Statistical interferometry based on a fully developed speckle field: an experimental demonstration with noise analysis

A novel interferometric method named statistical interferometry is proposed and studied. In the method, in contrast to the conventional deterministic interferometry, the complete randomness of the two interfering light fields, i.e., the random interference of the fully developed speckle fields, plays an essential role and is used as a standard of phase in a statistical sense. Preliminary experiments were conducted to verify the validity of the method, followed by a computer simulation. As an experimental result, the accuracy of the measurements of an out-of-plane displacement was confirmed up to lambda/800 by comparison with the heterodyne interferometer. The method has the advantage of simplicity of the optical system required, while at the same time providing high accuracy.     

Single-shot parallel four-step phase shifting using on-axis Fizeau interferometry

The purposes of the paper are threefold: (1) to show the possibility to perform parallel phase-shifting Fizeau interferometry by using a quarter waveplate with high flatness as a reference, (2) to present a comparative study between the phase-shifting algorithm and the off-axis geometry in surface microtopography measurement, and (3) to show the advantages of using the proposed common path Fizeau interferometry over the quasi-common path Michelson interferometry in terms of accuracy in measurement. The compelling advantage of the proposed parallel phase-shifting Fizeau interferometric technique is the long-term stability that leads to measuring objects with a high degree of accuracy.     

Three-dimensional shape measurement beyond the diffraction limit of lens using speckle interferometry

Speckle interferometry is generally known as a method for measuring the deformation of an object with rough surfaces. In this paper, a three-dimensional (3D) shape measurement method is proposed for superfine structures beyond the diffraction limit using the basic property of speckle interferometry. Since the differential coefficient distribution of the shape of such an object can be detected in speckle interferometry by imparting a known lateral shift to the measured object, the shape can be reconstructed by integrating the differential coefficient distribution. Based on experimental results obtained using diffraction gratings as measured objects, it is confirmed that the proposed method can measure 3D shapes that are beyond the diffraction limit of the lens.     

Dual-hologram shearing interferometry with regulated sensitivity

A novel optical diagnostic technique, namely, dual-hologram shearing interferometry with regulated sensitivity, is proposed for visualization and measuring of the density gradients of compressible flows in wind tunnels. It is superior to conventional shearing interferometry in both accuracy and sensitivity. The method is especially useful for strong turbulent or unsteady regions of the flows, including shock flows. The interferometer has proved to be insensitive to mechanical vibrations and has allowed us to record holograms during the noisy wind-tunnel run. The proposed approach is demonstrated by application to a supersonic flow over spherically blunted and sharp nose-cone-cylinder models. We believe that the technique will become an effective tool for receiving optical data in many flow facilities.     

Fourier‐series‐based virtual fields method combining with moiré interferometry for characterising elastic modulus distribution of laser repaired GH4169

Laser cladding is an effective technology for repairing damaged components with high efficiency and low cost. Characterisation for the mechanical properties of the repaired structure is of great importance to evaluate its reliability. In this study, the mechanical properties of laser repaired GH4169 are investigated by Fourier‐series‐based virtual fields method and moiré interferometry. The elastic modulus distribution of the whole structure is identified to understand the mechanical performance of the repaired zone and base material. A uniaxial tensile test is performed and the full‐field deformation is measured by moiré interferometry. With the measured strain field, the distribution of modulus in repaired structures can be calculated. In addition, simulation experiments of moiré interferometry are conducted to optimise the parameters of Fourier‐series‐based virtual fields method to improve the accuracy of the proposed method. On the basis of these results, experiments on the repaired GH4169 material are performed and the variation of modulus in the whole structure is identified. The results verify that the proposed method is effective for characterising modulus distribution of the laser repaired structures, and will have a good prospect for further application.     

Calibration method for high-accuracy measurement of long focal length with Talbot interferometry

In this paper, a new calibration method for accurate long focal-length measurements, based on Talbot interferometry, is presented. Error analysis is derived in detail by the numerical method, and an effective way to improve the accuracy is proposed. By this method, the systematic errors that are the main factors effecting accuracy are calibrated and reduced. Both simulation and experiments have been carried out to prove the effectiveness and advantages of the proposed method as compared to conventional approaches. The experimental results reveal that the relative error is lower than 0.02%, and the repeatability is better than 0.05%. This method is especially useful for measuring long focal-length lenses.     

