Rotation angle measurement based on white-light interferometry with a standard optical flat

We propose a simple white-light interferometric method of measuring a one-dimensional rotation angle with use of an optical plane parallel plate of standard refractive index. The phase change of the interference pattern of the interferometer during the rotation of the flat plate of known refractive index and thickness placed in one of the interferometer's arms is used for determination of the rotation angle. This method has been demonstrated for an accurate angle measurement over the angle range from 0° to 40° within a maximum uncertainty of 0.057°.     

Colorimetric method for phase evaluation

Measurements of very small phase changes in optical measurement techniques are usually performed with interferometric methods that are based on evaluation of interference patterns, which correspond to a phase change of the investigated wave field. If values of the phase change are small, it is difficult to determine accurately the phase values, and one needs very expensive measurement systems. We present a simple method for evaluation of small phase variations that uses the interference of polychromatic light. The phase change affects the color of the interference pattern, and the color of the interference pattern corresponds to a specific phase change that can be evaluated using colorimetric analysis. We describe and analyze our colorimetric phase evaluation method. The proposed method offers accurate results, and it may be suitable for practical utilization in the optical industry.     

Evaluation of Measurement Uncertainty for Absolute Flatness Measurement by Using Fizeau Interferometer with Phase-Shifting Capability

It is important to precisely measure flatness of the optical flats, as many industries use these as reference standards to ensure the quality of precision measurements and fabricated components. This paper describes identification of sources of error and measurement uncertainty evaluation for three flat test. Three flat test is used for absolute flatness measurement of optical flats, with the help of Fizeau interferometer (VerifireXP/D, with phase shift interferometry) established recently at National Physical Laboratory, India (NPL-I). The absolute profile of reference flat with higher accuracy can be determined using liquid level reference but liquid flat reference is more difficult to realize practically. Therefore three flat test is frequently adopted in standard interferometric measurements and traceability of this test can also be established by using a traceable laser head. This paper describes three flat method in detail along with observations and evaluation of measurement uncertainty as per ISO GUM is also done. Factors contributing to uncertainty of measurement of surface flatness have been indentified and detailed evaluation of uncertainty in measurements has been reported here.     

Modeling the interferometric radius measurement using Gaussian beam propagation

We model the interferometric radius measurement using Gaussian beam propagation to identify biases in the measurement due to using a simple geometric ray-trace model instead of the more complex Gaussian model. The radius measurement is based on using an interferometer to identify the test part's position when it is at two null locations, and the distance between the positions is an estimate of the part's radius. The null condition is observed when there is no difference in curvature between the reflected reference and the test wavefronts, and a Gaussian model will provide a first-order estimate of curvature changes due to wave propagation and therefore changes to the radius measurement. We show that the geometric ray assumption leads to radius biases (errors) that are a strong function of the test part radius and increase as the radius of the part decreases. We tested for a bias for both microscaled (<1 mm) and macroscaled parts. The bias is of the order of parts in 10(5) for micro-optics with radii a small fraction of a millimeter and much smaller for macroscaled optics. The amount of bias depends on the interferometer configuration (numerical aperture, etc.), the nominal radius of the test part, and the distances in the interferometer.     

Offset of coherent envelope position due to phase change on reflection

Different materials with different phase changes on reflection affect the surface-height measurement when interferometric techniques are employed for testing objects constructed of different materials that are adjacent to one another. We test the influence of this phase change on reflection when vertical scanning interferometry with a broadband source is used. We show theoretically and experimentally that the strong linear dependence of the dispersion of the phase change on reflection preserves the shape of the coherence envelope of the fringes but shifts it along the optical axis by approximately 10-40 nm for metallic surfaces.     

光功率热分析仪的温度校准方法研究

薄膜材料相变温度的准确测量是相变材料的应用关键.光功率热分析仪是基于薄膜材料相变前后光反射率发生突变的原理测量相变温度的新型仪器,采用真空红外加热方式达到相变温度.为了测量得到准确可靠的相变温度,通过对光功率热分析仪测量相变温度方式、标准热电偶原位校准仪器测温热电偶方法的研究,实现将相变温度溯源至SI单位,并且对在测温...     

Method of excess fractions with application to absolute distance metrology: theoretical analysis

The method of excess fractions (EF) is well established to resolve the fringe order ambiguity generated in interferometric detection. Despite this background, multiwavelength interferometric absolute long distance measurements have only been reported with varying degrees of success. In this paper we present a theoretical model that can predict the unambiguous measurement range in EF based on the selected measurement wavelengths and phase noise. It is shown that beat wavelength solutions are a subset of this theoretical model. The performance of EF, for a given phase noise, is shown to be equivalent to beat techniques but offers many alternative sets of measurement wavelengths and therefore EF offer significantly greater flexibility in experimental design.     

