Multiplicative electronic speckle-pattern interferometry fringes

A theoretical analysis of fringe patterns and its experimental corroboration obtained by multiplication of two speckled images with electronic speckle-pattern interferometry (ESPI) are reported. A specifically designed digital filter is used to enhance the contrast and visibility of the inherently noisy multiplication fringes. Phase retrieval is achieved by a phase-stepping technique. Experimental results are presented for the in-plane-sensitive optical ESPI setup; however, out-of-plane and shearing setups may be used as well. The method represents an alternative to the subtraction and addition techniques in ESPI.     

Heterodyne temporal speckle-pattern interferometry

In temporal speckle-pattern interferometry deformation information is extracted by a Fourier transform technique from the speckle pattern that is recorded over a period of time as the object is deformed. A limitation of the experimental arrangements reported to date is that the direction of the deformation cannot be determined. We propose removing this limitation by using the heterodyne principle. Some experimental results that were obtained by use of a rotating half-wave-plate frequency shifter are presented.     

Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry

We describe an electronic speckle-pattern interferometry system for analyzing addition fringes generated by the transient deformation of a test object. The system is based on a frequency-doubled twin Nd:YAG laser emitting dual pulses at a TV camera field rate (50 Hz). The main advance has been the automatic, quantitative analysis of dual-pulse addition electronic speckle-pattern interferometry data by the introduction of carrier fringes and the application of Fourier methods. The carrier fringes are introduced between dual pulses by a rotating mirror that tilts the reference beam. The resulting deformation-modulated addition fringes are enhanced with a deviation filter, giving fringe visibility close to that of subtraction fringes. The phase distribution is evaluated with a Fourier-transform method with bandpass filtering. From the wrapped phase distribution, a continuous phase map is reconstructed with an iterative weighted least-squares unwrapper. Preliminary results for a thin plate excited by an acoustic shock show the suitability of the system for the quantitative evaluation of transient deformation fields.     

Holographically recorded photopolymer diffractive optical element for holographic and electronic speckle-pattern interferometry

A diffractive optical element is described that can be used to implement a very simple self-aligning electronic speckle-pattern interferometer and holographic interferometer that requires only a laser source and a camera in the optical setup.     

Adaptive systems in speckle-pattern interferometry

The concept of adaptivity in television holography is discussed, and various realizations of adaptivity are presented. In one possible variation, functions of the components of the optical arrangement may be changed to adapt them to measurement conditions. An additional peculiarity of the technique is that reference waves are produced by holographically reconstructed virtual images. A method, believed to be new, is introduced for synthesizing the phase front of the master object beam that is produced by a simple holographic optical element and is used as a smooth or a speckled reference beam in the electronic speckle-pattern interferometer. An adaptive interferometer is presented as a measuring device for various measuring tasks. Selected applications are shown, demonstrating different aspects of adaptivity.     

Application of electronic speckle-pattern interferometry to measure in-plane thermal displacement in flip-chip packages

Electronic speckle-pattern interferometry (ESPI) was applied for noncontact, real-time evaluation of thermal deformation in a flip-chip package. The spatial resolution of ESPI was increased to submicron scale by magnifying the areas studied in order to measure the deformation of such small-scale components as the solder in the flip-chip package. Thermal deformation in the horizontal and vertical directions around the solder joints was measured as two-dimensional mappings during heating from 25 to 125 °C. ESPI was successful in obtaining information on the complicated deformation field around the solder joints. Furthermore, the shear strain could also be calculated using the measured thermal deformation around each solder joint. The applicability of ESPI to flip-chip packages was verified by comparing the ESPI results with those of finite-element analysis (FEA).     

Uncertainty analysis of displacements measured by in-plane electronic speckle-pattern interferometry with spherical wave fronts

Displacement measurements by optical interferometry depend on the induced phase difference and on the interferometer's sensitivity vector; the latter depends in turn on the illuminating sources and on the geometry of the optical arrangement. We have performed an uncertainty analysis of the in-plane displacements measured by electronic speckle-pattern interferometry with spherical incident wave fronts. We induced the displacements by applying a uniaxial tensile load on a nominally flat elastic sample. We approached the displacement uncertainty by propagating the uncertainties that we considered reasonable to assign to the measured phase difference and to the characteristic parameters of the interferometer's sensitivity vector. Special attention was paid to evaluating contributions to the displacement uncertainty. Moreover, we observed that the uncertainty decreases if the angles of incidence and the source-target distances are increased.     

Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps

Temporal and spatial phase shifting in electronic speckle-pattern interferometry are compared quantitatively with respect to the quality of the resultant deformation phase maps. On the basis of an analysis of the noise in sawtooth fringes a figure of merit is defined and measured for various in-plane and out-of-plane sensitive electronic speckle-pattern interferometry configurations. Varying quantities like the object-illuminating intensity, the beam ratio, the speckle size and shape, and the fringe density allows characteristic behaviors of both phase-shifting methods to be explored.     

