Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods

The measurement of dynamic displacements by use of speckle pattern interferometry and temporal phase unwrapping allows for the evaluation of large-object displacement fields without the propagation of spatial unwrapping errors. If a temporal carrier is introduced in one of the beams of the interferometer, phase data for whole-object displacement can be retrieved by use of a temporal phase-shifting method or a temporal Fourier transformation approach. We present a comparison between both methods of temporal phase measurement in terms of precision and execution speed. We performed the analysis by using computer-simulated speckle interferograms, an approach that allowed us to know precisely the original phase distribution and also to determine the spatial rms phase error as a function of the phase change introduced between two consecutive speckle interferograms. The performance of both methods to process experimental data is also illustrated by use of the results from a high-speed speckle interferometry study of a carbon fiber panel.     

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     

Estimation of a dense velocity field based on the statistics of dynamic speckle

This article presents a new technique for flow velocity estimation from ultrasound image sequences. The method is based on the analysis of the temporal statistics of the speckle pattern in motion. We demonstrate that the biased local temporal variance (LTV) of a single pixel within an image of dynamic speckle is related to velocity. This allows us to estimate the total velocity magnitude without the requirement of neither block matching nor autocovariance estimation. A new estimator, asymptotically without bias, called LTV is presented. Results conducted on experimental B mode sequences (40 MHz) of blood mimicking fluid with calibrated velocities are presented. Performances of the estimator are studied and results show good agreement with the statistical model. Magnitude of the 3D velocity vector in the range of 0.1–2 mm/s have been estimated with a standard deviation error of less than 12%. The validity of the method and its limitations are then discussed. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 268‐276, 2010     

Simulation of Time-evolving Speckle Patterns Using Kolmogorov Statistics

Abstract

We present a new approach for simulating time-evolving speckle patterns, by combining the shift of a rigid phase screen with its evolution. Thus, the two time-scales associated with speckle boiling and speckle motion can be adjusted independently. The statistical properties of the phase perturbation and the speckle pattern are investigated by using the temporal phase structure function and the temporal intensity correlation. We found a very good agreement with experimental results.     

Statistics of local speckle contrast

In describing the first-order properties of laser speckle under polarized illumination conditions, it is almost an article of faith that the contrast is unity. In many processing schemes, however, the contrast defined as the quotient of the standard deviation and the mean is calculated over a localized spatial region. In such cases, this local contrast displays a distribution of values that can depart substantially from unity. Properties of this distribution depend on details of the data acquisition and on the size of the local neighborhood over which the contrast is calculated. We demonstrate that this local contrast can be characterized in terms of a log-normal distribution. Further, we show that the two defining parameters of this model can in turn be expressed in terms of the minimum speckle size and the extent of the local neighborhood. Performance of the model is illustrated with some typical optical coherence tomography data.     

Shape Measurement by use of Temporal Fourier transformation in Dual-Beam Illumination Speckle Interferometry

We outline a novel method for determining the shape of an object by use of temporal Fourier-transform analysis in dual-beam illumination speckle interferometry. The object whose shape is to be determined is rotated about an axis, and a number of frames of the image of the object motion are acquired. Temporal in-plane displacement that is due to the object rotation is related to the shape of the object and is retrieved from this large set of data by Fourier transformation. With this method one can determine the absolute height of the object with variable resolution, thereby allowing shapes of objects with large and small slopes to be determined. The theory of the method along with experimental results is presented.     

Robustness of reduced temporal phase unwrapping in the measurement of shape

The predictions of success rate and depth uncertainty for the negative exponential sequence used for temporal phase unwrapping of shape data are generalized to include the effect of a reduced sequence and speckle noise in single-channel and multichannel systems, respectively. To cope with the reduction of the sequence, a scaling factor is introduced. A thorough investigation is made of the performance of this algorithm, called the reduced temporal phase-unwrapping algorithm. Two different approaches are considered: a single-channel approach in which all the necessary images are acquired sequentially in time and a multichannel approach in which the three channels of a color CCD camera are used to carry the phase-stepped images for each fringe density in parallel. The performance of these two approaches are investigated by numerical simulations. The simulations are based on a physical model in which the speckle contrast, the fringe modulation, and random noise are considered the sources of phase errors. Expressions are found that relate the physical quantities to phase errors for the single-channel and the multichannel approaches. In these simulations the single-channel approach was found to be the most robust. Expressions that relate the measurement accuracy and the unwrapping reliability, respectively, with the reduction of the fringe sequence were also found. As expected, the measurement accuracy is not affected by a shorter fringe sequence, whereas a significant reduction in the unwrapping reliability is found as compared with the complete negative exponential sequence.     

