Multiwavelength shearography for quantitative measurements of two-dimensional strain distributions

We report on the development of a multiwavelength speckle pattern shearing interferometer for the determination of two-dimensional strain distributions. This system is based on simultaneous illumination of the object with three diode lasers that emit at different wavelengths between 800 and 850 nm. Wavelength separation and image acquisition were performed with a special optical arrangement, including narrow-bandpass filters and three black-and-white cameras. The shearographic camera with a variable shearing element, in combination with the appropriate illumination geometry, permitted us to isolate all six displacement derivatives from phase-stepped fringe patterns. The optical system and the measurement procedure were validated with two different experiments. First, the shearographic sensor head was used for the determination of in-plane displacements, and, second, in-plane strain distributions of an aluminum block caused by temperature expansion were measured.     

Speckle dynamics for intensity-modulated illumination

We analyze the dynamics of laser speckle patterns, designed for sensing with a receiver, based on spatial filtering. The speckle translation arises after free-space propagation of light scattered from nonspecular surfaces of a solid object in motion. The speckle pattern is manipulated by modulating the intensity of the coherent light, illuminating the target. The space-time normalized cross covariance of speckle patterns incident on the spatial sensor is calculated for the field distribution of three Gaussian beams having arbitrary directions and separations when incident on the target. The modulation of the intensity distribution at the target introduce a higher spatial frequency component in the speckle pattern. The theoretical analysis provides the statistical parameters for both the speckles and the higher spatial frequency component. The analysis reveals that the speckles and the higher spatial frequency component do not necessarily translate as a rigid structure. The theoretical findings are supported by measurements.     

Strain compounding: a new approach for speckle reduction

A new compounding technique for reducing speckle brightness variations is proposed. This method exploits the decorrelation between signals under different strain states. The different strain states can be created using externally applied forces such as the ones used in sonoelastography. Such forces produce three-dimensional tissue motion. By correcting only the in-plane (i.e., axial and lateral) motion, the images under different strain states have similar characteristics except for speckle appearance caused by the uncorrected out-of-plane (i.e., elevational) motion. Additional speckle decorrelation is also introduced through tissue motion correction caused by the change of effective in-plane sample volume geometry. Therefore, these images can be combined for speckle reduction with less degradation in in-plane spatial resolution than conventional approaches. In this paper, three-dimensional tissue motion under various strain conditions were simulated. It was found that significant speckle decorrelation existed at strains achievable in some clinical situations. Experiments were also conducted to test efficacy of this approach. Pulse-echo data from a gelatin-based phantom were acquired using a 5-MHz, single crystal transducer, and both conventional and compound B-mode images were formed. Results indicated that speckle brightness variations were reduced, and detectability of low contrast objects was enhanced. Performance limitations and fundamental differences between the proposed technique and existing techniques are discussed     

Spatial filtering velocimetry of objective speckles for measuring out-of-plane motion

This paper analyzes the dynamics of objective laser speckles as the distance between the object and the observation plane continuously changes. With the purpose of applying optical spatial filtering velocimetry to the speckle dynamics, in order to measure out-of-plane motion in real time, a rotational symmetric spatial filter is designed. The spatial filter converts the speckle dynamics into a photocurrent with a quasi-sinusoidal response to the out-of-plane motion. The spatial filter is here emulated with a CCD camera, and is tested on speckles arising from a real application. The analysis discusses the selectivity of the spatial filter, the nonlinear response between speckle motion and observation distance, and the influence of the distance-dependent speckle size. Experiments with the emulated filters illustrate performance and potential applications of the technology.     

Accuracy in electronic speckle photography

Electronic speckle photography is an accurate, easy-to-use, video-based technique for the analysis of two- and three-dimensional deformation fields and in-plane strain fields, based on numerical cross correlation. Through the use of statistical optics, simulated speckle patterns, and experiments the accuracy in electronic speckle photography was found to depend on correlation, speckle size, window size, and correlation filter. The estimated correlation was found to be the combined effect of three mutually competing factors because of classical speckle correlation, subimage overlap, and displacement gradients. In many applications white-light speckle patterns provide a more accurate estimate of the displacement field than do laser speckle patterns.     

Correlation distance of dynamic speckles

The translational and boiling motions of dynamic speckles produced in the Fresnel diffraction field under illumination of a Gaussian beam are investigated in detail. The speckle motion is analyzed from the space-time cross-correlation function of speckle intensity fluctuations detected at the two points in the receiving plane. The correlation distance of time-varying speckles is compared with the translation distance of the spatial speckle pattern. The optical conditions for the translational and boiling motions of dynamic speckles are examined and expressed in a diagram. The characteristics for the correlation distance of time-varying speckle intensity fluctuations are finally verified by several experiments.     

Rigid rotations of a plate and the related speckle displacements in the image plane

We describe an optical setup created for the verification of theoretical results concerning the displacement of speckles in the plane imaging a surface, which performs rotational motion. On the whole, the experimental results are consistent with the theory: there is a linear relationship between the surface rotation and the speckle displacement. The sensitivity of this method is proportional to the distance from a lens to the observation plane.     