Vibration-induced phase errors in high-speed phase-shifting speckle-pattern interferometry

We present results from numerical simulations of a dynamic phase-shifting speckle interferometer used in the presence of mechanical vibrations. The simulation is based on a detailed mathematical model of the system, which is used to predict the expected frequency response of the rms measurement error, in the time-varying phase difference maps, as a result of vibration. The performance of different phase-shifting algorithms is studied over a range of vibrational frequencies. Phase-difference evaluation is performed by means of temporal phase shifting and temporal phase unwrapping. It is demonstrated that longer sampling windows and higher framing rates are preferred in order to reduce the phase-change error that is due to vibration. A numerical criterion for an upper limit on the length of time window for the phase-shifting algorithm is also proposed. The numerical results are finally compared with experimental data, acquired with a phase-shifting speckle interferometer of 1000 frames/s.     

Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method

The measurement of three-dimensional displacement by electronic speckle-pattern interferometry with three object beams and one reference beam is presented. Multiple interference fringes corresponding to different sensitivity vectors are recorded in a single interferogram and separated by means of the Fourier transform method to give three components of displacement. The relationship between the ratio of the speckle size to the pixel size of a TV camera and the measurement error is investigated experimentally and compared with the research of others. The optimum condition leading to a minimum measurement error occurs when the speckle size is approximately equal to the pixel size. With this condition satisfied, the measurement error varies from 1.5% to 6.0%.     

Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry

Fringe patterns generated by electronic speckle-pattern interferometry are full of high-spatial-frequency and high-contrast speckle noise. Filtering with contoured windows has proved to be an efficient approach to filtering out speckle noise while retaining the fringe patterns. Furthermore, with contoured windows the contoured correlation fringe pattern method can be used to derive smooth, normalized, consistent fringes. Contoured windows previously were determined by fringe orientation only, and this process generated accumulated errors. We propose two new algorithms with which to obtain the contoured windows according to the fringe intensity slope and the distance ratio to neighboring skeletons. These new techniques can determine contoured windows more precisely.     

Digital speckle-pattern interferometry: fringe retrieval for large in-plane deformations with digital speckle photography

The compensation of large in-plane motions in digital speckle-pattern interferometry (DSPI) with the use of digital speckle photography (DSP) is demonstrated. Ordinary recordings of DSPI are recombined and analyzed with DSP. The DSP result is used to compensate for the bulk speckle motion prior to calculation of the phase map. This results in a high fringe contrast even for deformations of several speckle diameters. In addition, for the case of an in-plane deformation, it is shown that the absolute phase change in each pixel may be unwrapped by use of the DSP result as an initial guess. The principles of this method and experiments showing the in-plane rotation of a plate and the encounter of two rounded plates are presented.     

Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps

Inasmuch as current fringe analysis techniques used in digital speckle-pattern interferometry (DSPI) yield a phase map modulo 2pi, phase unwrapping is the final step of any data evaluation process. The performance of a recently published algorithm used to unwrap DSPI phase maps is investigated. The algorithm is based on a least-squares minimization technique that is solvable by the discrete cosine transform. When phase inconsistencies are present, they are handled by exclusion of invalid pixels from the unwrapping process through the assignment of zero-valued weights. Then the weighted unwrapping problem is solved in an iterative manner by a preconditioned conjugate-gradient method. The evaluation is carried out with computer-simulated DSPI phase maps, an approach that permits the generation of phase fields without inconsistencies, which are then used to calculate phase deviations as a function of the iteration number. Real data are also used to illustrate the performance of the algorithm.     

Extended-range temporal electronic speckle pattern interferometry

In recent years the availability of high-speed digital video cameras has motivated the study of electronic speckle pattern interferometry (ESPI) in the time domain. To this end a properly sampled temporal sequence of N-fringe patterns is used to analyze the temporal experiment. Samples of temporal speckle images must fulfill the Nyquist criteria over the time axis. When the transient phenomena under study are too fast, the required sampling frequency over time may not be fulfilled. In that case one needs to extend the measuring range of the algorithm used to extract the modulating phase. We analyze how to use short laser pulses or short video acquisition times with fairly long temporal separation among them to estimate the modulating phase of a dynamic ESPI experiment. The only requirement is that the modulating phase being estimated be properly sampled in the spatial domain.     

Oblique incidence of waves on a boundary

Summary A two-step procedure is developed which allows the emergent modes to be determined when a discontinuity wave strikes obliquely on a boundary. Although the procedure is straightforward, oblique incidence gives rise to a few mathematical problems, which are discussed in detail.With 1 Figure     

Measurement of in-plane strains using electronic speckle and electronic speckle-shearing pattern interferometry

Abstract

This letter reports the application of the electronic speckle and electronic speckle-shearing pattern interferometry for determining the first-order partial derivatives of in-plane displacements. Two possibilities of obtaining the in-plane strain contours are described. Experimental results showing the in-plane strain and the in-plane shearing strain contours on a tensile test specimen are presented.     

Holographically recorded axicon for grazing incidence interferometry

Abstract

A diffractive axicon for grazing incidence interferometry of cylindrical objects is presented. For industrial measurement, an element with a diameter of 8 cm was manufactured. The axicon was recorded in dichromated gelatine (DCG) with a high-precision rotating stage. The diffraction theory for the design of the element is presented. The axicon was tested interferometrically. Some possible errors are discussed.