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.     

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.     

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.     

Speckle-based three-dimensional velocity measurement using spatial filtering velocimetry

We present an optical method for measuring the real-time three-dimensional (3D) translational velocity of a diffusely scattering rigid object observed through an imaging system. The method is based on a combination of the motion of random speckle patterns and regular fringe patterns. The speckle pattern is formed in the observation plane of the imaging system due to reflection from an area of the object illuminated by a coherent light source. The speckle pattern translates in response to in-plane translation of the object, and the presence of an angular offset reference wave coinciding with the speckle pattern in the observation plane gives rise to interference, resulting in a fringe pattern that translates in response to the out-of-plane translation of the object. Numerical calculations are performed to evaluate the dynamic properties of the intensity distribution and the response of realistic spatial filters designed to measure the three components of the object's translational velocity. Furthermore, experimental data are presented that demonstrate full 3D velocity measurement.     

Optical in-plane strain field sensor

A whole-field speckle strain sensor is presented. The speckle strain sensor allows the measurement of all three in-plane components of the strain field simultaneously without touching the surface of the sample. The strain fields are extracted from the in-plane motion of defocused laser speckles in a telecentric imaging system. To distinguish the contribution to the speckle motion from surface translation, rotation, and strain, the speckle motion from three lasers with different illumination directions and wavelengths has to be analyzed separately. Simultaneous acquisition of the three individual speckle patterns is achieved by means of splitting the light from the lasers onto separate but synchronized detectors with the aid of dichroic mirrors. The motion of the speckles is calculated with digital speckle photography (speckle correlation), which enables the strain sensor to measure strain fields with noise levels as low as 10 microstrain.     

Distance measurements by speckle correlation of objective speckle patterns, structured by the illumination

Objective speckles produced by two beams overlapping and interfering on a rough object surface contain information about the angle of incidence of the two beams, and how well they overlap. We obtain the autocovariance function for such a speckle pattern, and demonstrate how the information carried by the objective speckles can be used to probe the distance between the object and the observation plane. From a distance of 75 mm to a distance of 150 mm, and using an angle of 0.3 deg between the two incident beams, we can measure the actual distance with an uncertainty of better than ±0.1% of the full range. As long as the beams overlap at the object surface, the proposed method can measure distance with an uncertainty inversely proportional to the spot size at the object.     

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.     

Real-time optical image subtraction and edge enhancement using ferroelectric liquid-crystal devices based on speckle modulation

We carried out real-time optical image subtraction and edge enhancement based on a speckle modulation technique by using ferroelectric liquid-crystal polarization switches and a ferroelectric liquid-crystal spatial light modulator. A ferroelectric liquid-crystal spatial light modulator is employed as a real-time and multiple-exposure optical device, and successful results are obtained from three-exposure images modulated by speckles. Thus, image subtraction and edge enhancement are realized in real time. The whole operation is performed within several milliseconds with modest operating conditions. Because the spatial light modulator has a high resolution of greater than 100 line pairs/mm and can store fine speckle patterns, the image qualities we obtained are quite satisfactory.     

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     

Speckle orientation in paraxial optical systems

The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.     

Femtosecond laser speckles

The concept of femtosecond laser speckles is put forward. The theory of a speckle pattern in light of finite bandwidth is applied to describe femtosecond laser speckles. Basic representations of the contrast and the spectral correlation of femtosecond laser speckles are presented. The relationship between the speckle contrast and the bandwidth of a femtosecond laser is given. Experimental results are given that indicate an obvious difference between the speckle patterns produced by a continuous-wave laser and those produced by a femtosecond laser.     

Speckle reduction in laser projection systems by diffractive optical elements

In laser projection systems the observer in the far field of the image points on the screen will recognize serious speckle noise. There are many methods to reduce or eliminate speckles in the near field by reducing or eliminating temporal or spatial coherence of the laser. But for the far field it is hardly possible to change the coherence properties of laser sources so that speckles will disappear. We propose a new method for eliminating speckles in the far field by using a diffractive optical element. The intensity modulation depth in the far-field speckle pattern can be reduced to a few percent while good beam quality is preserved.     