In-plane dynamic speckle interferometry: comparison between a combined speckle interferometry/speckle correlation and an update of the reference image

A common problem during study of, for instance, tensile tests with interferometers is that the sample moves too much so that the speckles decorrelate and no phase information is obtained. Two ways to overcome this problem are compared: a combination of speckle interferometry and speckle correlation and a method in which the reference image is updated during the experiment. The comparison shows that both techniques can be used to measure the deformation of an object even if it is exposed to rigid body motions. Both techniques are applied to measurements of microscale deformation fields of an adhesive joint in a carbon-fiber epoxy composite.     

Uneven intensity change correction of speckle images using morphological Top-Hat transform in digital image correlation

By comparing two digital speckle images recorded before and after deformation, two-dimensional digital image correlation (DIC) method can accurately determine the in-plane displacement fields and strain fields. In a practical measurement, however, the variance of light source intensity, location and direction will cause the random uneven intensity change of the random speckle images and will lead to the obvious measurement error. Numerical simulation experiment is first carried out to analyse the influence of the recorded speckle images undergoing uneven light variation on DIC measurement accuracy. Then, a correction method for speckle images with uneven intensity change is proposed based on morphological Top-Hat transform. In addition, quantitative measurements of both in-plane rotation of a rigid body and three-point bending beam are investigated experimentally by DIC to verify the feasibility of the correction method. Experimental results show that the measurement accuracy of DIC is improved dramatically after the procedure of uneven light variation correction.     

Theory and Applications of Dynamic Laser Speckles Due to In-plane Object Motion

The dynamic behaviour of laser speckle caused by uniform in-plane motion of a diffuse object has been studied by deriving the cross-correlation functions of the complex disturbance and the intensity in a field where the speckle is observed. The expressions for the diffraction and the image fields are calculated from general formulae for a linear coherent system. On the basis of these functions two characters in the dynamic behaviour of speckle, a bodily translation and a gradual change in structure, are discussed quantitatively. The velocity of the translation and the rate of the structure change have been derived. As applications of the relations obtained several new methods have been proposed for measuring pattern correlations, MTF of imaging systems, in-plane velocity of diffuse objects, and eye accommodation state.     

Mechanical stress measurement by an achromatic optical digital speckle pattern interferometry strain sensor with radial in-plane sensitivity: experimental comparison with electrical strain gauges

This paper shows the optical setup of a radial in-plane digital speckle pattern interferometer which uses an axis-symmetrical diffractive optical element (DOE) to obtain double illumination. The application of the DOE gives in-plane sensitivity which only depends on the grating period of the DOE instead of the wavelength of the laser used as illumination source. A compact optical layout was built in order to have a portable optical strain sensor with a circular measurement area of about 5 mm in diameter. In order to compare its performance with electrical strain sensors (strain gauges), mechanical loading was generated by a four-point bending device and simultaneously monitored by the optical strain sensor and by two-element strain gauge rosettes. Several mechanical stress levels were measured showing a good agreement between both sensors. Results showed that the optical sensor could measure applied mechanical strains with a mean uncertainty of about 5% and 4% for the maximum and minimum principal strains, respectively.     

Lenticular array for spatial filtering velocimetry of laser speckles from solid surfaces

We present a low-cost optical design for the detection of speckle translation, which can provide measures of in-plane translation or the rotation of a solid structure. A nonspecular target surface is illuminated with coherent light. The scattered light is propagated through an optical arrangement that has been particularly designed for the type of mechanical measurand for which the sensor is intended. The dynamics of the speckle field that arise from the target surface are projected onto a lenticular array, constituting a narrow spatial bandpass filter for the speckle spectrum. The filter provides access to the full phase information of the temporal quasi-sinusoidal intensity output; thus differential arrangements of photodetectors can provide suppression of low-frequency oscillations and higher harmonics, and the direction of the speckle translation can be determined. The spatial filter of the sensor is characterized, and the precision of the sensor when it is integrated with an electronic zero-crossing-detection processor is investigated. The best measurement accuracy obtained at constant velocity is 1% at 1.6-mm translation; the relative standard deviation decreases with the square root of the distance traveled.     

The Extension of the Electronic Speckle Photography to the Measurement of In-Plane Displacement

In this paper, a modified speckle photography technique is demonstrated for the measurement of a variable range of the in-plane displacement. The modification focuses on coupling the diode pump solid state laser DPSS with the conventional speckle photography technique. The DPSS laser emerges different wavelengths to provide speckle patterns of suitable size to measure the desired range of the in-plane displacement. The second harmonic generation in a nonlinear crystal of wavelength 532 nm and the principle diode laser wavelength 808 nm are employed in identifying the object positions within a lateral displacement made by a standard linear stage in the range from few microns up to 1.2 mm. The sensitivity and the correlation of the speckles formed by both wavelengths suit both small and large movements. A continues measurement by the modified technique can be achieved by identifying a scale factor in the uniform area in which both wavelengths are effective, and high correlation between the results obtained by 532 and 808 nm is maintained. The uncertainty in measuring 1.2 mm lateral movement by the modified speckle photography is found to be 26.8 μm.     