Heterodyne grating interferometer based on a quasi-common-optical-path configuration for a two-degrees-of-freedom straightness measurement

We present a heterodyne grating interferometer based on a quasi-common-optical-path (QCOP) design for a two-degrees-of-freedom (DOF) straightness measurement. Two half-wave plates are utilized to rotate the polarizations of two orthogonally polarized beams. The grating movement can be calculated by measuring the phase difference variation in each axis. The experimental results demonstrate that our method has the ability to measure two-DOF straightness and still maintain high system stability. The proposed and demonstrated method, which relies on heterodyne interferometric phase measurement combined with the QCOP configuration, has the advantages of high measurement resolution, relatively straightforward operation, and high system stability.     

Precise interferometric length and phase-change measurement of gauge blocks based on reproducible wringing

A modern fringe-pattern-analyzing interferometer with a resolution of 1 x 10(-9) and without exclusion of systematic uncertainties owing to optic effects of less than 1 nm was used to test a new method of interferometric length measurement based on a combination of the reproducible wringing and slave-block techniques. Measurements without excessive wringing film error are demonstrated for blocks with nominal lengths of 2-6 mm and with high surface flatness. The uncertainty achieved for these blocks is less than 1 nm. Deformations of steel gauge blocks and reference platens, caused by wringing forces, are investigated, and the necessary conditions for reproducible wringing are outlined. A subnanometer uncertainty level in phase-change-correction measurements has been achieved for gauge blocks as long as 100 mm. Limitations on the accuracy standard method of interferometric length measurements and shortcomings of the present definition of the length of the material artifact are emphasized.     

Direct Static Strain Measurement Utilizing Signal Fading and Spectrum Analysis in a Fibre Optic Interferometric Sensor

Abstract

An accurate linear method of static phase shift measurement in a fibre optic interferometric strain sensor, based on the concurrent utilization of signal fading, photovoltage spectrum analysis and the arctangent function, is presented. The static phase shift is superimposed on a controlled dynamic phase modulation derived from an optical phase modulator in one arm of the interferometer. Good agreement is demonstrated between the phase shift obtained through experiment and that from the theoretical expression. This detection scheme has wide applications to static and dynamic phase shift measurements in fibre optic interferometric sensors, and to optical interferometry in general.     

Correcting for stage error motions in radius measurements

Traceable radius of curvature measurements are critical for precision optics manufacturing. An optical bench measurement is repeatable and is the preferred method for low-uncertainty applications. With an optical bench, the displacement of the optic is measured as it is moved between the cat's eye and the confocal positions, each identified using a figure measuring interferometer. The translated distance is nominally the radius of curvature; however, errors in the motion of the stage add a bias to the measurement, even if the error motions are zero on average. Estimating the bias and resulting measurement uncertainty is challenging. We have developed a new mathematical definition of the radius measurand that intrinsically corrects for error motion biases and also provides a means of representing other terms such as figure error-correction, wave-front aberration biases, displacement gauge calibration and their uncertainties. With this formalism, it is no long necessary to design a high-quality radius bench to carry out a precision measurement; rather a lower quality is adequate, provided that error motions are repeatable and characterized and error motion measurement uncertainties are estimated.     

利用计量型原子力显微镜进行纳米台阶高度测量

计量型原子力显微镜纳米测量系统主要由扫描器、测针位置传感器和一体化微型激光干涉三维测量系统等部分构成．针对计量型原子力显微测量系统,采用三维激光干涉测量系统作为测量基准,以实现原子力测量系统的纳米尺度量值溯源和校准工作．建立了校准模型,分析了扫描器9项主要误差项,并将该模型应用到原子力显微镜扫描器的校准中．校准后的结果表明,除z轴位置误差不超过±2nm外,其他8项的残余误差均不超过±1nm．通过台阶高度国际比对,建立了台阶高度标准计算方法及不确定度分析模型．台阶高度国际比对的测量结果表明,计量型原子力显微镜的测量值与参考值相差均小于1．5nm．     

Application of an interferometric phase contrast method to fabricate arbitrary diffractive optical elements

A novel approach for the fabrication of diffractive optical elements is described. This approach is based on an interferometric phase contrast method that transforms a complex object wavefront into an intensity pattern. The resulting intensity pattern is used to expose a photoresist layer on a substrate. After development, a diffractive phase object with an on-axis diffraction pattern is achieved. We show that the interferometric phase contrast method allows a precise control of the resulting intensity pattern. An array of blazed Fresnel lenses is realized in photoresist by using kinoform or detour-phase computer holograms for the interferometric phase contrast setup.     

