimental testing was conducted. High accuracy and repeatability are demonstrated.     

Wavelength shift determination using a dual-path heterodyne Mach-Zehnder interferometer

This paper introduces a dual-path heterodyne Mach-Zehnder interferometer adopted for wavelength shift determinations. In this interferometer, two parallel incident beams are separated into two interference pairs which are then recombined to generate two interference signals. A parallel plate is placed on the path of one wave of an interference pair, so the phase difference of the interference signals is a function of the plate and beam wavelength, and the interferometer is thus able to determine the wavelength shift of the incident beam. A setup constructed to realize the proposed interferometer is described, it shows that the interferometer has a resolution up to 1.1 × 10⁻¹⁰ (λ²/nm), and the experimental results of applying this setup not only agree the validity of the interferometer but also indicate that the interferometer has a stability of 6.5 × 10⁻¹⁰ (λ²/nm).     

Modified super-wide-angle Sagnac imaging interferometer based on LCoS for atmospheric wind measurement

The modified super-wide-angle Sagnac imaging interferometer (MSASII) based on liquid crystals on silicon (LCoS) is proposed as a novel device for the detection of the upper atmospheric wind field. This device employs the phase-only modulation (POM) of LCoS coupled with the MSASII, and can measure phase changes in multi-band emissions without moving mirror. It can be used to replace the conventional Michelson’s interferometer with step-moving mirror device. The optical path difference (OPD) equation of MSASII-LCoS is derived, and the four compensation conditions (field, chromatics, thermal and achromaticity of thermal compensations) are discussed within the scope of wind measurement. The real parameters of LCoS and optical glasses are selected for numerical simulation and analysis. Three aurora lines (732.0, 630.0 and 557.7 nm) are considered, and their phase variations are 3.61, 2.02 and 0.15 fringes at the same incident angle of 3°, respectively. The rate of change of OPD with temperature is the magnitude of 10⁻⁶ cm/K, and the corresponding phase variations are within 0.09 fringes. The accuracy of phase modulation can be 0.614×10⁻² rad when LCoS of 10-bits is used. The novel model MSASII-LCoS shows its advantage for atmospheric wind measurement in the aspects of the overall structure, anti-vibration, operational flexibility and detection accuracy.     

基于平行平板的折射率高精度非接触测量

常用的测量折射率的方法如偏向角法、自准直法、临界角法、 V棱镜法等,这些方法通常需特制三棱镜与待测件。待测样品不一致且过程复杂,测试定标周期长,难于自动化。为了保证待测材料的完整及实现自动化测量,进行了基于平行平板的折射率非接触测量的尝试。运用该方法进行折射率的测量,不需特制三棱镜并且待测件与待测样品一致。分析表明,通过选择合适的测量角度,该方法旋转角度精度为a=0.003（即10）,导轨精度为L=0.000 8 mm,平行平板厚度测量精度为d=0.001 mm。