Comment on "Precision refractive index measurements of air, N2, O2, Ar, and CO2 with a frequency comb"

The measured oxygen refractive index formulas are still not sufficient for precise metrological applications. Thus, a new dispersion formula for the molecular oxygen refractive index at standard conditions is derived. The agreement of the standard air refractive index obtained from indices of its components with recent dry air refractive index formulas is within a few billionths.     

Refractive index of air. 2. Group index

In a previous paper [Appl. Opt. 35, 1566 (1996)] one of us presented new equations for evaluation of the phase refractive index of air over a range of wavelengths and atmospheric parameters. That paper also gave an incorrect, although sufficiently accurate, procedure for calculating the group refractive index. Here we describe the results of a more rigorous derivation of the group index that takes proper account of the Lorentz-Lorenz formula, and we demonstrate that deviations from the Lorentz-Lorenz formula are insignificant to within a foreseeable precision of dispersion measurements for atmospheric conditions. We also derive and evaluate a simplification of the resultant equation that is useful for exploratory calculations. We clarify the limits of validity of the standard equation for the group refractive index and correct some minor errors in the previous paper.     

基于Edlén公式空气折射率测量系统的校准研究

为了检验对激光干涉仪测量精度有很大影响的空气折射率测量系统的测试性能,提出一种可用于基于Edlén公式的空气折射率测量系统的校准方法,并且设计了专门的校准装置,该装置主要由温度、气压以及湿度测量系统组成。实验证明：取包含因子k=2时,温度在(5~40)℃区间,测量不确定度U优于0.02 ℃;气压在(66~105)kPa区间,U=18 Pa;湿度在(10~90)%RH区间,U=2.0%RH,等效于整个系统对应的空气折射率测量的相对不确定度优于1×10^-7     

High-precision diode-laser-based temperature measurement for air refractive index compensation

We present a laser-based system to measure the refractive index of air over a long path length. In optical distance measurements, it is essential to know the refractive index of air with high accuracy. Commonly, the refractive index of air is calculated from the properties of the ambient air using either Ciddor or Edlén equations, where the dominant uncertainty component is in most cases the air temperature. The method developed in this work utilizes direct absorption spectroscopy of oxygen to measure the average temperature of air and of water vapor to measure relative humidity. The method allows measurement of temperature and humidity over the same beam path as in optical distance measurement, providing spatially well-matching data. Indoor and outdoor measurements demonstrate the effectiveness of the method. In particular, we demonstrate an effective compensation of the refractive index of air in an interferometric length measurement at a time-variant and spatially nonhomogeneous temperature over a long time period. Further, we were able to demonstrate 7 mK RMS noise over a 67 m path length using a 120 s sample time. To our knowledge, this is the best temperature precision reported for a spectroscopic temperature measurement.     

基于传感器阵列的野外基线环境参数自动测量系统研制

为了保证野外测距精度,研制了一套环境参数自动测量系统,该系统通过在野外基线沿线布置密集的气温、气压与湿度传感器阵列,精确测量光路气温、气压及湿度等环境参数,进行空气折射率修正。采用μ-base测距仪在不同气候条件下进行验证实验,测量距离为144 m。实验结果表明,采用该系统测量环境参数,进行空气折射率修正,其修正误差引入的距离测量不确定度优于3.0×10^-7(k=2)。     

Active suppression of air refractive index fluctuation using a Fabry-Perot cavity and a piezoelectric volume actuator

Air refractive index fluctuation (Δn(air)) is one of the largest uncertainty sources in precision interferometry systems that require a resolution of nanometer order or less. We introduce a method for the active suppression of Δn(air) inside a normal air-environment chamber using a Fabry-Perot cavity and a piezoelectric volume actuator. The temporal air refractive index (n(air)) at a local point is maintained constant with an expanded uncertainty of ~4.2 × 10(-9) (k = 2), a sufficiently low uncertainty for precise measurements unaffected by Δn(air) to be made inside a chamber.     

