Phase-measuring interferometry: new methods and error analysis

New methods that can be used to determine phase in phase-stepping interferometry are presented. It is shown that a combination of some of these methods can be used to reduce the error introduced by phase-stepper miscalibration and nonlinearity. Moreover these new algorithms can also be used to detect the presence of miscalibration or phase-shifter nonlinearity. A simplified approach to understanding the error introduced by miscalibration and nonlinearity of the phase stepper and its reduction in phase-shifting interferometry is also presented.     

Detecting Localized Plastic Strain by a Scanning Collinear Wave Mixing Method

When the frequencies of a pair of collinear shear and longitudinal waves satisfy the resonant condition, mixing of these two primary waves generates a third, resonant shear wave that propagates in the direction opposite to the propagating direction of the primary shear wave. In this study, experiments were conducted to demonstrate that the acoustic nonlinearity parameter at the location of the mixing zone can be obtained by measuring the resonant shear wave. Since the location of the mixing zone can be controlled by adjusting the trigger time of the transducers that generate the primary waves, this collinear wave mixing technique enables the scanning of a bar sample to measure the distribution of acoustic nonlinearity along the bar. To demonstrate this scanning capability, bar samples with non-uniform acoustic nonlinearity parameters were fabricated by inducing localized plastic deformation at known locations. Scanning collinear wave mixing tests conducted on such bar samples clearly identified the locations of the plastic zone. These results show that collinear wave mixing is a promising method for scanning the test sample to map out the distribution of localized plastic deformation.     

Resonant holographic interferometry with ZnTe:V:Mn

The photorefractive semiconductor ZnTe:V:Mn is investigated for use in real-time resonant holographic interferometry applications. Experimental results of two-wave and four-wave mixing with pulsed dye and cw diode lasers are presented; in addition holographic image transfer, as well as two-wavelength resonant holographic interferometry, are demonstrated. Species-specific interferograms of potassium seeded into various combustion environments are captured at video-frame rates. Calculations of the species measurement sensitivity and dynamic range are presented, and design considerations for resonant holographic interferometry systems employing photorefractive materials are outlined.     

光学倍频影响激光外差干涉测量精度的机理

为了同时提高激光外差干涉测量的分辨力和精度,必须深入分析光学倍频对激光外差干涉测量精度的影响机理。在此基础上,建立了光学倍频相位测量模型,从理论上证明,光学倍频能够实现对激光外差干涉信号的细分,提高测量分辨力。光学倍频改变非线性误差的相位而使非线性误差减小,但同时改变了激光干涉多普勒频移的v/c平方项,使得残余累计误差增大。仿真结果表明,光学N倍频使非线性误差减小到原来的1/N,但使残余累计误差增大N2倍。因此,光学倍频仅适用于低速测量的场合。     

Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems

Most homodyne interferometers have a quadrature detector system that includes two polarizing beam splitters that cause nonlinearity of the order of a few nanometers by phase mixing. Detectors should have the same gains to reduce nonlinearity under the assumption that there is no loss in optical components. However, optical components exhibit some loss. We show that nonlinearity can be reduced to an order of 0.01 nm when the detector gains are adjusted by simulation to include the optical characteristics. The compensated nonlinearity is 18 times smaller than that when the four detector gains are set to be equal.     

Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer

Wavelength-scanning interferometry permits the simultaneous measurement of variations in surface shape and optical thickness of a nearly parallel plate. Interference signals from both surfaces of the test plate can be separated in frequency space; however, these frequencies are shifted from the expected frequency by the refractive-index dispersion of the test plate and any nonlinearity that is due to wavelength scanning. Conventional Fourier analysis is sensitive to this detuning of the signal frequency and suffers from multiple-beam interference noise. We propose new wavelength-scanning algorithms that permit a large tolerance for dispersion of the test plate and nonlinearity of scanning. Two 19-sample algorithms that suppress multiple-interference noise up to the second order of the reflectance of the test plate are presented. Experimental results show that the variation in surface shape and optical thickness of a glass parallel plate of 250-mm diameter was measured with a resolution of 1-2 nm rms.     

Linearization and flattening technique for fringe analysis and its application to holographic interferometry

A simple technique for correcting the nonlinearity of a camera-digitizer system is presented. With this technique cameras that are extremely nonlinear but which enhance fringe contrast can be used. The technique can also reduce the number of phase-shifted interferograms required for quantitative analysis from three to two or (with some restrictions) to one. The last option is important for the interpretation of transient phenomena. The technique is demonstrated for the strain analysis of a pressure vessel by holographic interferometry (HI). The contribution to suitable noise elimination is also described.     

Dispersion compensation in stellar interferometry

In long-baseline stellar interferometry, spectrometers are used to disperse starlight for measuring visibility at multiple wavelengths and for fringe tracking with channeled spectra. However, neither prisms nor gratings are well suited to the observation of fringes with wide spectral bandwidths because the mapping from wave number to detector coordinate is nonlinear. The visibility-measurement and fringe-tracking performance are affected by nonlinearity and in many cases it is important to compensate for this. Longitudinal-dispersion correctors may be used to compensate for differential air paths in an interferometer, and we show that these may also be used to correct the nonlinear mapping of a spectrometer.     

