Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI)

Hitherto no method, to our knowledge, was known to incorporate spatial phase shifting for the measurement of pure in-plane displacements. We demonstrate that the modified Duffy two-aperture configuration [Opt. Lett. 22, 1958 (1996)], which is sensitive to only the in-plane displacement component and offers increased sensitivity, lends itself to measurement with spatial phase shifting. The configuration can also be used for obtaining displacement derivatives by the introduction of shear with the tilt of a mirror.     

Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors

The advantages of spatial phase shifting (SPS) compared with temporal phase shifting in the field of electronic speckle pattern interferometry are described. Some periodic phase reconstruction errors occurring in SPS are discussed. It is shown that these errors become minimal for a spatial phase-shift angle of 2pi/3. Furthermore, a modified phase reconstruction formula is presented by which the noise in the reconstructed phase map is reduced.     

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.     

Increased sensitivity to in-plane displacements in electronic speckle pattern interferometry

We describe an optical arrangement that increases the sensitivity to in-plane displacement in an electronic speckle-pattern interferometric system. This is accomplished by oblique illumination and observation along the direction of illumination. An anamorphic prism placed in front of the object is used to correct for the eccentricity in the image caused by the oblique observation. The sensitivity to in-plane displacement can be increased to a maximum of approximately λ/2. Experimental results including phase stepping are presented.     

Least-squares phase estimation with multiple parameters in phase-shifting electronic speckle pattern interferometry

We have developed an accurate and robust phase-estimation method in phase-shifting electronic speckle pattern interferometry. Unlike other methods that assume a constant phase within a fitting window, our method treats the phase variation with a gradient. A cost function that can utilize the information of pixel positions is formulated on the basis of a least-squares criterion. Powell's iteration method is applied to it to derive the phase and its gradient. An automatic consistency-checking routine and an algorithm that improves the initial guess of the iteration are developed for severe situations with large noise and steep phase variations.     

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.     

Digital speckle pattern interferometry using spatial phase shifting: influence of intensity and phase gradients

Spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS) provides the phase information due to the object displacement from two images, one stored before and other after loading. The technique needs a carrier fringe system. The double aperture mask in front of the imaging system is one of the methods for introducing the spatial carrier frequency for phase evaluation. The size of the apertures and their separation are important criteria to obtain appropriate phase shift/column within the desired size of the speckle for phase retrieval. The assumptions of constant intensity and phase on adjacent pixels of the camera while calculating phase in spatial phase shifting (SPS) are not met as the speckled object wave contains intensity and phase gradients, resulting in distortions in the calculated phase profiles. In this paper we discuss a strategy to overcome these problems. The contrast of the correlation fringe obtained using this approach is much improved. It also eliminates the distortion in the unwrapped phase map like wave ripples. The experimental results on an edge clamped circular plate loaded at the center are presented.     

Phase-shifting algorithms for electronic speckle pattern interferometry

A set of innovative phase-shifting algorithms developed to facilitate metrology based on electronic speckle pattern interferometry (ESPI) are presented. The theory of a phase-shifting algorithm, called a (5,1) algorithm, that takes five phase-shifted intensity maps before a specimen is deformed and one intensity map after a specimen is deformed is presented first. Because a high-speed camera can be used to record the dynamic image of the specimen, this newly developed algorithm has the potential to retain the phase-shifting capability for ESPI in dynamic measurements. Also shown is an algorithm called a (1,5) algorithm that takes five phase-shifted intensity maps after the specimen is deformed. In addition, a direct-correlation algorithm was integrated with these newly developed (5,1) or (1,5) algorithms to form DC-(5,1) and DC-(1,5) algorithms, which are shown to improve significantly the quality of the phase maps. The theoretical and experimental aspects of these two newly developed techniques, which can extend ESPI to areas such as high-speed dynamic measurements, are examined in detail.     

Vibration analysis of logs with electronic speckle pattern interferometry

Electronic speckle pattern interferometry combined with phase-shifting techniques for vibration analysis of logs is presented. Changes in the vibration pattern were followed on a television monitor at the video rate. We determined resonant vibrations by scanning through the frequency range of interest and by changing the point of excitation. We observed bending and torsional modes of vibration by changing the support and point of excitation. The vibrational modes reflect the structural properties of the material. The longitudinal modulus of elasticity and the shear modulus were calculated, giving valuable information for the strength grading of logs.     

Contrast enhancement of electronic speckle pattern interferometry addition fringes

The electronic speckle pattern interferometer in the double-pulse addition mode can be used to measure physical parameters in unstable environmental conditions. Owing to additive optical noise, however, the fringe patterns obtained have poor contrast. Some methods that use subtraction of addition double-pulsed fringe patterns improve fringe visibility but impose a limitation in measurement time ranges. To increase this range, to be limited by only the pulse separation, the contrast enhancement of double-pulsed addition-fringe patterns with a spatial filter based on local-standard-deviation measurements is investigated. Computer simulations and experimental results are presented.     

Measuring mixing dynamics of transparent fluids with electronic speckle pattern interferometry

Electronic speckle pattern interferometry (ESPI) combined with phase-shifting techniques is used for studying the mixing dynamics of transparent fluids. The potentials of the technique for studying fluid mixing are illustrated for simple examples of water flow and moving water droplets in water. With ESPI we could actually follow water droplets moving in water and water flowing in water on a television monitor at the video rate. A He-Ne laser (lambda(0) = 632.8 nm) was used as the light source, and phase stepping was applied, giving an interferometric sensitivity better than lambda(0)/10. The observed phase changes are due to changes in the refractive index caused by small temperature differences between the droplets and the surrounding water. Temperature differences of less than 0.1 K are detectable for droplets of a diameter of 4 mm.     