Retrieving ESPI Map of Discontinuous Objects via a Novel Phase Unwrapping Algorithm

Abstract:  This work presents an effective scheme for the phase unwrapping of electronic speckle pattern interferometry (ESPI) map of discontinuous objects. ESPI is a highly effective measurement approach for industry and academia. However, due to the speckle noise, its unwrapping job is quite difficult, especially, when treating ESPI maps obtained from the deformation field of an object containing height discontinuities. The minimum L^p norm method developed by Ghiglia and Romero can treat the aforementioned problem with acceptable accuracy, but takes a long time to run. Therefore, this study presents a novel method based on a hybrid of the regional algorithm proposed by Gierloff, the branch cut method presented by Goldstein et al . and the (spatially) parallel unwrapping method with region-referenced algorithm developed by Huang and He. The proposed algorithm can retrieve ESPI maps with height discontinuities within acceptable accuracy and effectiveness.     

高加速度超精密激光外差干涉测量模型

为了精确地描述激光外差干涉在高加速度超精密测量中加速度对位移测量精度的影响机理与规律,建立了高加速度超精密激光外差干涉位移测量模型.通过分析测量棱镜三维运动对多普勒频移的影响,推导出高加速度激光外差干涉位移测量模型.理论分析和仿真实验表明,当测量加速度为9m/s2,匀加速运行的位移为500mm时,由于加速度变化引起的相对论性效应对测量精度的影响为5nm.高加速度超精密激光外差干涉位移测量模型的建立,可提高激光外差干涉在高加速度超精密测量中的测量精度,为激光外差干涉在高速和超高速测量领域的应用提供了理论依据.     

利用空域采样相移干涉计量法测量微小位移

提出了一种利用空域采样实现相移干涉计量的新方法和实验演示装置。演示装置使用倾斜镜或阶梯镜作为相移器件,线阵CCD做为光学传感器。实验表明:此方法非常适用于测量快速变化的目标或动态过程,其测量精度与传统时域采样相移技术相当但具有更好的稳定性和更高的测量速度,而测量范围是离焦量的2倍。     

Complete fringe order determination in scanning white-light interferometry using a Fourier-based technique

White-light interferometry uses a white-light source with a short coherent length that provides a narrowly localized interferogram that is used to measure three-dimensional surface profiles with possible large step heights without 2π-ambiguity. Combining coherence and phase information improves the vertical resolution. But, inconsistencies between phase and coherence occur at highly curved surfaces such as spherical and tilted surfaces, and these inconsistencies often cause what are termed ghost steps in the measurement result. In this paper, we describe a modified version of white-light interferometry for eliminating these ghost steps and improving the accuracy of white-light interferometry. Our proposed technique is verified by measuring several test samples.     

全视场外差白光干涉测量技术

为了解决传统白光干涉测量技术中对线性位移机构的位移精度要求过高的问题,本文提出了一种全视场外差白光干涉测量技术。该技术主要通过使用存在差频的白光干涉信号作为光源来实现在大扫描步长和低扫描精度条件下相干峰位置的高精度检测。本文首先建立了白光外差干涉的数学模型,再根据数学模型提供的光强信号特性提出了整体系统设计方案,然后对测量方案的可行性进行了实验验证。最后针对多种误差对算法计算精度的影响进行了理论分析和数据对比。误差分析的结果表明:白光外差干涉测量技术提供更高的测量精度和更好的抗干扰性能,有效地降低了传统白光干涉测量对线性位移机构精度的严苛依赖,为光学自由曲面检测技术提供了更多的可选解决方案。     

Nanometer measurement with a dual fabry-perot interferometer

On the basis of analyzing sinusoidal phase-modulating Fabry-Perot interferometry, a method, believed to be novel, is proposed for achieving nanometer measurement accuracy by measuring the time interval between equal amplitudes of the two elementary frequency signals of the transmitted intensities of a dual Fabry-Perot interferometer. A nanometer measurement system based on the method was designed and tested. The experimental results show that the displacement resolution of the system is 0.32 nm at a 1-kHz modulating signal.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

