Pseudo-Stokes Vector Correlation From Complex Signal Representation of a Speckle Pattern and Its Applications to Micro-Displacement Measurement

Abstract:  As an improvement of the intensity correlation used widely in conventional electronic speckle photography, we propose a new technique for displacement measurement based on correlating Stokes-like parameters derivatives for transformed speckle patterns. The method is based on a Riesz transform of the intensity speckle pattern, which converts the original real-valued signal into a complex signal. In closest analogy to the polarisation of a vector wave, the Stokes-like vector constructed from the spatial derivative of the generated complex signal has been applied for correlation. Experimental results are presented that demonstrate the validity and advantage of the proposed pseudo-Stokes vector correlation technique over conventional intensity correlation technique.     

Analysis of correlation coefficient filtering in elasticity imaging

Correlation-based speckle tracking methods are commonly used in elasticity imaging to estimate displacements. In the presence of local strain, a larger window size results in larger displacement error. To reduce tracking error, we proposed a short correlation window followed by a correlation coefficient filter. Although simulation and experimental results demonstrated the efficacy of the method, it was not clear why correlation coefficient filtering reduces tracking error since tracking error increases if normalization before filtering is not applied. In this paper, we analyzed tracking errors by estimating phase variances of the cross-correlation function and the correlation coefficient at the true time lag based on statistical properties of these functions' real and imaginary parts. The role of normalization is clarified by identifying the effect of the cross-correlation function's amplitude fluctuation on the function's imaginary part. Furthermore, we present analytic forms for predicting axial displacement error as a function of strain, system parameters (signal-to-noise ratio, center frequency, and signal and noise bandwidths), and tracking parameters (window and filter sizes) for cases with and without normalization before filtering. Simulation results correspond to theory well for both noise-free cases and general cases with an empirical correction term included for strains up to 4%.     

Surface displacement imaging by interferometry with a light emitting diode

We present an imaging technique to measure static surface displacements of electronic components. A device is supplied by a transient current that creates a variation of temperature, thus a surface displacement. To measure the latter, a setup that is based on a Michelson interferometer is used. To avoid the phenomenon of speckle and the drawbacks inherent to it, we use a light emitting diode as the light source for the interferometer. The detector is a visible CCD camera that analyzes the optical signal containing the information of surface displacement of the device. Combining images, we extract the amplitude of the surface displacement. Out-of-plane surface-displacement images of a thermoelectric device are presented.     

Numerical simulation of speckle noise in laser vibrometry

The fundamental mechanism by which speckle noise is generated in laser vibrometry before describing a new numerical simulation for prediction of speckle noise level in a real measurement is considered. Factors within the simulation include rate of change of phase within individual speckle transitions, low-pass filtering to match the frequency range of experimental data with which comparison is to be made, a track-and-hold facility for periods of low signal amplitude, and wavefront curvature effects. The simulation data provide real insight into the phase and amplitude modulation of the Doppler signal, and good agreement is found in the final comparison with experimental data from a measurement on a rotating target.     

Imaging with a rectangular phase grating applied to displacement metrology

We achieved displacement metrology with a high-amplitude signal by using a rectangular phase grating as the pupil in a grating imaging system. The imaging phenomenon with a pupil transmission grating that has a bilevel profile with a 50% duty ratio is discussed on the basis of the optical transfer function. By optimizing the imaging condition, we obtained high-contrast images with high light power under a magnified or demagnified imaging system. The amplitude of the signal in the displacement measurement was four times higher than that of the conventional grating imaging system with amplitude gratings.     

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.     

Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: statistical properties of the analytic signal of a white-light speckle pattern applied to the microdisplacement measurement

To provide a theoretical background for the superiority of the signal-domain phase-only correlation (SDPOC) technique proposed here for microdisplacement measurement, we study the first- and the second-order statistical properties of the complex amplitude of an analytic signal of a white-light speckle pattern, under the assumption of a Gaussian random process, and give a formula for the autocorrelation function of the pseudophase associated with the complex analytic signal. Based on these results, we show mathematically that SDPOC has a performance advantage over conventional intensity-based correlation techniques.     