Spectral and Dispersion Analysis of Laser Sources and Multimode Fibres Via the Statistics of the Intensity Pattern

Abstract

The statistics of an intensity pattern at the exit face of a multimode fibre excited by a quasimonochromatic source is analysed by means of an expression for speckle pattern contrast. Theoretical considerations that take advantages of both classical coherence formalism and guided-mode field representation of light propagating in multimode fibres lead to two equivalent expressions for speckle pattern contrast; the first is expressed in the time domain by using a source temporal coherence function and the second is expressed in the frequency domain by using a frequency correlation function of the source spectral density. Moreover, the modal guiding conditions in multimode fibre are in both expressions governed by a maximum group delay time difference. The feasibility of both expressions, especially the second, is demonstrated by analytic expressions for the speckle pattern contrast for seven different spectra, that is the influence of the source temporal coherence as well as the modal dispersion is thus clearly shown.     

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.     

Speckle motion artifact under tissue rotation

Speckle patterns in ultrasound images may move in a way which bears no simple relationship to the motion of the corresponding tissues. In some instances the speckle motion replicates the underlying tissue motion, in others it does not. The authors name “speckle motion artifact” the difference between the speckle and the underlying tissue motion. An echographic image formation model is used to study the motion artifact produced by a rotating phantom and observed by a linear scan imaging system with a Gaussian beam. The authors propose that when the tissue is modeled as a random array of small and numerous scatterers, such motion aberration be accounted for by the 2D phase characteristics of the imaging system. An analytic prediction of this motion artifact in relation to the imaging system characteristics (beam width, transducer frequency, pulse duration) is presented. It is shown that the artifact results from the curvature of the system point spread function, which in turn determines the curvature of the 2D phase characteristics. To the authors' knowledge, it is the first time a comprehensive model of ultrasonic speckle motion artifact is presented. The model has been developed to study rotation-induced artifact; the method is however quite general and can be extended to study the effects of other tissue motion, in particular deformation and shear     

Can laser speckle flowmetry be made a quantitative tool?

The ultimate objective of laser speckle flowmetry (and a host of specific implementations such as laser speckle contrast analysis, LASCA or LSCA; laser speckle spatial contrast analysis, LSSCA; laser speckle temporal contrast analysis, LSTCA; etc.) is to infer flow velocity from the observed speckle contrast. Despite numerous demonstrations over the past 25 years of such a qualitative relationship, no convincing quantitative relationship has been proven. One reason is a persistent mathematical error that has been propagated by a host of workers; another is a misconception about the proper autocorrelation function for ordered flow. Still another hindrance has been uncertainty in the specific relationship between decorrelation time and local flow velocity. Herein we attempt to dispel some of these errors and misconceptions with the intent of turning laser speckle flowmetry into a quantitative tool. Specifically we review the underlying theory, explore the impact of various analytic models for relating measured intensity fluctuations to scatterer motion, and address some of the practical issues associated with the measurement and subsequent data processing.     

Filter-based compounded delay estimation with application to strain imaging

Ultrasonic wave interference produces local fluctuations in both the envelope, known as speckle, and phase of echoes. Furthermore, such fluctuations are correlated in space, and subsequent motion estimation from the envelope and/or phase signal produces patterned, correlated errors. Compounding, or combining information from multiple decorrelated looks, reduces such effects. We propose using a filter bank to create multiple looks to produce a compounded motion estimate. In particular, filtering in the lateral direction is shown to preserve delay estimation accuracy in the filtered sub-bands while creating decorrelation between sub-bands at the expense of some lateral resolution. For Gaussian apodization, we explicitly compute the induced signal decorrelation produced by Gabor filters. Furthermore, it is shown that lateral filtering is approximately equivalent to steering, in which filtered sub-bands correspond to signals extracted from shifted sub-apertures. Field II simulation of a point spread function verifies this claim. We use phase zero and its variants as displacement estimators for our compounded result. A simplified deformation model is used to provide computer simulations of deforming an elastic phantom. Simulations demonstrate root mean square error (RMSE) reduction in both displacement and strain of the compounded result over conventional and its laterally blurred versions. Then we apply the methods to experimental data using a commercial elastic phantom, demonstrating an improvement in strain SNR.     

Speckle interferometry with temporal phase evaluation for measuring large-object deformation

We propose a new method for measuring large-object deformations byusing temporal evolution of the speckles in speckleinterferometry. The principle of the method is that by deformingthe object continuously, one obtains fluctuations in the intensity ofthe speckle. A large number of frames of the object motion arecollected to be analyzed later. The phase data for whole-objectdeformation are then retrieved by inverse Fourier transformation of afiltered spectrum obtained by Fourier transformation of thesignal. With this method one is capable of measuring deformationsof more than 100 mum, which is not possible using conventionalelectronic speckle pattern interferometry. We discuss theunderlying principle of the method and the results of theexperiments. Some nondestructive testing results are alsopresented.     