浮法玻璃表面光学常数分析

本文通过光谱椭偏仪测量浮法玻璃空气面和锡面的偏振信息,利用Cauchy光学模型分析得到浮法玻璃两表面的布鲁斯特角和光学常数,分析结果表明浮法玻璃空气面、锡面、理想玻璃界面的布鲁斯特角分别为56.7°、57°和56.8°,空气面形成疏松的表面层,厚度为2.75nm,折射率小于玻璃本底,锡面形成锡扩散表面层,厚度为81.29nm,折射率大于玻璃本底折射率,并且随厚度呈现出非线性梯度变化,结合透光率数据分析得到玻璃消光系数在10-6量级。由于浮法玻璃空气面和锡面的折射率明显不同,需要在后续玻璃镀膜光学设计时区别对待。     

Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry

We describe a low-coherence interferometric technique for simultaneous measurement of geometric thickness and group refractive index of highly dispersive samples. The technique is immune to the dispersion-induced asymmetry of the interferograms, thus overcoming limitations associated with some other low-coherence approaches to this simultaneous measurement. We use the experimental configuration of a tandem interferometer, with the samples to be characterized placed in an air gap in one arm of the measurement interferometer. Unambiguous, dispersion-insensitive measurements of critical group-delay imbalances in the measurement interferometer are determined from the optical frequency dependence of interferogram phases, by means of dispersive Fourier transform spectrometry. Sample thickness and group refractive index are calculated from these group delays. A thickness measurement precision of 0.2 mum and group index measurement accuracy of 5 parts in 10(5) across a wavelength range of 150 nm have been achieved for BK7 and fused-silica glass samples in the thickness range 2000 to 6000 mum.     

Refractive index of air: 3. The roles of CO2, H2O,and refractivity virials

The author's recent studies of the refractive index of air are extended, and several assumptions made therein are further examined. It is shown that the alternative dispersion equations for CO2, which are due to Edlen [Metrologia 2, 71 (1966)] and Old et al. [J. Opt. Soc. Am. 61, 89 (1971)] result in differences of less than 2 x 10(-9) in the phase refractive index and less than 3 x 10(-9) in the group refractive index for current and predicted concentrations of CO2. However, because the dispersion equation given by Old et al. is consistent with experimental data in the near infrared, it is preferable to the equation used by Edlen, which is valid only in the ultraviolet and the visible. The classical measurement by Barrell and Sears [Philos. Trans. R. Soc. London Ser. A 238, 1 (1939)] on the refractivity of moist air is shown to have some procedural errors in addition to the one discussed by Birch and Downs [Metrologia 30, 155 (1993)]. It is shown that for normal atmospheric conditions the higher refractivity virial coefficients related to the Lorentz-Lorenz relation are adequately incorporated into the empirically determined first refractivity virial. As a guide to users the practical limits to the calculation of the refractive index of the atmosphere that result from the uncertainties in the measurement of the various atmospheric parameters are summarized.     

Development of interference filters based on multilayer porous silicon structures

Porous silicon (PS) has a great potential in optical applications due to its tuneable refractive index. In particular, multilayer structures consisting of alternating PS layers with different refractive indices can be used as interference filters for applications in the field of optoelectronics and sensors. In the present work, the optical properties of PS single layers and multilayer structures were studied. Since the refractive index of PS varies depending on the air content of the porous matrix, the PS structures were modelled as an homogeneous mixture of silicon and air, according to the effective medium theories (EMTs). By adjusting the refractive index and thickness of each individual layer, we can obtain a stack of PS layers with the desired optical properties, resulting in interference filters of predetermined bandwidth.     

基于模式搜索法的低气压段Edlen公式的改进

Edlen公式是修正空气折射率的基本公式。针对Edlen公式在常压段修正空气折射率的这一局限性,设计并进行了低气压段的空气折射率与温度及气压关系的实验。采用无约束变量最优化理论中的模式搜索法,对适用于常压段的Edlen公式进行了改进,使其也适用于低气压段。修正詹公式的精度与常压段Edlen公式的精度基本相同。     

Determination of film thickness and refractive index in one measurement of phase-modulated ellipsometry

Ellipsometry is often used to determine the refractive index and/or the thickness of a polymer layer on a substrate. However, simultaneous determination of these parameters from a single-wavelength single-angle measurement is not always possible. The present study determines the sensitivity of the method to errors of measurement for the case of phase modulated ellipsometry and identifies conditions for decoupling film thickness and refractive index. For a specific range of film thickness, both the thickness and the refractive index can be determined from a single measurement with high precision. This optimal range of the film thickness is determined for organic thin films, and the analysis is tested on hydrogel-like polymer films in air and in water.     

