Discontinuous surface measurement by wavelength-tuning interferometry with the excess fraction method correcting scanning nonlinearity

Wavelength-tuning interferometry can measure surface shapes with discontinuous steps using a unit of synthetic wavelength that is usually larger than the step height. However, measurement resolution decreases for large step heights since the synthetic wavelength becomes much larger than the source wavelength. The excess fraction method with a piezoelectric transducer phase shifting is applied to two-dimensional surface shape measurements. Systematic errors caused by nonlinearity in source frequency scanning are fully corrected by a correlation analysis between the observed and calculated interference fringes. Experiment results demonstrate that the determination of absolute interference order gives the profile of a surface with a step height of 1?mm with an accuracy of 12?nm.     

Measurement of the spatial coherence of light influenced by turbulence

To evaluate the Earth's surface with a sensor on a satellite, it is important for one to use a correction factor such as atmospheric turbulence. The spatial coherence of light influenced by turbulence was measured in the laboratory by use of a simulator equipped with a multiple reflection system. The turbulence was generated by changing the ambient temperatures from 32 to 48 degrees C. It was found that the spatial coherence of light that passed through the turbulent region decreased when the temperature increased. Double-slit interference fringes were analyzed by a photographic method. The visibility of the interference fringes is the degree of coherence.     

Effect of wavefront corrugations on fringe motion in an astronomical interferometer with spatial filters

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is < or = 30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is < or = 30%.     

Temporal coherence requirement in a symmetric-path grating interferometer

The depth of fringes is obtained for a polychromatic point source at an arbitrary incidence angle. The path difference, calculated by ray tracing, at the plane where the interference fringes vanish indicates that the temporal coherence length is the same as that in other interferometers. It is also found that the equivalent path difference, introduced by relative phase modulation on two interfering rays by two gratings, is as important as the actual path-length difference but in the opposite sign.     

Multiple-reflection effects in photoelastic stress analysis

The interpretation of fringes observed in photoelastic stress measurements made with coherent well-collimated optical radiation such as a laser beam and slab specimens with parallel surfaces is affected by multiple internal reflections of light within the sample, which are usually negligible when incoherent light is used. An analysis of the multiple-reflection effects in photoelastic measurements involving the plane polariscope configuration is presented. The results show that the isochromatic fringes are modified by the interference of multiply reflected waves. The multipass differential phase accumulations that display oscillatory magnitudes as functions of the model thickness and the optical wavelength result in a shifted and altered intensity profile across the isochromatic fringes. It is shown that for large values of reflectivity, as in the case of samples with reflective coating or partial mirrors, the bright fringes split into multiple peaks.     

Multiple reflections in a wide-angle Michelson interferometer

The effect of multiple reflections from a semireflecting surface such as an interference filter located in front of or behind a wide-angle Michelson interferometer (WAMI) is examined. By considering the instrument as a complex operator on the incident electric field, theoretical results are obtained which describe a large variety of configurations. Experimental results are presented which are consistent with these results. It is concluded that since the presence of these reflections changes the form of the observed fringes and affects measurements of the phase and visibility of the fringes, care must be taken to avoid such reflections in designing WAMIs.     

Generation of carrier fringes in holography and shearography

Double-exposure holography and double-exposure shearography are often used together with the carrier fringe technique, which requires additional shifting of the light source in a prescribed manner between exposures. In the holographic carrier fringe technique, difficulty in prescribing a suitable movement of the light source may be alleviated through visualization of the moiré fringes that are reconstructed by slight displacement of two overlaid families of ellipsoids in a holodiagram. Because shearography is the first differential of holography, it is often impractical to perform two successive optical differentiations on the ellipsoids to visualize the shearographic carrier fringes. A simple method of discerning holographic and shearographic carrier fringes is described. The method is based on the hyperboloids in a holodiagram that represent Young's (interference) fringes produced by the interference of two point sources. The hyperboloids are analogous to holographic carrier fringes, whereas the moiré patterns reconstructed from two overlaid hyperboloids are analogous to shearographic carrier fringes. Use of this method for explaining the formation of deformation fringes in plate bending, as well as the effect of light-source movement on the deformation fringes, is also illustrated.     

