Residual stress release characteristics of hole-drilling determined by in-plane three-directional optical interference moiré

By adopting a new stress calibration method, a grating rosette moiré interferometry and incremental hole-drilling combined system is developed to determine the magnitud of the residual stress in aluminium plate subjected to a uniform uniaxial tensile load. Performing in-plane three-directional fringe analysis, the optical data contained in the moiré interferograms are converted into values of the strains in three directions corresponding to the grating rosette. The evaluation is carried out through the measurement of the in-plane displacement field in three directions generated by the introduction of the small incremental hole. The in-plane three-directional displacement fields are determined from the calculation of the optical in-plane three-directional phase distribution by means of a phase-shifting method. A new finite element calibration analysis that is general axisymmetric elements instead of 3-D block element and harmonic axisymmetric element is adopted to relate the relieved displacement field to the magnitude of the residual stress. The magnitude of the principal stresses is finally evaluated through a least-squares calculation and is also compared with the stress value applied to the specimen measured with strain gauges.     

Straightness measurements by use of a reflection confocal optical system

Straightness measurement is a very important technique in the field of mechanical engineering. A particular application for straightness measurement is high-accuracy machining on a diamond-turning lathe. We propose a novel, to our knowledge, optical method for measuring the straightness of motion, and its mathematical analysis is outlined. The technique is based on measurement of the lateral displacement of point images by use of reflection confocal optical systems. The advantages of this method are that (i) the lateral displacements in the direction of the two axes perpendicular to the optical axis can be measured, (ii) the rotation angles around all three axes can be measured, and (iii) reflection optical systems are more compact in length than are transmission optical systems.     

Phase object data obtained from defocused laser speckle displacement

An optical technique that is based on defocused digital speckle photography is proposed for the evaluation of phase objects. Phase objects are different kinds of transparent or semi-transparent media that allow light to be transmitted. A phase object inserted in a laser speckle field introduces speckle displacement, from which information about the object may be extracted. It is shown that one may use speckle displacements to determine both the phase gradients and the positions of phase objects. As an illustration the positions and focal lengths of two weak lenses have been derived from defocused laser speckle displacement.     

Measurement of longitudinal displacement using lateral shearing cyclic path optical configuration setup and phase shifting interferometry

We present a technique for the measurement of longitudinal displacement using a lateral shearing cyclic path optical configuration (CPOC) setup and phase shifting interferometry. In the technique, a plane mirror mounted on a linear translation stage, placed slightly away from the focal plane of a lens, introduces a longitudinal focal shift to the incident focusing beam. The resulting spherical wavefront emerging from the lens is sheared into two orthogonally polarized beams using the CPOC setup. By applying polarization phase shifting interferometry (PPSI), the longitudinal focal shift of the beam focus is calculated by determining the slope of the optical path difference variation between the sheared beams. Similarly, the additional focal shift introduced due to longitudinal translation of the mirror, by an unknown amount, is determined using PPSI. Half of the difference between the two longitudinal focal shifts measured gives the longitudinal displacement of the mirror. The technique can be used for an extended range of distance measurement. The novelty of the technique is the introduction of CPOC for the distance measurement. The advantages of the technique compared to other related methods are discussed.     

Three-dimensional phase imaging with a scanning optical-fiber interferometer

We describe a quantitative method for measuring the phase of a propagating wave field in three dimensions by use of a scanning optical-fiber interferometer. Because phase modulation in the reference arm is exploited, this technique is insensitive to large variations in the intensity of the field being studied and is therefore highly suitable for measurement of phase within spatially confined optical beams. It uses only a single detector and is not reliant on lock-in electronics. The technique is applied to the measurement of the near field of a cleaved optical fiber and is shown to produce results in good agreement with theory.     

光纤位移干涉仪测高速漫反射面速度误差分析

首次从理论上分析基于单模光纤的位移干涉仪用于高速漫反射面速度测量的相位误差,包括来源和大小及其与系统各参量的关系.计算了光束从光纤出射,经漫反射面反射,再耦合进单模光纤的光场表达式.结果表明,相位误差的来源包括两部分:光束传输衍射效应及漫反射面表面的随机相位特性.由相位误差引起的位移和速度相对误差都在10-6量级,并且同时采用VISAR和光纤位移干涉仪来测量爆轰加载下铜飞片的速度轨迹.实验结果表明,单模光纤位移干涉仪的实际测量精度可以和VISAR相当,证明了单模光纤位移干涉仪用于高速漫反射面速度测量的可行性.     

Local strain in a 3D nano-crystal revealed by 2D coherent X-ray diffraction imaging

The coherent X-ray diffraction from an isolated strained nano-crystal is given by the Fourier transform of a complex-valued electron density where the modulus and phase are linked to the physical electron density and the displacement field, respectively. The possibility to reconstruct a complex-valued object from a coherent diffraction pattern is demonstrated using iterative algorithms. In the case of a 2D intensity slice, the reconstructed 2D object is strongly dependent on the distribution function of the displacement field values along the direction perpendicular to the observation plane. It is shown that valuable 3D information can, however, still be extracted. This work is of particular interest as soon as the complete 3D measurement is not accessible.     