Multiwavelength electronic speckle pattern interferometry for surface shape measurement

Profilometry by electronic speckle pattern interferometry with multimode diode lasers is both theoretically and experimentally studied. The multiwavelength character of the laser emission provides speckled images covered with interference fringes corresponding to the surface relief in single-exposure processes. For fringe pattern evaluation, variations of the phase-stepping technique are investigated for phase mapping as a function of the number of laser modes. Expressions for two, three, and four modes in four and eight stepping are presented, and the performances of those techniques are compared in the experiments through the surface shaping of a flat bar. The surface analysis of a peach points out the possibility of applying the technique in the quality control of food production and agricultural research.     

Digital processing of electronic speckle pattern interferometry addition fringes

A digital image-processing method for analyzing double-pulsed electronic speckle pattern interferometry addition fringes is described. The procedure consists of three steps, forming a combination particularly suited to addressing some important practical limitations of the measurement system. In the first step it is shown that in certain cases fringe visibility may be enhanced by subtraction of a reference interferogram, so that a pattern with a quality similar to that of a subtraction one is obtained. In the second step noise is reduced by the application of a spectral subtraction image-restoration method. The third step concerns the calculation of the wrapped phase by means of a Fourier transform method with bandpass filtering. Preliminary experimental results that illustrate the performance of this approach are presented.     

Theoretical investigations on dual-beam illumination electronic speckle pattern interferometry

Contrary to what is found in most of the existing scientific literature, where a specific frame is developed, the theory of speckle interferometry is (conveniently) presented here as a particular case of the more general theory of holographic interferometry. In addition to the intellectual benefit of dealing with a single unified theory, this brings about many advantages when it comes to discuss fundamental topics such as the three-dimensional evolution of the complex amplitude of the diffuse optical wavefronts, the degree of approximation of the leading formulas, the loss of fringe contrast, the decorrelation effects, the real influence of the terms generally neglected in out-of-focus regions. In the same way, the statistical properties of the speckle fields, usually treated as a separate subject matter, are also integrated in the theory, thus providing a comprehensive knowledge of the qualitative features of speckle interferometry methods, otherwise difficult to understand.     

Phase extraction from electronic speckle pattern interferometry addition fringes

Addition fringes are obtained in real time from electronic speckle pattern interferometry (ESPI) by use of a twin-pulsed laser when two pulses are fired during a single field of a CCD camera. This enables object deformations to be studied in harsh environmental conditions. However, the fringe patterns have poor visibility because optical noise is additive. To our knowledge automatic phase extraction from addition fringes has not previously been achieved: Low-pass filtering to suppress random speckle noise also eliminates the fringes because of their low visibility. Two phase-stepping algorithms that calculate phase from ESPI fringes without the need for a preprocessing filter are presented. In the first ESPI subtraction fringes are considered, for which an improvement in accuracy is seen, and in the second ESPI addition fringes are considered, which, we believe, has enabled the phase to be extracted for the first time. The algorithms are demonstrated with theoretical data and with experimental ESPI fringepatterns recorded with a cw laser. As presented, they form the first step toward a procedure that can beused with twin-pulsed ESPI.     

Double-exposure phase calculation method in electronic speckle pattern interferometry based on holographic object illumination

Multiple-exposure phase calculation procedures are widely used in electronic speckle pattern interferometry to calculate phase maps of displacements. We developed a double-exposure process based on holographic illumination of the object and the idea of the spatial carrier phase-shifting method to examine transient displacements. In our work, computer-generated holograms and a spatial light modulator were used to generate proper coherent illuminating masks. In this adjustment all phase-shifted states were at our disposal from one recorded speckle image for phase calculation. This technique can be used in the large scale of transient measurements. In this paper we illustrate the principle through several examples.     

Transient deformation measurement with electronic speckle pattern interferometry and a high-speed camera

To the best of our knowledge, transient deformations have been measured in real time with microsecond temporal resolution for the first time with speckle pattern interferometry. The short exposure period and high framing rate of a high-speed camera at as many as 40, 500 frames per second allow low-power continuous-wave laser illumination and fiber-optic beam delivery to be used. We have applied the technique to measure both harmonic vibration and transient deformation.     

Localized Fourier transform filter for noise removal in electronic speckle pattern interferometry wrapped phase patterns

This article is concerned with frequency filtering for electronic speckle pattern interferometry wrapped phase patterns. We propose a robust localized Fourier transform filter which is an extension of the root filtering method (RFM). We improve the RFM from a simple technical process and a filter function in the frequency domain. In our method, the proposed filter function is taken as the power spectrum of the convolution of an image and a Gaussian function to the power α. We test the proposed method on two computer-simulated wrapped phase fringe patterns and one experimentally obtained wrapped phase pattern, and compare our models with the widely used, well-known RFM and windowed Fourier filtering (WFF). The experimental results have demonstrated that our localized Fourier transform filter outperforms the RFM and is comparable to WFF. Our method depends on fewer parameters, as compared with WFF, and can achieve a better balance between the computational complexity and the filtered results.     

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.