A fast hybrid algorithm combining regularized motion tracking and predictive search for reducing the occurrence of large displacement errors

A hybrid approach that inherits both the robustness of the regularized motion tracking approach and the efficiency of the predictive search approach is reported. The basic idea is to use regularized speckle tracking to obtain high-quality seeds in an explorative search that can be used in the subsequent intelligent predictive search. The performance of the hybrid speckle-tracking algorithm was compared with three published speckle-tracking methods using in vivo breast lesion data. We found that the hybrid algorithm provided higher displacement quality metric values, lower root mean squared errors compared with a locally smoothed displacement field, and higher improvement ratios compared with the classic block-matching algorithm. On the basis of these comparisons, we concluded that the hybrid method can further enhance the accuracy of speckle tracking compared with its real-time counterparts, at the expense of slightly higher computational demands.     

Large deformation mechanical testing of biological membranes using speckle interferometry in transmission. II: Finite element modeling

In holography and speckle interferometry the measurement range is generally limited by the greatest number of fringes that can be resolved in a single image. As a result these techniques have been generally confined to small displacement measurement applications. In the case of out-of-plane measurements one can overcome this limitation by simply adding incremental measurements at individual detector pixels. In the case of in-plane measurements, however, summing incremental measurements is not a straightforward procedure since the interference pattern moves laterally across the detector as the material deforms. We describe a modeling technique based on finite elements which solves this problem. In combination with a full field method such as holography or speckle interferometry, it provides a very sensitive measurement technique with dense spatial sampling and large dynamic range. Experimental results of speckle interferometry operating in transmission to measure in-plane displacements of biological membranes are presented, where total material displacements are of the order of millimeters. The results also demonstrate how the finite strain tensor is calculated analytically from the data at any point on the material.     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

Noise and speckle reduction in synthetic aperture radar imagery by nonparametric Wiener filtering

We present a Wiener filter that is especially suitable for speckle and noise reduction in multilook synthetic aperture radar (SAR) imagery. The proposed filter is nonparametric, not being based on parametrized analytical models of signal statistics. Instead, the Wiener-Hopf equation is expressed entirely in terms of observed signal statistics, with no reference to the possibly unobservable pure signal and noise. This Wiener filter is simple in concept and implementation, exactly minimum mean-square error, and directly applicable to signal-dependent and multiplicative noise. We demonstrate the filtering of a genuine two-look SAR image and show how a nonnegatively constrained version of the filter substantially reduces ringing.     

Ultrasound-modulated optical tomography with intense acoustic bursts

Ultrasound-modulated optical tomography (UOT) detects ultrasonically modulated light to spatially localize multiply scattered photons in turbid media with the ultimate goal of imaging the optical properties in living subjects. A principal challenge of the technique is weak modulated signal strength. We discuss ways to push the limits of signal enhancement with intense acoustic bursts while conforming to optical and ultrasonic safety standards. A CCD-based speckle-contrast detection scheme is used to detect acoustically modulated light by measuring changes in speckle statistics between ultrasound-on and ultrasound-off states. The CCD image capture is synchronized with the ultrasound burst pulse sequence. Transient acoustic radiation force, a consequence of bursts, is seen to produce slight signal enhancement over pure ultrasonic-modulation mechanisms for bursts and CCD exposure times of the order of milliseconds. However, acoustic radiation-force-induced shear waves are launched away from the acoustic sample volume, which degrade UOT spatial resolution. By time gating the CCD camera to capture modulated light before radiation force has an opportunity to accumulate significant tissue displacement, we reduce the effects of shear-wave image degradation, while enabling very high signal-to-noise ratios. Additionally, we maintain high-resolution images representative of optical and not mechanical contrast. Signal-to-noise levels are sufficiently high so as to enable acquisition of 2D images of phantoms with one acoustic burst per pixel.     

Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier

We present an optical phase measurement method based on the Hilbert transform for the analysis of a time series of speckle interferograms modulated by a temporal carrier. We discuss the influence of nonmodulating pixels, modulation loss, and noise that affect the bias and modulation intensities of the interferometric signal and propose the application of the empirical mode decomposition method for its minimization. We also show the equivalence between the phase recovery approaches that are based on the Hilbert and the Fourier transforms. Finally, we present a numerical comparison between these methods using computer-simulated speckle interferograms modulated with a temporal carrier.     