Spatial speckle correlometry in applications to tissue structure monitoring

Asymptotic behavior of temporal autocorrelation functions of speckle intensity fluctuations induced by tissue scanning with a focused probe beam is experimentally studied for the transition from a single-scattering to a multiple-scattering mode. Such parameters as the exponential factor (or the Hurst coefficient) and the Hausdo dimension are proposed for the characterization and the visualization of the variations of the studied tissues' optical properties in generalized form. We studied reversible transition between various scattering modes stimulated by the application of certain chemical agents to the human sclera samples using speckle intensity correlation analysis; corresponding results are presented. The possibilities of the scattering structures imaging with local estimations of the exponential factor of speckle intensity fluctuations are shown in in vitro experiments with samples of human skin epidermis.     

High-speed dynamic speckle interferometry: phase errors due to intensity, velocity, and speckle decorrelation

The recently developed technique of high-speed phase-shifting speckle interferometry combined with temporal phase unwrapping allows dynamic displacement fields to be measured, even for objects containing global discontinuities such as cracks or boundaries. However, when local speckle averaging is included, small phase errors introduced at each time step are accumulated along the time axis, yielding total phase values that depend strongly on the speckle rereference rate. We present an analysis of the errors introduced in the phase evaluation by three sources: intensity errors, velocity errors, and speckle decorrelation. These errors are analyzed when they act both independently and together, for the most commonly used phase-shifting algorithms, with computer-generated speckle patterns. It is shown that, in a controlled out-of-plane geometry, errors in the unwrapped phase map that are due to speckle decorrelation rise as the time between rereferencing events is increased, whereas those due to intensity and velocity errors are reduced. It is also shown that speckle decorrelation errors are typically more important than the intensity and velocity errors. These results provide guidance as to the optimal speckle rereferencing rate in practical applications of the technique.     

Temporal response of a random medium from speckle intensity frequency correlations

We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diffusion regime are in excellent agreement with the intensity temporal response measured directly with an ultrafast pulse laser and a streak camera. Our speckle correlation measurements also demonstrate sensitivity to inhomogeneous samples, highlighting the potential application for imaging within a scattering medium.     

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.     

Absolute measurement of roughness and lateral-correlation length of random surfaces by use of the simplified model of image-speckle contrast

We present a method of image-speckle contrast for the nonprecalibration measurement of the root-mean-square roughness and the lateral-correlation length of random surfaces with Gaussian correlation. We use the simplified model of the speckle fields produced by the weak scattering object in the theoretical analysis. The explicit mathematical relation shows that the saturation value of the image-speckle contrast at a large aperture radius determines the roughness, while the variation of the contrast with the aperture radius determines the lateral-correlation length. In the experimental performance, we specially fabricate the random surface samples with Gaussian correlation. The square of the image-speckle contrast is measured versus the radius of the aperture in the 4f system, and the roughness and the lateral-correlation length are extracted by fitting the theoretical result to the experimental data. Comparison of the measurement with that by an atomic force microscope shows our method has a satisfying accuracy.     

Reduced peak-hopping artifacts in ultrasonic strain estimation using the Viterbi algorithm

Internal strain resulting from tissue deformation can be estimated by correlation processing of speckle patterns within complex (i.e., radio frequency) ultrasound images acquired during deformation. At large deformations, the magnitude of the correlation coefficient peak can be significantly lower than unity, so that random speckle correlations will exceed the true peak. This effect is called ?peak hopping? and causes significant errors in displacement and deformation estimates. Here we investigate the Viterbi algorithm, a dynamic programming procedure, to overcome peak-hopping artifacts by finding the most likely sequence of hidden states in a sequence of observed events. It is well suited to motion estimation in elasticity- imaging studies because adjacent tissue elements remain adjacent following deformation. Particularly, tissue elements along an ultrasonic beam in one image lie along a 3-D continuous curve in the next image instant. The observed event in this case is the correlation coefficient of a pixel at a certain displacement. Radio-frequency data were generated before and after deformation with an average strain of 6%. Simulations were performed for a homogenous medium and for a medium with a stiffer inclusion. Results show that Viterbi processing of speckle-tracking outputs can significantly reduce peak-hopping artifacts.     

Determination of Teflon thickness with laser speckle. I. Potential for burn depth diagnosis

A quantitative method for determining the depth of burn eschar would aid surgeons in determining whether to excise and subsequently graft a burn wound. We hypothesize that tissue viability could be assessed by an analysis of the spatial modulation of near-field laser speckle by flowing blood. A feasibility study of the technique was performed with two-layer tissue phantoms used to simulate a burn wound. A sheet of polytetrafluoroethylene (PTFE) was used to simulate nonperfused burn eschar, and tissue perfusion within deeper layers was represented by Brownian motion from a scattering solution. A low-power He-Ne laser was focused onto the target, and the resulting speckle image was captured with a CCD camera and stored on a computer for further processing. The diameter of the speckle pattern was found to be directly proportional to the thickness of the overlying layer. These data suggest that the thickness of PTFE can be determined to ±100-μm accuracy with 95% confidence and may be suitable for burn depth detection in vivo.