偏振干涉相位细分的误差分析与补偿

高分辨率、高精确度的偏振干涉测长方法在几何量测量中得到了广泛的应用。本文应用严格的数学方法分析了它的测量误差，并提出补偿与消减该项误差的方法。     

Interframe intensity correlation matrix for self-calibration in phase-shifting interferometry

A new method of estimating reference phase shifts in phase-shifting interferometry is proposed. The reference phase shifts are determined from a matrix that represents the interframe intensity correlation (IIC) of phase-shifted interferograms. The root-mean-square error of intensity measurement is automatically obtained from the smallest eigenvalue of the IIC matrix. The proposed method requires only four interferograms, unlike others, and can extract phase shifts reliably even from interferograms without well-defined fringes, such as speckle patterns. In typical conditions, reference phase shifts and wave-front phases can be determined with an accuracy of lambda/6310 and lambda/150, respectively. The validity of the method is tested by comparing it with other methods in experiments and simulations.     

回转运动坐标定位精度的检测与误差补偿模型

在对回转运动坐标定位精度的干涉测量原理和方法进行深入研究的基础上,采用激光干涉法检测混联机床C轴的定位精度和重复定位精度,并做出了基于测量数据的混联机床C轴单向均位偏差特性曲线,推导出了C轴顺、逆时针旋转定位误差数学模型。利用最小二乘法拟合得到了机床回转运动坐标目标位置的均值误差补偿数学模型,提出了一种回转运动坐标定位精度的激光干涉测量方法和误差补偿模型的建模方法。     

测量薄膜折射率的光栅衍射干涉方法

根据光的干涉理论,讨论了条纹周期数对测量薄膜折射率不确定性的影响,推导出干涉条纹错位量与薄膜折射率和厚度的关系式。由此提出采用光栅衍射干涉测量薄膜折射率的方法和实验方案。实验表明:该方法的干涉条纹测量精度达λ/10~λ/20,薄膜折射率测量精度可达 0.01 以上。     

A review of recent work in sub-nanometre displacement measurement using optical and X-ray interferometry

This paper reviews recent work in the field of displacement measurement using optical and X-ray interferometry at the sub-nanometre level of accuracy. The major sources of uncertainty in optical interferometry are discussed and a selection of recent designs of ultra-precise, optical-interferometer-based, displacement measuring transducers presented. The use of X-ray interferometry and its combination with optical interferometry is discussed.     

Speckle interferometry by using virtual speckle pattern based on Carré algorithm

Dynamic deformation measurement with a large deformation is effectively performed by using virtual speckle patterns. The virtual speckle pattern has been generally produced by using the operation based on Fourier transform. However, it takes a long calculating time to produce a virtual speckle pattern, because the method requires Fourier transform operation at each pixel of CCD. In the proposed method, virtual speckle patterns are produced by Carré algorithm without any operation by Fourier transform. The method is applied to the in-plane deformation measurement in this paper. As the results, it is confirmed that the calculating cost of virtual speckle patterns is improved remarkably, and that the measurement accuracy of the new method is also equal to the ordinary methods. It is also confirmed that the proposed method will expand the use of the speckle interferometry based on virtual speckle pattern technology.     

Wavenumber scanning-based Fourier transform white-light interferometry

Fourier transform white-light interferometry recovers the optical path difference of an interferometer by measuring the phase change caused by scanning wavelength. However, the optical spectrum, obtained by wavelength scanning method (λ-method), contains a chirp in period. The chirp would induce deviation and decrease the measurement accuracy. An improved method, the wavenumber scanning method (k-method), is proposed and experimentally demonstrated, in which there is no chirp in the optical spectrum. The measurement results using the k-method and the λ-method are compared experimentally. The experimental results show that the standard deviation of the measurement results decreases from 0.015 to 0.004?μm, when an extrinsic Fabry-Perot interferometer with a cavity length of 387?μm is interrogated.