Simultaneous measurement of velocity and length of moving surfaces by a speckle velocimeter with two self-mixing laser diodes

A novel laser speckle velocimeter with two self-mixing laser diodes (SM-LD's) for velocity and length measurements of moving surfaces is reported. The mean frequency of the speckle signal obtained in the measurement system depends on the surface path illuminated by the SM-LD. This behavior of the speckle signal in the SM-LD's is exploited to detect the front and the end edges of a target surface by sampling continuously the number of intensity changes in a speckle signal waveform. Once the edges are determined, the velocity and the length of the surface are calculated easily. The error for length and velocity measurements of a target with a homogeneous rough plane surface of 60-mm length, moving at a velocity of 200 mm/s, can be as low as 2.1% and 1.75%, respectively.     

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.     

Signal-to-noise based local decorrelation compensation for speckle interferometry applications

Speckle-based interferometric techniques allow assessing the whole-field deformation induced on a specimen due to the application of load. These high sensitivity optical techniques yield fringe images generated by subtracting speckle patterns captured while the specimen undergoes deformation. The quality of the fringes, and in turn the accuracy of the deformation measurements, strongly depends on the speckle correlation. Specimen rigid body motion leads to speckle decorrelation that, in general, cannot be effectively counteracted by applying a global translation to the involved speckle patterns. In this paper, we propose a recorrelation procedure based on the application of locally evaluated translations. The proposed procedure implies dividing the field into several regions, applying a local translation, and calculating, in every region, the signal-to-noise ratio (SNR). Since the latter is a correlation indicator (the noise increases with the decorrelation) we argue that the proper translation is that which maximizes the locally evaluated SNR. The search of the proper local translations is, of course, an interactive process that can be facilitated by using a SNR optimization algorithm. The performance of the proposed recorrelation procedure was tested on two examples. First, the SNR optimization algorithm was applied to fringe images obtained by subtracting simulated speckle patterns. Next, it was applied to fringe images obtained by using a shearography optical setup from a specimen subjected to mechanical deformation. Our results show that the proposed SNR optimization method can significantly improve the reliability of measurements performed by using speckle-based techniques.     

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.     

Random phase plate for wavefront sensing via phase retrieval and a volume speckle field

A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.     

Optimum determination of speckle size to be used in electronic speckle pattern interferometry

Characteristics of the fringe pattern detected by an electronic speckle pattern interferometer, in conditions in which a test object deforms in an arbitrary direction and the speckle intensity is detected over a pixel area in the TV camera to be used, have been investigated from two aspects: speckle noise reduction and fringe contrast. The main result is that the fringes are obtained with high contrast and low speckle noise, if the speckle size is selected by the optical system so as to be smaller than the pixel size. This result is applicable to highly accurate measurements of the out-of-plane displacements of the test object, whose in-plane displacement is small.     

Speckle reduction in optical coherence tomography by adaptive total variation method

An adaptive total variation method based on the combination of speckle statistics and total variation restoration is proposed and developed for reducing speckle noise in optical coherence tomography (OCT) images. The statistical distribution of the speckle noise in OCT image is investigated and measured. With the measured parameters such as the mean value and variance of the speckle noise, the OCT image is restored by the adaptive total variation restoration method. The adaptive total variation restoration algorithm was applied to the OCT images of a volunteer’s hand skin, which showed effective speckle noise reduction and image quality improvement. For image quality comparison, the commonly used median filtering method was also applied to the same images to reduce the speckle noise. The measured results demonstrate the superior performance of the adaptive total variation restoration method in terms of image signal-to-noise ratio, equivalent number of looks, contrast-to-noise ratio, and mean square error.     

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.     

Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.     

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.     

Optimization of fringe pattern calculation with direct correlations in speckle interferometry

A direct correlation technique is used to calculate correlation fringe patterns from consecutive speckle patterns acquired with a dual-beam electronic speckle interferometer. Although more calculations are required than in standard image differencing routines, an advantage of the method is that the illumination over the surface of the object need not be uniform. In the method, Pearson's coefficient of correlation between the intensities within a set of adjacent pixels is calculated. This has the added advantage of being directly related to the theoretical phase-dependent correlation. A mapping of this measure of correlation results in the correlation fringe pattern. Laboratory tests were carried out with in-plane translations ranging from 5 to 45 mum. The correlation calculations were carried out by using cells (square sets of pixels) in the raw speckle images with dimensions ranging from 2 pixels x 2 pixels to 19 pixels x 19 pixels. Both cell dimension and translation magnitude dependent decorrelation effects influence the quality of the correlation fringe patterns.     

Nontranslational three-dimensional profilometry by chromatic confocal microscopy with dynamically configurable micromirror scanning

A confocal microscope profilometer, which incorporates chromatic depth scanning with a diffractive optical element and a digital micromirror device for configurable transverse scanning, provides three-dimensional (3D) quantitative measurements without mechanical translation of either the sample or the microscope. We used a microscope with various objective lenses (e.g., 40x, 60x, and 100x) to achieve different system characteristics. With a 100x objective, the microscope acquires stable measurements over a 320 mum x 240 mum surface area with a depth resolution of 0.39 mum at a 3-Hz scan rate. The total longitudinal field of view is 26.4 mum for a wavelength tuning range of 48.3 nm. The FWHM value of the longitudinal point-spread function is measured to be 0.99 mum. We present 3D measurements of a four-phase-level diffractive element and an integrated-circuit chip. The resolution and the accuracy are shown to be equivalent to those found with use of conventional mechanical scanning.     