Toward a real-time simulation of ultrasound image sequences based on a 3-D set of moving scatterers

Data simulation is an important research tool to evaluate algorithms. Two types of methods are currently used to simulate medical ultrasound data: those based on acoustic models and those based on convolution models. The simulation of ultrasound data sequences is very time-consuming. In addition, many applications require accounting for the out-ofplane motion induced by the 3-D displacement of scatterers. The purpose of this paper is to propose a model adapted to a fast simulation of ultrasonic data sequences with 3-D moving scatterers. Our approach is based on the convolution model. The scatterers are moved in a 3-D continuous medium between each pair of images and then projected onto the imaging plane before being convolved. This paper discusses the practical implementation of the convolution that can be performed directly or after a grid approximation. The grid approximation convolution is obviously faster than the direct convolution but generates errors resulting from the approximation to the grid?s nodes. We provide the analytical expression of these errors and then define 2 intensity-based criteria to quantify them as a function of the spatial sampling. The simulation of an image requires less than 2 s with oversampling, thus reducing these errors. The simulation model is validated with first- and second-order statistics. The positions of the scatterers at each imaging time can be provided by a displacement model. An example applied to flow imaging is proposed. Several cases are used to show that this displacement model provides realistic data. It is validated with speckle tracking, a well-known motion estimator in ultrasound imaging.     

Zero reference signal for displacement measuring systems by use of speckle

An optical method for generating a reference signal for an incremental displacement measurement system is proposed. We achieved this zero reference signal by comparing two speckle patterns arriving from two symmetric diffusers, which are used as natural random codes that are identical only when the reading head is located equidistantly between the diffusers. The comparison of the speckles is obtained either by interference, as in a Michelson interferometer, or by intensity correlations.     

Spatially integrated speckle intensity: maximum resistance to decorrelation caused by in-plane target displacement

Laser speckle produced from a diffuse object can be used in determining the angular position of a rotating object. When the object rotates the backscattered speckle pattern, which changes continuously but repeats exactly with every revolution, is sampled by a suitably positioned photodetector. The photodetector output signal is periodic, and one period is stored in the memory as a reference. Shaft position can then be determined by the comparison of this stored reference signal with the current photodetector output signal. When the shaft is axially displaced, for example, by vibration, the backscattered speckle pattern changes on the photodetector and the similarity between the reference signal and the current signal is reduced. We examine the cross correlation of the real-time photodetector output signal and the stored reference signal as a function of axial shaft position. Use of a rotating shaft when collecting data is shown to be an efficient means by which to make effectively several thousand independent estimates of the maximum axial displacement tolerable before decorrelation of the photodetector output. Theoretical results and experiments conducted show that the decorrelation displacement varies, according to optical configuration, to a maximum value of 0.7 of the beam diameter. This has important implications for a proposed laser torquemeter as well as additional applications in which changes to the sampled speckle pattern, including decorrelation, are either desirable or undesirable.     

Noncontact speckle-based velocity sensor [laser Doppler vibrometer]

Laser light illuminating a rough surface generates speckle phenomena in the space around the surface. In this paper, the authors propose a noncontact laser Doppler vibrometer (LDV) sensor, using the speckle phenomena, for the assessment of target velocity and displacement at low vibration frequencies. The sensor is realized using few optical components in a very simple optical configuration. The methodology for the experimental and analytical determination of the sensor sensitivity is reported, and two speckle-processing algorithms have been used to appraise the best cross-correlation function for target velocity measurement. The algorithms are based on binary correlation and fast Fourier transform analysis. Experimental results coming from the comparison of both the proposed techniques are reported. Moreover, results obtained with the proposed speckle sensor have been compared with reference measurement systems. Results show that this noncontact sensor is characterized by a reduced optical complexity and low cost. It appears to be particularly suitable for use in the analysis of low velocity rough surfaces.     

Displacement Discontinuity or Complex Shape of Sample: Assessment of Accuracy and Adaptation of Local DIC Approach

In this paper, we study the impact of a complex shape of sample and the appearance of a displacement discontinuity on performances of measurement by local Digital Image Correlation (DIC). Both cases are modelled from synthetic images into two parts: one with a speckle field and another part without speckle or two parts with similar speckle fields but with different kinematics. The accuracy of displacement measurements assessed for DIC subsets crossing the boundary between the two parts is lower than the one obtained without discontinuity and justifies adapting DIC method. A new local DIC process is presented in detail. It is an alternative way able to take into account any shape of sample and several curved lines of discontinuity in the same subset. Two experimental examples are presented: displacement and strain fields obtained by DIC and adapted DIC are compared. We can conclude that it is possible to lead a mechanical analysis until the limits of the sample and even during the appearance and the propagation of a crack.     

Internal displacement and strain imaging using ultrasonic speckletracking

Previous ultrasound speckle tracking methods have been extended, permitting measurement of internal displacement and strain fields over a wide dynamic range of tissue motion. The markedly increased dynamic range of this approach should lead to enhanced contrast resolution in strain and elasticity images. Results of experiments on gelatin-based, tissue equivalent phantoms show the capabilities of the method