高精度空气折射率测量系统设计与实现

针对商用空气折射率测量装置受到传感器采集性能和解算公式准确度的影响使得实际测量精度较低的问题,基于便携式多环境参数采集装置,设计了一套空气折射率测量系统,采集环境中的温湿度、大气压强状态信息,对3种折射率间接测量公式进行误差分析,并和商用环境补偿器进行性能对比。实验结果表明:在压强为100.17~100.21kPa,温度为21.1~21.9℃,湿度为45.9~58.0% RH的实验条件下,该测量系统的测量偏差比商用环境补偿器低2.69×10^-7。     

Extracting concentrated guided light

The maximum concentration of radiation is proportional to the square of the refractive index of the medium in which it propagates. A medium with a high refractive index can also serve as a lightguide for concentrated radiation. However, if concentrated radiation is extracted from one medium, with a high refractive index, to another, whose index is lower (e.g., from fused silica into air), part of the radiation may be lost because of the total internal reflection at the interface. We present polygonal shapes suitable for efficient extraction of the concentrated radiation in a controllable way, without increasing the cross-section area (or diameter) of the lightguide. It is shown analytically and experimentally that the use of a secondary concentrator, followed by such a light extractor, both having a high refractive index, can provide considerably more power to a solar receiver with a specific aperture.     

玻璃材料折射率及色散的高准确度测量

使用德国Triotics公司生产的SpectroMaster HR UV-VIS-IR型折射率测量设备,对FK5玻璃块的e、d、g、F′和C′谱线的折射率值进行高准确度测量,并修正至标准环境条件下的折射率值。用得到的折射率值进行曲线拟合,验证Cauchy色散公式和Sellmeier色散公式。     

Guiding radar signals by arrays of laser-induced filaments: finite-difference analysis

Circular arrays of plasma filaments induced by femtosecond laser pulses in atmospheric air are shown to support guided modes of electromagnetic radiation in the centimeter and millimeter wavelength range. With the refractive index of laser-induced filaments being lower than the refractive index of nonionized air, arrays of such filaments can serve as a structured waveguide cladding, providing an index guiding of radar signals in a nonionized gas region. In spite of attenuation of radar radiation induced by plasma absorption, filament-array waveguides are shown to enhance radar signal transmission relative to freely propagating radar beams.     

Propagation losses in a potassium-ion-exchanged waveguide with a superstrate

The influence of the refractive index of a superstrate on propagation losses of an optical waveguide is measured. A 72-cm-long channel waveguide is made by potassium ion exchange in microscope slides. Propagation losses are reduced from 0.4 dB/cm with air as the superstrate to 0.28 dB/cm with a liquid superstrate of refractive index 1.46.     

A new refractometer by combining a variable length vacuum cell anda double-pass Michelson interferometer

A new refractometer with a variable length vacuum cell has been developed to eliminate errors caused by deformations in optical windows of the cell. The refractive index of air is determined by measuring the changes in the optical path difference between the air of interest and a vacuum as a function of the changes in the cell length. An optical phase modulation technique and a dark fringe detection method are used to obtain a high resolution in measuring the optical path difference by a double-pass Michelson interferometer. A combined standard uncertainty of 5×10^-9 in the measurement of the refractive index of air has been achieved     

传输紫外激光用空芯光纤结构设计

对传输紫外激光用空芯光纤结构进行了研究.铝膜是从紫外到红外都有很高反射率的理想材料,用它来研制的空芯光纤的直线损耗和弯曲损耗均较小.在铝膜上涂覆设计厚度的低折射率膜可进一步提高系统的反射率,增加传输效率,并保护铝膜免受大气侵蚀.     

基于系列离子液体的折射率研究

离子液体作为新颖的"软"功能材料已成为目前研究的新热点。折射率的研究对了解离子液体这种新型光学材料的结构性质具有重要意义。对选取的系列离子液体{[Cnmim]BF4(n=6,8,10,12),[Cnmim]PF6(n=8,10,12),[Cnmim]I(n=7,8,10),[Cnmim]Cl(n=10,12,14),[CnPy]BF4(n=9,11,13)等}在空气中的折射率进行了测试和理论分析,结果表明,(1)若阴离子为BF4-和PF6-,离子液体的折射率随阳离子侧链的增长而线性增加;若阴离子为Cl-和I-,离子液体的折射率随离子液体阳离子侧链的增长而线性减小,相关系数R分别是0.98854、0.98004、0.99942、-0.97888、-0.9793;(2)当阳离子一定时,阴离子体积越大,折射率越小,单元素阴离子比多元素阴离子的离子液体折射率要大;(3)离子液体的折射率随温度升高而减小,卤盐离子液体与四氟硼酸盐和六氟磷酸盐离子液体相比对温度变化更敏感。