Improved speckle projection profilometry for out-of-plane shape measurement

An improved speckle projection profilometry that combines the projection of computer generated random speckle patterns using an ordinary LCD projector and the two-dimensional digital image correlation technique for in-plane displacements measurement is proposed for accurate out-of-plane shape and displacement measurements. The improved technique employs a simple yet effective calibration technique to determine the linear relationship between the out-of-plane height and the measured in-plane displacements. In addition, the iterative spatial domain cross-correlation algorithm, i.e., the improved Newton-Raphson algorithm using the zero-normalized sum of squared differences correlation criterion and the second-order shape function was employed in image correlation analysis for in-plane displacement determination of the projected speckle patterns, which provides more reliable and accurate matching with a higher correlation coefficient. Experimental results of both a regular cylinder and a human hand demonstrate that the proposed technique is easy to implement and can be applied to a practical out-of-plane shape and displacement measurement with high accuracy.     

Displacement measurement of speckles using a 2-D level-crossing technique

This paper proposes a new displacement method for measuring speckles using a 2-D level-crossing technique. The crossing points in space of the speckle intensity traversing a specified level are analyzed two-dimensionally by using a TV-computer system. In an actual analysis, an occurrence rate histogram of the distance vectors determined by connecting the crossing points obtainable before and after displacement of speckles is investigated. It is found that the vectorial displacement of speckles can be measured from the position of the maximum occurrence in the bivariate histogram with respect to the magnitude and angle by which the displacement vector is characterized. The vectorial displacement of speckles is related to the movement of an object.     

Diversity detection of speckles for double-wavelength interferometry on rough surfaces

When the topography of a rough surface is measured with a double-wavelength interferometer, the phase error of the signal corresponding to the synthetic wavelength increases in the vicinity of dark speckles. To overcome this problem we perform an amplitude-dependent averaging of the synthetic phase over independent speckles (diversity detection). We either use spatially neighboring speckles or in the case of depolarizing surfaces, we use speckles of the same spatial mode, but with orthogonal polarizations. For the latter case the lateral resolution stays unaffected. The reduction of the speckle noise is demonstrated experimentally for a laterally scanning double-wavelength interferometer with superheterodyne detection of the synthetic phase.     

High resolution speckle interferometry using virtual speckle pattern produced by information of deformation process

A high resolution new fringe analysis method for ESPI with only one camera is proposed by using features of speckle interferometry in a deformation process of a measured object. The profile of intensity of each speckle of the speckle patterns in the deformation process is analyzed by the Hilbert transform. A virtual speckle pattern for creating a carrier fringe image is produced artificially by using the information of profiles of intensities of speckles. The deformation map of the measured object can be detected by the virtual speckle pattern in an operation based on the spatial fringe analysis method. Experimental results show that the difference between the results by the new and the ordinary methods is 0.1 rad as standard deviation. From the results, it is confirmed that the high resolution measurement can be performed by this method the same as compared to the ordinary measurement method which needs to employ three speckle patterns.     

Three-dimensional deformation field measurement with digital speckle correlation

Digital speckle correlation is based on a detailed analysis of changes in speckle images that are recorded from laser-illuminated rough surfaces. The two in-plane components are obtained by cross-correlation of corresponding subimages, a method also known as digital speckle photography. The local gradient of the hitherto inaccessible out-of-plane component is determined from the characteristic dependence of the speckle correlation on the spatial frequency. A detailed experimental study is carried out to analyze the new technique for systematic and random measuring errors. For moderate decorrelation the accuracy of the out-of-plane measurement is better than lambda/10 and thus comparable with interferometric techniques. Yet the extremely simple and robust optical setup is suited to nondestructive-testing applications in harsh environments. The quality of the deformation maps is demonstrated in a practical application.     

Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.     

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.