Vibration Analysis of Plate and Shell by Laser Speckle Interferometry

When an optically rough structure is illuminated by laser light, speckles are created throughout the space in front of the surface covered by the reflected wavelets When the surface is under steady-state vibration these speckles also vibrate accordingly. By recording the speckles contained in a plane in front of the surface as a time average the resulting speckle interferogram will yield a variety of information upon proper Fourier filtering. One can obtain a complete anti-nodal pattern, a partial anti-nodal pattern, and partial slope contours from which bending moments can be calculated The method is applied to shell as well as plate vibration problems.     

Noise reduction in speckle photography Young's fringes by an unique averaging method

We present and experimentally verify an averaging method to reduce significantly the speckle noise in the pattern of Young's fringes in speckle photography. With a rigid-body in-plane surface motion and a common photographic film, we observed a significantly noisy fringe pattern. Upon averaging several patterns taken from different parts of the transparency, the contrast and effect of the speckle noise are progressively averaged out to yield virtually a noise-free fringe pattern.     

3D strain mapping in rocks using digital volumetric speckle photography technique

Speckle photography technique is a versatile displacement/deformation mapping technique that can be applied to almost any material. It has its genesis in the laser speckle interferometry technique whereby the natural speckles created by illuminating an optically rough surface using a coherent laser beam are used as displacement gauging elements. It evolves into the white light speckle photography technique whereby a random pattern of any type is used as a displacement measurement transducer. With the advent of digital cameras and ubiquitous usage of computers, the digital version of the technique is developed. Up to now, the technique is essentially limited to 2D applications. Recently, we extended the technique into the 3D domain by using the volumetric imaging capabilities of CT or MRI. In this paper, we apply this technique to measuring the internal deformation of rocks. It so happens that certain rocks have natural density variation at various places such that when imaged by CT these impurities can be treated as 3D speckles. The elements of volumetric speckle photography technique are as follows. A reference volumetric image of the rock is recorded by a micro-CT scan and stored as a reference. Under load, the deformed CT image of the rock is also recorded. Both volume images are divided into subsets of certain voxel arrays. Each corresponding pair of the subsets is “compared” via a two-step 3D Fourier transform analysis. The result is a 3D map of displacement vectors representing the collective displacement experienced by all the speckles within the subset of voxels. The strain distribution of the entire rock specimen can then be calculated using appropriate displacement strain relations. The application of this technique to strain mapping of red sandstone and argillite rocks is presented.     

Improved white-light interferometry on rough surfaces by statistically independent speckle patterns

White-light interferometry (WLI) on rough surfaces is based on interference from individual speckles. The measurement uncertainty of WLI is limited by a random shift of these individual interference patterns. The statistical error in each measurement point depends on the brightness of the corresponding speckle: a dark speckle yields a larger error than a bright speckle. In this paper, a novel method is presented to reduce the measurement uncertainty significantly: by sequentially switching the direction of the illumination, the camera sees several independent speckle patterns in sequence. From each pattern, the brightest speckles are selected to eventually calculate an accurate height map. This height map displays no outliers, and the measured surface roughness is close to the stylus measurements.     

Strain engineering of piezoelectric properties of strontium titanate thin films

The in-plane and out-of-plane piezoelectric properties of (001) strontium titanate (SrTiO₃, STO) epitaxial thin films on pseudo-cubic (001) substrates are computed as a function of in-plane misfit strain. A nonlinear thermodynamic model is employed, which takes into account the appropriate mechanical boundary conditions, the electromechanical coupling between the polarization and the in-plane lattice mismatch, and the self-strains of the ferroelastic and ferroelectric phase transformations. The piezoelectric behavior of epitaxial STO films is described in various strain-induced ferroelectric phase fields in a temperature range from ?50 to 50 °C. The calculations show that by carefully tailoring in-plane misfit strains in both tensile and compressive ranges, piezoelectric coefficients that are of the order of prototypical lead zirconate titanate and other lead-based piezoceramics can be realized. These results indicate that strain engineered STO films may be employed in a variety of sensor and actuator applications as well as surface acoustic wave devices and thin-film bulk acoustic resonators.     

Systematic and random errors in electronic speckle photography

Electronic speckle photography offers a simple and fast technique for measuring in-plane displacement fields in solid and fluid mechanics. Errors from undersampling, illumination divergence, and displacement magnitude have been analyzed and measured. The nature of the systematic error is such that a drift toward the closest integral pixel value is introduced. Because of the finite extent of the sensor area, considerable undersampling is tolerable before systematic errors occur. The random errors are mainly dependent on the effective ?-number of the imaging system and speckle decorrelation introduced by object displacement. When sampling at a rate of ~ 70% of the Nyquist frequency, we avoided systematic errors and minimized random errors.