Nonlinear Optical Properties of a Soluble Form of Polyisothionaphthene

Abstract

The third-order nonlinearity of a low-bandgap conjugated organic polymer has been assessed. Degenerate four-wave mixing experiments (at 1·064 μm using picosecond pulses from a passively mode-locked neodymium-doped yttrium aluminium garnet laser) on solutions of the polymer have permitted the determination of the microscopic third-order nonlinearity γ. The polymer exhibits unusual behaviour which is solution concentration dependent. This behaviour is thought to be due to aggregation effects and strongly suggests that the bulk response of the material is large, the third-order nonlinearity being of the order of ten times greater than that of polythiophene.     

外差干涉仪频率混叠误差分析

研究了激光外差干涉仪中存在的频率混叠现象、误差形成机理和变化规律,重点分析了在共光路外差干涉仪中由激光光源的椭圆偏振化和Ｗｏｌｌａｓｔｏｎ棱镜的安装方位角引起的频率混叠误差的大小及变化规律,对进一步提高共光路外差干涉测量精度具有现实意义。     

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.     

Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera

Recently, a new method to measure object shape and deformation with temporal evolution of speckles in speckle interferometry was reported. In this method, certain parameters, sensitive to shape or deformation are changed continuously, and the fluctuations in the irradiance of each speckle is recorded. The information over the whole object deformation is retrieved by Fourier-transformation techniques. We present a detailed theory and analyze the influence of decorrelation due to longitudinal and lateral size of the speckles. It is also shown that the method can be used to measure small deformations (less than 5 mum) with higher resolution. Further, the nonlinearity of the camera is shown to enhance the sensitivity.     

Predicting phase steps in phase-shifting interferometry in the presence of noise and harmonics

A novel method for estimating pixelwise phase step values in phase-shifting interferometry is presented. The method is based on the linear prediction property of the intensity fringes recorded temporally at a pixel on the charged-coupled device. The salient features of the method lie in their ability to handle linear miscalibration errors, to compensate for the presence of harmonics in an optical configuration and detector nonlinearity, and to allow for the use of arbitrary phase steps. The robustness of the proposed method is studied in the presence of noise and a comparison with several benchmarking algorithms is performed. The simulation results show the efficiency of the algorithm in retrieving the wrapped phase.     

Sandwich, double-reference-wave, holographic, phase-shift interferometry

Phase-shift interferometry has provided a straightforward method for converting interferograms to phase maps. Unfortunately, some of the most powerful pulsed holographic interferometry techniquesare generally not compatible with phase-shift interferometry. One solution is to employ two reference waves, one for each of the two object waves to be interfered, that can be phase stepped during reconstruction. Practical aberration and alignment problems render this approach difficult. A simple method that employs a second hologram, sandwiched with the first, which produces the required two reference waves during reconstruction, is presented. The process compensates for both chromatic and geometric aberrations that otherwise render the phase-shift method unusable.     

White-light interferometry using a channeled spectrum. I. General models and fringe estimation algorithms

Astrometric measurements using stellar interferometry rely on the precise measurement of the central white-light fringe to accurately obtain the optical path-length difference of incoming starlight to the two arms of the interferometer. Because of dispersion in the optical system the optical path-length difference is a function of the wavelength of the light and extracting the proper astrometric signatures requires accommodating these effects. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the path-length delay. Because of throughput considerations these channels are made sufficiently broad so that monochromatic models are inadequate for retrieving the phase/delay information. The presence of dispersion makes the polychromatic modeling problem for phase estimation even more difficult because of its effect on the complex visibility function. We introduce a class of models that rely on just a few spectral and dispersion parameters. A phase-shifting interferometry algorithm is derived that exploits the model structure. Numerical examples are given to illustrate the robustness and precision of the approach.     

Comparison of strain gage and interferometric detection for measurement and control of piezoelectric actuators

The capability of controllable and repeatable positioning in the subnanometer range is fundamental not only for scanning probe microscope applications, but also for nanotechnology in general. Up to now, piezoceramic actuators have been used for this purpose. However, these actuators are far from being ideal transducers. For precise metrological applications, as well as for general use in scanning probe microscopy, some method has to be implemented to correct creep and nonlinearity of piezoceramic materials. In the present study, two different position measuring systems have been implemented—one based on strain gage detection and the other on interferometry. The corresponding results are presented and the performance of both setups compared.     

四步相移数字全息干涉术相移提取和物光重建

提出广义相移干涉术中结合广义四步公式改进最小二乘法抽取任意相移进而重建复波的方法.利用广义相移数字全息算法的物波重建公式替代传统最小二乘法来提取参考光相位和重建物体波前,大幅减小迭代循环的计算量.使用该方法,每一次迭代计算参考相位只需要一个最小二乘法,同时利用物波前重建公式计算物光相位.这种方法的可行性和有效性已被计算...     

近表面疲劳裂纹的水浸式非共线横波混频检测方法研究

针对近表面疲劳裂纹检测问题,开展了水浸式非共线横波混频检测方法研究。在材料非线性、水/试件界面和疲劳裂纹不同非线性源情况下,分析相互作用角和频率比对混频非线性效应的影响规律。在此基础上,对有无近表面疲劳裂纹试件沿着深度方向进行扫查检测。结果表明,在不同非线性源情况下,混频特征图具有显著差异,根据混频特征图中和频纵波峰值及其对应相互作用角可对试件近表面疲劳裂纹进行检测;水/试件界面对近表面疲劳裂纹非共线横波混频检测具有一定影响,去参考检测方法可显著降低水/试件界面的影响,实现对近表面疲劳裂纹的有效检测。     

Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry

Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.     

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.