Simple model for image-plane polychromatic speckle contrast.

A simple geometrical model was developed for calculation of the contrast of a polychromatic image-plane speckle pattern from a source of light with high spatial coherence. It is based on counting the number of independent speckle patterns that contribute to a given point in the image plane. This results in a simple equation for the contrast as a function of imaging geometry; relative orientation of the projection direction, observation direction, and specimen normal; bandwidth of the light source; and surface roughness. Its validity was established by comparison with an exact solution: rms errors in the calculated contrast were only 0.033 over a wide range of parameter values likely to be encountered in practice.     

Speckle contrast of the sum of N partially correlated speckle patterns

In this paper a general method is presented for calculating the theoretical speckle contrast of a sum of correlated speckle patterns, motivated by the need to suppress the presence of speckle in laser projection displays. The method is applied to a specific example, where correlated speckle patterns are created by sequentially passing light through partially overlapping areas on a diffuser, before being projected onto a screen. This design makes it possible to find a simple expression for the correlation between speckle patterns. When the set of correlations involves symmetry, it is shown that the expression for the speckle contrast becomes simpler. The difference in performance between discretely and continuously varying speckle patterns is also investigated. In an example with speckle reduction by a rotating sinusoidal grating, it is found that continuous variation gives a speckle contrast that is 0.61 times the contrast obtained by discretely summing the maximum number of independent patterns.     

Experimental Study of the Laser Speckle Phase in the Image Field

Statistical properties of the laser speckle phase in the image field were experimentally studied under the condition that the speckle field obeys Gaussian statistics. The speckle phase was measured in relation to the phase variations of light passing through a diffuse object and the defocusing of the imaging system. It is found that the phase variations of speckles at the image plane are smaller than those of light passing through the object. The anomaly of the speckle phase in the neighbourhood of the Gauss image plane is also found and interpreted in relation to the dip phenomenon of the speckle contrast.     

Speckle suppression in projection displays by using a motionless changing diffuser

Speckle suppression in projection displays with a laser light source can be achieved by imaging a changing diffuser with random phase cells onto the screen. Theoretical expressions for the speckle contrast in this method have been earlier obtained in the case when different realizations of the phase diffuser produced statistically independent patterns of the light field on the screen. In the present paper, these expressions are generalized in the case when different realizations of the phase diffuser produce partly correlated speckle patterns. The possible structure of a motionless changing diffuser is presented. It includes a dynamic diffractive optical element (DDOE) and a light homogenizer. The DDOE can be based on the electrically controlled spatial light modulator (SLM) with a deformable polymer layer. This type of SLM can handle high light power and, therefore, can be used in projection displays with powerful laser beams.     

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.     

Ultrasound-modulated optical tomography of biological tissue by use of contrast of laser speckles

Ultrasound-modulated optical tomography based on the measurement of laser-speckle contrast was investigated. An ultrasonic beam was focused into a biological-tissue sample to modulate the laser light passing through the ultrasonic column inside the tissue. The contrast of the speckle pattern formed by the transmitted light was found to depend on the ultrasonic modulation and could be used for imaging. Variation in the speckle contrast reflected optical inhomogeneity in the tissue. With this technique, two-dimensional images of biological-tissue samples of as much as 25 mm thick were successfully obtained with a low-power laser. The technique was experimentally compared with speckle-contrast-based, purely optical imaging and with parallel-detection imaging techniques, and the advantages over each were demonstrated.     

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     

Quantitative determination of dynamical properties using coherent spatial frequency domain imaging

Laser speckle imaging (LSI) is a fast, noninvasive method to obtain relative particle dynamics in highly light scattering media, such as biological tissue. To make quantitative measurements, we combine LSI with spatial frequency domain imaging, a technique where samples are illuminated with sinusoidal intensity patterns of light that control the characteristic path lengths of photons in the sample. We use both diffusion and radiative transport to predict the speckle contrast of coherent light remitted from turbid media. We validate our technique by measuring known Brownian diffusion coefficients (D(b)) of scattering liquid phantoms. Monte Carlo (MC) simulations of radiative transport were found to provide the most accurate contrast predictions. For polystyrene microspheres of radius 800 nm in water, the expected and fit D(b) using radiative transport were 6.10E-07 and 7.10E-07 mm2/s, respectively. For polystyrene microspheres of radius 1026 nm in water, the expected and fit D(b) were 4.7E-07 and 5.35 mm2/s, respectively. For scattering particles in water-glycerin solutions, the fit fractional changes in D(b) with changes in viscosity were all found to be within 3% of the expected value.     

Dependence of polychromatic-speckle-pattern contrast on imaging and illumination directions

An analytical relationship between the contrast in polychromatic image speckle patterns and the positions of the diffuse object's surface normal, the illumination, and the axis of the imaging system has been obtained. When the axis coincides with the direction in which the mirror reflects the illumination about the normal, the contrast in the image speckle pattern is the greatest. Some qualitative experimental results are also given.     

激光散斑引起象强度中心漂移的计算机模拟

本文对这个基本不确定度进行了计算机模拟研究，所得模拟曲线与Ｒ．Ｇ．Ｄｏｒｓｃｈ，Ｇ．Ｈａｕｓｌｅｒ等人的研究基本一致。此外，还对基本不确定度与表面粗糙度的关系，基本不确定度与成象系统点扩散函数内所包含的相关单元的关系进行了研究。     

用点扩展函数确定卫星反射后的脉冲强度

卫星激光测距系统是一个非相干成象光学系统。卫星形状效应是由于卫得上不同位置的反射器对光子反射的时间不同而引起的脉冲强度重新分布的现象。非相干成象系统在等晕区内是空间不变性的光强线性系统。成象光学系统中象强度等于输入物强度与光瞳点扩展函数的卷积。用卫星的点扩展函数描述卫星形状效应,能非常简便地计算出被卫星反射后的脉冲强度分布。讨论了激光测距卫星的点扩展函数的求解方法和表达形式,并分别推导和计算了Lageos卫星和自行设计卫星的点扩展函数以及点扩展函数作用后的脉冲强度分布。     

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.     