Automatic measurement of velocity and length of moving plate usingself-mixing laser diode

We propose and demonstrate to automatically measure both a velocity and a length of a moving plate, employing a novel laser speckle velocimeter using a self-mixing laser diode (SM-LD). We derive two empirical equations including velocity of length of a moving plate made of white paper or plastic. After determining a pair of constants fs(0) and β in advance calibration, we can automatically obtain velocity or length from the measured mean speckle signal frequency and/or the number of speckle pulses counted during the measuring time. The investigated range of velocity and length is 100 mm/s to 950 mm/s, and 10 mm to 100 mm, respectively. The measurement accuracy of the velocity and the length is approximately 1% and a few percent, respectively     

Speckle properties of the logarithmically transformed signal in optical coherence tomography

We discuss the statistical properties of speckle of the logarithmically transformed signal in optical coherence tomography (OCT) both theoretically and experimentally. OCT signals of Intralipid solution with different volume particle concentrations ρ (correspondingly, scattering coefficient μ(s) ranges from 1.25 to 25.11 mm(-1)) were measured and analyzed under two different focusing conditions [numerical apertures (NAs) of the objective lens of 0.13 and 0.25]. We found that the effect of the speckle noise can be suppressed by displaying OCT images in the logarithmic scale and by using the objective lens with a higher NA. We also found that the speckle properties are correlated with the scattering properties of the sample, which may be used to characterize the scattering properties of biological tissue. The simulated OCT image and the in vitro OCT image of a rat liver are used as examples to demonstrate the feasibility of the method.     

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.     

Phase-shifted dynamic speckle pattern interferometry at 1 kHz

We describe a phase-shifting out-of-plane speckle interferometer operating at 1 kHz for studying dynamic events. The system is based on a Pockels cell that is synchronized to a high-speed video camera to ensure that the phase shifting occurs between frames. Phase extraction is performed by use of a standard four-frame algorithm, and temporal phase unwrapping allows sequences of several hundred absolute (rather than relative) displacement maps to be obtained fully automatically. The maximum theoretical surface velocity of 67 mum s(-1) is a factor of 40 greater than can be achieved with a speckle interferometer based on a conventional video camera. We test the system using a target that is displaced with constant speed in a direction normal to its surface by means of a piezoelectric transducer. The system's performance in a practical situation is illustrated with measurements on a thin plate undergoing out-of-plane deformation.     

Experimental investigation of saturated degenerate four-wave mixing for quantitative concentration measurements

Degenerate four-wave mixing (DFWM) line shapes and signal intensities are measured experimentally in well-characterized hydrogen-air flames operated over a wide range of equivalence ratios. We use both low (perturbative) and high (saturating) beam intensities in the phase-conjugate geometry. Resonances in the A 2Sigma+ -X 2II (0,0) band of OH are probed with multiaxial-mode laser radiation. The effects of saturation on the line-center signal intensity and the resonance linewidth are investigated. The DFWM signal intensities are used to measure OH number densities in a series of near-adiabatic flames at equivalence ratios ranging from 0.5 to 1.5. Use of saturating pump intensities minimizes the effects of beam absorption, providing more-accurate number density measurements. The saturated DFWM results are in excellent agreement with OH absorption measurements and equilibrium calculations of OH number density. The polarization dependence of the P(1)(2) and R(2)(1) resonances is investigated in both laser intensity regimes. There is a significant change in relative reflectivities for different polarization configurations when saturated.     

A laser-based strain sensor with optical preprocessing

This paper is concerned with a method of non-contacting measurement of mechanical strain within specimen. It describes a new optical setup to perform high-speed digital laser-speckle correlation with the ultimate aim to deduce surface element displacements associated with the translation of laser-speckles emanating from those surface elements. The novel optical setup combined with the application of line-scan cameras attached to a digital signal processor allows measurement rates that for most practical purposes are only limited by the integration time of the camera necessary to obtain properly exposed images. Instead of obtaining a two dimensional vector by searching for the best space-lag of a digitally calculated cross-correlation estimate of the initial and translated speckle images, a single displacement value (associated only with the sensitive direction) is obtained by finding the space-lag of optically preprocessed almost one-dimensional speckle fields. The necessary optical preprocessing is performed in the Fourier-plane of the imaging optics. This way the numerical complexity of the algorithm running on the digital signal processor is greatly reduced resulting in lower processing time per frame. System considerations for practical strain measurements are detailed     

Speckle-motion artifact under tissue shearing

Research has shown that, for a rotating phantom, the speckle pattern may not replicate the phantom motion, rather it may show a large lateral translation component in addition to rotation. This translation effect was labeled speckle-motion artifact. An image formation model has been shown to explain the phenomenon, pointing to the curvature of the imaging system point spread function (PSF) at the origin of this effect. The present paper extends this analysis and proposes a model, which predicts that a lateral motion artifact also would occur with shear motion. In the model, the artifact is found to be proportional to the shear angle and dependent of shear orientation, being maximal for shear that runs parallel to the axial direction; as for rotation, the artifact increases with frequency and beamwidth. This would mean that, when viewing a parabolic flow in the far field or with a highly curved PSF, an apparent contraction/expansion pattern in the direction of the vessel wall would be superimposed to the real velocity profile. In elastography, when viewing an inclusion subjected to an axial strain, four motion artifact regions are expected near the inclusion. The model is developed using the Fourier domain representation of the speckles for tissue-motion compensated signals, also called Lagrangian speckle. It can explain the artifact in terms of a simple spectral translation of a parabolic phase profile; given this, it is shown the artifact would be proportional to the lateral derivative of the axial displacement field. The spectral representation of Lagrangian speckle, for shear, also provides a simple geometrical interpretation for speckle decorrelation in terms of the shear strength and orientation, and in terms of the beam characteristics, i.e., the axial and lateral bandwidth.     

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.