The Source Width and Its Influence on Interference Phenomena in a Fresnel Electron Bi-prism

Expressions for the dependence of interference fringes contrast in a Fresnel electron bi-prism on source width or virtual sources distance are stated in the first part of the paper. For given working conditions the influence of the virtual sources distance on interference fringes contrast at different source widths is given. First disappearance of the contrast at a constant source width is experimentally verified.     

Development of a phase-displacement equation for panoramic interferometry

We developed the parametric equations that are needed to quantify the modulations in the sensitivity vector that occur when the phase-displacement equation is applied to make panoramic interferometric measurements. The measurement system relies on two collinear panoramic annular lenses, one to illuminate and the other to image their surroundings. When a coherent light source is used and a reference beam is added, interference occurs over the region of interest defined by the illuminating and viewing lenses. A holographic system is used to demonstrate the approach and quantify the analysis. We obtained interference fringes in real time by comparing holograms recorded before and after a section of cylindrical pipe is displaced relative to the measurement system. The annular images and the holographic fringes are acquired and stored digitally in a computer system, and image transformation algorithms are applied to remove optical distortions in the holographic patterns. Excellent agreement is obtained when the fringe loci are compared with those predicted on the basis of theory.     

Self-referenced interferometry for the characterization of axicon lens quality

A simple interferometer for the characterization of axicon lenses is presented. The phase cone acquired by a wave propagating through an axicon, when interfered with a collinear reference wave, produces a nearly cylindrically symmetric self-referenced interference pattern from which the distortions of the axicon surface may be readily obtained. Comparison with two-dimensional off-axis interferometry is used to validate the self-referenced technique. The measurements are based on retrieval of the accrued spatial phase distribution from interference fringes with on- and off-axis reference beams and are found to be equivalent. We use the ellipticity of the phase maps to qualify axicon lenses, which are expected to exhibit radial symmetry and engage the self-referential capability of the on-axis method to derive deviation maps that characterize the surface quality of the axicons.     

A New Method of Processing Mach–Zehnder Interference Fringe Data in Determination of Diffusion Coefficient

Laser holographic interferometry is the newest method to measure the mass diffusion coefficient and has been widely used in recent years. The processing of interference fringe images is a critical step of getting the final precise experimental results. On the basis of Fourier transformation and phase measurements, a new method of processing Mach–Zehnder interference fringes is introduced in this article. By experimental verification and uncertainty analysis, the accuracy of this method is validated. Mass diffusion coefficients of ethylene glycol dimethyl ether and diethylene glycol dimethyl ether, two new fuel additives in air were measured with the method introduced in this study.     

角位移Fabry-Perot干涉测量

提出了一种基于Fabry-Perot板干涉的角位移测量新方法。此方法采用函数近似,只需将初始入射角确定在40°到50°之间,即可由角位移与干涉信号条纹数变化间的函数关系,高精度测量角位移。解决了采用F-P板干涉法测量角位移需精确确定入射光初始角的问题。使用计算机处理采集的干涉信号,对干涉条纹进行细分,实现干涉信号相位测量的高分辨力。理论模拟和实验结果得出本方法可以实现精度为10-5rad数量级的角位移测量。该方法的测量装置采用带尾纤的半导体激光作为光源,由自聚焦透镜准直,出射光束直径为0.5mm,使探测头为小光斑。该装置结构简单,能实现小型化。     

Spectral interference Mirau microscope with an acousto-optic tunable filter for three-dimensional surface profilometry

A nonmechanical scanning Mirau-type spectral interference microscope has been developed for the measurement of three-dimensional surface profiles of discontinuous objects. An acousto-optic tunable filter (AOTF) is used as a high-resolution spectral filter, which scans the optical frequency of the broadband light emitted from a superluminescent diode. To generate spectral fringes that make full use of the limited coherence length of the filtered light we unbalanced the Mirau interferometric system by positioning the reference mirror nearly halfway between the top and the bottom of the step height. When the frequency of the broadband light source is scanned by an AOTF, the interference fringes move in opposite directions on the top and the bottom of the object. To uniquely determine the sign of the fringe movement over the large area of the object, we developed a three-dimensional Fourier-transform technique, and from the detected sign of the fringe movement and phase information, we determined the three-dimensional step height. Experimental results of the measurement of 100-microm step height are presented. The main advantages of the proposed system are that it provides nonmechanical scanning and a large measurement range without ambiguity in the sign of the phase.     