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.     

Calculation of speckle displacement, decorrelation, and object-point location in imaging systems

My purpose here is to outline a method for calculating the fundamental behavior of speckle patterns in imaging systems. The theory of speckle displacement and decorrelation to include imaging at a general oblique angle is extended to more imaging systems, and explicit formulas are given for the image-point-object-point relationship that is important when defocused speckle is used. The intermediate results can be reused for optical systems other than those presented here. The image-speckle displacement analyzed in the three systems is expressed equivalently. The speckle decorrelation is in general larger in a single-lens system than in a two-lens system and can be minimized by proper design of the system.     

Determination of optimal exposure time for imaging of blood flow changes with laser speckle contrast imaging

Laser speckle contrast imaging is becoming an established method for full-field imaging of cerebral blood flow dynamics in animal models. The sensitivity and noise in the measurement of blood flow changes depend on the camera exposure time. The relation among sensitivity, noise, and camera exposure time was investigated experimentally by imaging the speckle contrast changes in the brain after electrical forepaw stimulation in rats. The sensitivity to relative changes in speckle contrast was found to increase at longer exposure times and to reach a plateau for exposure times greater than approximately 2 ms. However, the speckle contrast noise also increases with exposure time and thus the contrast-to-noise ratio was found to peak at an exposure time of approximately 5 ms. Our results suggests that approximately 5 ms is an optimal exposure time for imaging of stimulus-induced changes in cerebral blood flow in rodents.     

Surface roughness measurement by means of polychromatic speckle elongation

A new approach for determining the roughness of engineering surfaces that is applicable to industrial in-process measurements is introduced. Laser speckle patterns, arising from light scattered from rough surfaces that are illuminated by polychromatic laser light, are detected in the far-field region. The incoherent superposition of these light intensities and the angular dispersion cause the effect of speckle elongation. This is characterized by increasing speckle widths and leads to a radial structure of the speckle patterns. With increasing surface roughness, the elongation is replaced more and more by the decorrelation of the monochromatic speckle patterns for the different wavelengths. Such effects were detected with the CCD technique and analyzed by local autocorrelation functions of intensity fluctuations that were calculated for different areas of the speckle patterns. The results of surface-roughness determination by means of the speckle elongation effect are presented.     

Application of bispectral speckle imaging to near-diffraction-limited imaging in the presence of unknown aberrations

A laboratory experiment that demonstrates near-diffraction-limited imaging of a detailed object in the presence of unknown fixed aberrations in the imaging system is described. A random-phase plate is introduced in a pupil plane of the imaging system to eliminate the effect of fixed aberrations in the system. We employ a bispectral speckle imaging technique to recover the object from speckled images affected by both the random-phase fluctuations induced by the random-phase plate and the fixed aberrations present in the imaging system. For the case where the random phase is assumed to obey Gaussian statistics an approximate form of the bispectral speckle transfer function is obtained with an asymptotic expansion. This approximate form of the transfer function shows the diffraction-limited nature of bispectral speckle imaging when the standard deviation of the random-phase fluctuations is of the order of a wavelength of light. Experimental results are presented for fixed aberrations associated with lens tilt and defocus in the imaging system.     

Speckle in the 4F optical system

We provide a comprehensive analysis of the space and wavelength dependence of speckle generated by a thin diffuser and imaged by a 4F optical system. The use of this space-invariant system is shown to lead to the well-known features of speckle patterns in an analytically simple and elegant manner, thereby providing a clear insight into speckle in an optical configuration that includes the Fresnel zone, the optical Fourier transform plane, and the image plane. In our analysis we assume a white-noise diffuser. The spatial variation mainly depends on the imaging system, whereas the wavelength dependence is related to diffuser heights. Motion dynamics of speckle are also included.     

Influence of geometry on polychromatic speckle contrast

Understanding speckle behavior is very important in speckle metrology application. The contrast of a polychromatic speckle depends not only on surface roughness and the coherence length of a light source, as shown in previous works, but also on optical geometry. We applied the Fresnel approach of diffraction theory for the free-space geometry and derived a simple analytical relationship between contrast, coherence length, size of illuminated spot, and distances between source, object, and observation plane. The effect of contrast reduction is found to be significant for low-coherence light sources.     

Aspect ratio of elongated polychromatic far-field speckles of continuous and discrete spectral distribution with respect to surface roughness characterization

Here polychromatic speckle patterns generated either by a polychromatic light source that emits at discrete frequencies or by a light source showing a continuous narrow-band spectral distribution are studied. The purpose here is the application of polychromatic speckle-pattern analysis to an in-process surface roughness characterization. To compare the coherence properties of the different polychromatic light sources, first a modified definition of the coherence length is introduced. Furthermore, the relevant optical phenomena, namely, the speckle elongation caused by the angular dispersion and the roughness-dependent speckle decorrelation, are summarized. It is shown that light sources with a continuous spectral distribution have essential advantages in comparison with discrete wavelength sources. The theoretical results are confirmed by experimental investigations based on a digital algorithm for the evaluation of CCD images of polychromatic speckle patterns, which are recorded in the Fourier plane of a Fourier-transforming lens.