Accuracy of a multiple height-transfer interferometric technique for absolute distance metrology

A multiple height-transfer interferometric technique was developed to increase the absolute distance measurement capability of a metrology system that uses a tunable laser. Using multiple accurately calibrated reference heights, this technique relaxes the requirement of knowing accurate wavelength information for multiple wavelength interferometry while maintaining its advantages. We present an uncertainty analysis, analyze the primary sources of uncertainties limiting the performance of this technique, and discuss how errors can be minimized. Measurement results of 3D images obtained from a variety of objects are presented. The measurement uncertainty is experimentally demonstrated to be 0.3?μm over 50?mm for two discontinuous surfaces with a confidence level of 95% in a lab environment.     

Grating-based real-time polarization phase-shifting interferometry: error analysis

A phase Ronchi grating-based real-time polarization phase-shifting method can be efficiently used for dynamic phase measurement in optical interferometry. A thorough error analysis is required for exhibiting how error sources influence phase-measurement results. We analyze the phase-measurement errors that are induced by the retardation error and azimuth angle error of the quarter-wave plate, the azimuth angle error of polarizers, the phase and intensity aberrations of diffractive wave fronts, and pixel mismatch of the interferometric patterns. The results will also be useful for evaluating the phase-measurement accuracy of other similar systems.     

Orthogonal polarization fiber gyroscope with increased stability and resolution

The orthogonal polarization fiber gyroscope (OPFG) is an interferometric fiber gyroscope design that requires no phase bias in the fiber ring and is insensitive to light-source intensity noise. However, in the original OPFG [Hitachi Rev. 33, 215 (1984)], environmental changes caused first-order false rotation signals. We propose and experimentally verify modifications that eliminate the first-order sensitivity to environmental changes and that improve the gyroscope's resolution as well. We believe that this modified OPFG is the first interferometric fiber gyroscope capable of stable, high-sensitivity measurement that contains only reciprocal optical elements.     

Optical phase step method for absolute ranging interferometry using computer-generated holograms

One main problem of an interferometric measurement is to evaluate the object distance from the interference function. One of the known methods that delivers the object phase is the phase step method. Here we introduce computer-generated holograms to realize parallel phase steps without phase modulation of the reference path.     

Working-point control method for readout of dynamic phase changes in interferometric fiber-optic sensors by tuning the laser frequency

A simple but reliable method, namely the working-point control by tuning the laser frequency, for the dynamic phase shift measurement in a passive homodyne interferometric fiber-optic sensor is proposed. A dc voltage calculated from the photodetector output is applied to the light source to control the interferometer at the condition of maximum sensitivity. Then the signal's phase shift can be obtained from the components of zero and fundamental frequencies. To test the method, an all polarization-maintaining Mach-Zehnder interferometer with a piezoelectric ceramic (PbZrTiO(3), or PZT) cylinder in one arm is constructed. The experimental results show that the simulation signal's phase shift generated by the PZT cylinder can be read out correctly with the method. It has the advantages of simplicities of operation, no-active element in the sensing head, and large operating bandwidth. It can be used for readout of dynamic phase shifts in various interferometric fiber-optic sensors.     

光干涉绝对重力仪衍射修正

针对绝对重力仪的衍射修正进行研究计算。在光干涉绝对重力仪测量原理基础上,分析并得到激光的高斯特性给重力加速度测量带来的影响。利用90/10刀口法测算激光特性参数(束腰半径),推算得到光衍射(激光的高斯特性)引入的重力加速度值相对修正量。结果表明:激光束腰半径为1.158 6 mm,使用该高斯激光束给重力加速度值引入的偏差,其相对修正量为7.56×10^-9。该方法适用于光干涉绝对重力衍射修正量的计算。     

Novel approaches to the design of halftone masks for analog lithography

We report novel approaches to the design of halftone masks for analog lithography. The approaches are derived from interferometric phase contrast. In a first step we show that the interferometric phase-contrast method with detour holograms can be reduced into a single binary mask. In a second step we introduce the interferometric phase-contrast method by interference of the object wavefront with the conjugate object wavefront. This method also allows for a design of a halftone mask. To use kinoform holograms as halftone phase masks, we show in a third step the combination of the zeroth-order phase-contrast technique with the interferometric phase-contrast method.