Laser-Doppler velocity profile sensor with submicrometer spatial resolution that employs fiber optics and a diffractive lens

We report a novel laser-Doppler velocity profile sensor for microfluidic and nanofluidic applications and turbulence research. The sensors design is based on wavelength-division multiplexing. The high dispersion of a diffractive lens is used to generate a measurement volume with convergent and divergent interference fringes by means of two laser wavelengths. Evaluation of the scattered light from tracers allows velocity gradients to be measured in flows with submicrometer spatial resolution inside a measurement volume of 700-microm length. Using diffraction optics and fiber optics, we achieved a miniaturized and robust velocity profile sensor for highly resolved velocity measurements.     

SAW velocity measurement of crystals and thin films by the phasevelocity scanning of interference fringes

We present principle and application of a novel noncontact velocity measurement of surface acoustic waves (SAW) on crystals and thin films using laser interference fringes scanned at the phase velocity of SAW. The scanning interference fringes (SIF) are produced by intersecting two laser beams with a frequency difference. The SAW velocity within the laser beam spot is measured as the ratio of observed SAW frequency and predetermined wave number of the SIF. The frequency measurement can be quite precise because of a large number of generated SAW carriers and amplitude enhancement effect. The SAW velocity measurement is free from the water loading effect accompanying the leaky SAW measurements. This principle was successfully applied to evaluate Si ₃N₄ and SiO₂ films deposited on Si (001) surface     

High-speed measurement of three-dimensional surface profiles up to 10 μm using two-wavelength phase-shifting interferometry utilizing an injection locking technique

High-speed two-wavelength phase-shifting interferometry is presented. The technique is aimed at high-speed in-line inspection of spacers in liquid crystal display panels or wafer bumps where the measuring range is well determined and high-speed measurements are essential. With our test setup, the measuring range is extended to 10 μm by using two injection locked frequency scanning lasers that offer fast and equidistant phase shifting of interference fringes. A technique to determine the unwrapped phase map in a frequency scanning phase-shifting interferometry without the ordinary phase-unwrapping process is proposed.     

Lensacon

A diffractive optical element has been synthesized with laser phototechnology. It can transform a point source into a bright caustic (a light line) stretched along the optical axis. The element transforms a spherical wave into a conic and a point source in the object space to a ring structure in the image space. We investigated how the parameters of the light line (the length and the effective diameter) depend on the wavelength of the light source and the movement of the source along the optical axis. Also the interference field outside the caustic (Fresnel and Poisson fringes) was investigated. For an explanation of experimental data the geometrical theory of interferometers was used. The conditions for the appearance of fringes in white light are given. A device for rectilinear control of large tool beds and for centering machine components was manufactured. Experiments on determining the macroshape and the microshape of objects were performed.     

用散斑干涉光谱分布检测瞬态温度

为了提高对瞬态温度检测的灵敏度,提出了基于散斑干涉条纹光谱分析的瞬态温度反演算法.系统利用散斑干涉形成干涉条纹,由于瞬态温度的变化会使材料应变,从而使散斑干涉条纹改变.被测表面形变前后获得的干涉条纹由面阵 CCD 采集,其对应的光谱密度分布函数也会发生相应的改变,即由散斑干涉条纹反演得到的中心波长振幅发生改变.通过对两次中心波长幅值的比值的检测和计算,即可获得被测的瞬态温度.在分析计算了瞬态温度变化与材料应变、材料应变与干涉条纹变化的函数关系的基础上,推导了瞬态温度变化与干涉条纹振幅及相位函数关系.实验采用660 nm 半导体激光器,SI6600型面阵 CCD 探测器,从获得的光谱分布函数中提取中心波长处幅值比值,通过计算和标定,最终温度检测精度可达到±2℃.相比传统的直接检测干涉条纹的变化量,由被测面形变量推导温度的方法精度提高了近一个数量级,其精度更高、检测均匀性更好、稳定性更好.     

Dual-channel heterodyne measurements of atmospheric phase fluctuations

A dual-channel fiber-coupled laser heterodyne system operating at a 1.55-microm wavelength is used to investigate phase fluctuations induced on a laser beam by propagation through turbulent air. Two receivers are used to characterize spatial and temporal variations produced by a turbulent layer of air in the laboratory. The system is also used for measurements through extended turbulence along an 80-m outdoor atmospheric path. Phase structure functions, power spectral densities, and cross correlations are presented.