Optical phase contrast measurement of ultrasonic fields

This report describes an optical phase contrast imaging technique for the measurement of wide bandwidth ultrasound fields in water. In this method, a collimated optical wavefront (λ_l = 810 nm) impinges on a wide bandwidth ultrasound pulse. The method requires that refractive index perturbations induced by the ultrasound field be sufficiently small. Specifically, on exit from the acoustic field, the phase of the optical wavefront must be proportional to the ray sum of local density taken in the direction of propagation of the incident optical wave. A similar restriction is placed on the dimensions of the ultrasound pulse. Repeated measurement of this phase as the ultrasound field is rotated through 180° about an axis normal to the direction of propagation of the incident optical wave generates the Radon transform of the ultrasonically induced refractive index perturbation. Standard tomographic reconstruction techniques are used to reconstruct the full three-dimensional refractive index perturbation. A simple two-lens imaging system and an optical signal processing element from phase contrast microscopy provide a method of directly measuring an affine function of the desired optical phase for small optical phase shifts. The piezo- and elasto-optic coefficients (the first partial derivatives of refractive index with respect to density and pressure) relate refractive index to density and pressure via a linear model. The optical measurement method described in this paper provides a direct, quantitative measurement of the piezo- and elasto-optic coefficients (from the density or pressure fields)     

Polarization mode dispersion measurement based on continuous polarization modulation

A novel technique is proposed for measurement of the group delay (GD) and the differential group delay (DGD) of optical material, components, and fiber. This new method is based on continuous polarization modulation of the stimulus optical field as opposed to sequential polarization state switching used in the traditional phase shift method. A new complete derivation of the phase shift method, based on the modified Jones calculus of elementary matrices, is presented. The derivation reveals that the phase shift measurement actually depends on all eight elementary parameters that represent DGD and optical frequency derivatives of polarization-dependent loss (PDL). Thus, the new expression for the phase shift includes the combined effect of PDL and DGD. The proposed method is evaluated by measuring a section of polarization-maintaining fiber and a 50 km length of single-mode fiber over a wavelength range from 1530 to 1610 nm. Measurements of DGD in a long single-mode fiber are shown to be highly insensitive to environmentally induced GD drift.     

Time-resolved vibration measurement with temporal speckle pattern interferometry

Temporal speckle pattern interferometry (TSPI) is an optical measurement procedurefor measuring the displacement of rough technical surfaces. The time-dependent speckle modulation due to optical path difference changes is tracked during the whole displacement of the surface and then evaluated pointwise without referring to neighboring pixels. This feature allows for its use as independent point sensors. This aspect of incremental phase tracking enables TSPI to be used to measure time-resolved mechanical vibrations. It also reduces the deteriorating effect of the decorrelation. Therefore large displacements can be measured. A concept for an inexpensive fiber-optical point sensor was developed and the theoretical accuracy for vibration measurement was investigated. The TSPI measurement of a loudspeaker membrane is compared with a high-precision vibrometer measurement. The first results show good agreement.     

Phase object data obtained by pulsed TV holography and defocused laser speckle displacement

Transient events in optically transparent media occur in many engineering applications. Using pulsed TV holography to capture a laser speckle field propagated through an optical disturbance makes it possible to obtain both the position and the phase gradients of the disturbance. The technique depends on the fact that speckles transmitted through an optical disturbance will be displaced by an amount that depends on the relation of the defocus to the object. First the speckle field is captured holographically, without and with disturbance present. Then the recorded fields are numerically refocused in a computer to a number of different focal planes. With a cross-correlation technique a number of speckle displacement fields are obtained, and from them the data about the disturbance are obtained. So far the technique has been shown to work for thin objects.     

Large-scale optical-field measurements with geometric fibre constructs

Optical fields are measured using sequential arrangements of optical components such as lenses, filters, and beam splitters in conjunction with planar arrays of point detectors placed on a common axis. All such systems are constrained in terms of size, weight, durability and field of view. Here a new, geometric approach to optical-field measurements is presented that lifts some of the aforementioned limitations and, moreover, enables access to optical information on unprecedented length and volume scales. Tough polymeric photodetecting fibres drawn from a preform are woven into light-weight, low-optical-density, two- and three-dimensional constructs that measure the amplitude and phase of an electromagnetic field on very large areas. First, a three-dimensional spherical construct is used to measure the direction of illumination over 4pi steradians. Second, an intensity distribution is measured by a planar array using a tomographic algorithm. Finally, both the amplitude and phase of an optical wave front are acquired with a dual-plane construct. Hence, the problem of optical-field measurement is transformed from one involving the choice and placement of lenses and detector arrays to that of designing geometrical constructions of polymeric, light-sensitive fibres.     

High-resolution laser speckle correlation for displacement and strain measurement

A laser speckle correlator with high optical magnification is presented, and its performance in the measurement of strain is demonstrated experimentally. Two separated areas on a test specimen are illuminated with laser beams, and displacements of each area are measured by performance of laser speckle correlation on successive magnified images. The interplay of magnification, lens aperture, surface roughness, pixel spacing on the CCD array sensor, and the attainable precision of correlation are investigated theoretically and experimentally. Resolutions that are usually considered accessible only to interferometric techniques are achieved: displacement resolutions of less than 50 nm and strain measurements of less than 10 mustrain across distances of the order of 10 mm are demonstrated. At high magnification, speckle decorrelation due to out-of-plane displacement becomes a stringent restriction, and surface height correlation effects may limit speckle contrast and broaden speckle correlation peaks.     

Fresnel transform phase retrieval from magnitude

This report presents a generalized projection method for recovering the phase of a finite support, two-dimensional signal from knowledge of its magnitude in the spatial position and Fresnel transform domains. We establish the uniqueness of sampled monochromatic scalar field phase given Fresnel transform magnitude and finite region of support constraints for complex signals. We derive an optimally relaxed version of the algorithm resulting in a significant reduction in the number of iterations needed to obtain useful results. An advantage of using the Fresnel transform (as opposed to Fourier) for measurement is that the shift-invariance of the transform operator implies retention of object location information in the transformed image magnitude. As a practical application in the context of ultrasound beam measurement we discuss the determination of small optical phase shifts from near field optical intensity distributions. Experimental data are used to reconstruct the phase shape of an optical field immediately after propagating through a wide bandwidth ultrasonic pulse. The phase of each point on the optical wavefront is proportional to the ray sum of pressure through the ultrasound pulse (assuming low ultrasonic intensity). An entire pressure field was reconstructed in three dimensions and compared with a calibrated hydrophone measurement. The comparison is excellent, demonstrating that the phase retrieval is quantitative.     

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.     

线激光位移传感器像素当量标定方法

为了满足线激光位移传感器的应用测试需求,提出一种基于高度块的线激光位移传感器像素当量的现场标定方法。其中,高度方向上的像素当量利用台阶高度进行标定,以修正厂家设定的像素当量的线性误差;宽度方向上的像素当量则利用台阶块结合传感器的横向移动位移的计算方法得到。考虑到线激光位移传感器可能存在安装倾斜误差,利用台阶块宽度在不同位置的高度差对倾斜角进行了标定,并修正了由倾斜角引入的高度测量误差。经实验证明,本文提出的方法很好地解决了线激光位移传感器在多位置测量时轮廓不连续的问题。     

An overview and a contribution to the optical measurement of lineardisplacement

The present work is a contribution to the field of linear displacement measurements by optical means. For that purpose, a brief overview of some existing solutions is presented and two systems for axial linear displacement measurement based on light intensity detection are introduced. The systems have redundancy and were designed with the purpose of achieving identification and automatic correction of errors arising from inadvertent angular variations between the sensor and the light beam positions     

Improving the measurement performance for a self-mixing interferometry-based displacement sensing system

Approaches that are, to our knowledge, novel, are proposed in this paper to improve the accuracy performance of self-mixing interferometry (SMI) for displacement measurement. First, the characteristics associated with signals observed in SMI systems are studied, based on which a new procedure is proposed for achieving accurate estimation of the laser phase. The studies also revealed the reasons for the inherent errors associated with the existing SMI-based techniques for displacement measurement. Then, this paper presents a new method for estimating the optical feedback level factor (denoted by C) in real time. Combining the new algorithms for estimating the laser phase and updating C value, the paper finally presents a novel technique for displacement measurement with improved accuracy performance in contrast to existing techniques. The proposed technique is verified by both simulation and experimental data.     

Dispersion error in white-light linnik interferometers and its implications for evaluation procedures

White-light interferometry is a standard optical tool with which to measure profiles of discontinuous structures such as diffractive optical elements. But there is one outstanding technological problem: The interferometers have to be symmetric; i.e., the geometrical path lengths in glass have to be the same for both interferometer arms. If these paths in glass are not equal within the field of view, a dispersion error will occur that is rather complicated to compensate for. The error appears in the measured profile in the form of steps of lambda/2 in height. A simulation of interferograms disturbed by dispersion deviations is presented, and an algorithm is introduced that eliminates the steps without changing the actual phase information or averaging neighboring pixels. The results are shown with simulated and real data.     

Effect of compensation for spherical aberration on the transverse displacement of laser speckle patterns

When a rough surface illuminated by coherent light is displaced perpendicularly to the optical axis of an imaging optical system the speckle pattern in the conjugate plane is transversally displaced too. This displacement has two components. The first one is proportional to the object displacement, and the second one depends on wave-front aberrations and, consequently, is strongly related to the optical system that is used. Usually, well-corrected photographic objectives are used for the measurement of transverse displacements by double-exposure laser speckle photography. Since in well-corrected objectives aberrations tend to compensate one another, it seems that the complementary displacement of the speckle pattern, caused by aberrations, is near zero and does not affect the accuracy of the measurement. Here it is analytically shown that the compensation of spherical aberrations does not guarantee a negligible complementary displacement. From the results obtained it follows that well-corrected objectives for laser speckle photography can be regarded as a particular class of photographic objectives, since they not only yield high-quality images but also minimize complementary displacement.