Measurement of surface roughness properties using speckle patterns with non-gaussian statistics

The surface roughness properties (i.e. the rms surface roughness and the correlation length) of strong diffuse objects are investigated by using the speckle patterns which obeys the non-gaussian statistics. The intimate linear relation is found to exist between the rms surface roughness of objects and the maximum contrast obtained from the varying curves of the average image speckle contrast as a function of the point spread of an optical imaging system. The correlation length of surface roughness of objects is related to the averaged intensity distribution of speckle patterns produced at the far-field diffraction plane. It now becomes clear that the rms roughness and the correlation length of strong diffuse objects are determined, respectively, from the maximum speckle contrast at the image plane and the averaged speckle intensity distribution at the far-field diffraction plane.     

First order statistics of speckle produced by weak scattering media

A weak scattering medium produces random phases in a transmitted or reflected wavefront distributed over less than 2π. The far-field speckle pattern has a central maximum. The statistics of intensity in this maximum are calculated and the applications of the results to surface roughness measurement are indicated.     

Simulation of dynamic speckle sequences and its application to the analysis of transient processes

Dynamic speckle has been used in recent years to analyse several transient processes that are produced in industrial and biological applications. We present here a numerical simulation to generate a temporal sequence of dynamic speckle patterns which is based on a model used for speckle formation by the superposition of waves from discrete scattering centres. It is demonstrated that the first and second statistics of the intensity of each speckle image, the time history of the speckle pattern, the temporal evolution of the correlation coefficient, and the power spectral density of the intensity generated by the proposed model reproduce quite well those obtained from experimentally recorded data. The process of a fast drying paint is presented as an example of the application of the proposed numerical model.     

Speckle evolution of diffusive and localized waves

We show that while the statistics of static speckle patterns are generic, fluctuations in the change within speckle patterns are greatly enhanced in the localization transition. The probability distributions of the displacement of phase singularities and the standard deviations of the changes of phase and intensity with frequency shift of incident microwave radiation are given in terms of the same expression which describes the probability distribution of total transmission. This function depends only upon a single parameter, the variance of the corresponding variable. The changing statistics in the localization transition reflects the number of underlying electromagnetic modes with which the incident wave interacts.     

Singularities in speckled speckle

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields, namely, optical vortices in scalar (one polarization component) fields and C points in vector (two polarization components) fields. In single correlation length fields both types of singularities tend to be more or less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous; for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices and azimuthal extrema can outnumber C points by factors that can easily exceed 10(4) for experimentally realistic source parameters.     

Comparison between instantaneous and integral intensities in dynamic speckle pattern interferometry

A new speckle measurement technique called temporal speckle pattern interferometry or time sequential speckle pattern interferometry has been developed recently. Its principle is that by capturing the temporal speckle patterns related to the object deformation or displacement, the whole-field displacement, the amplitude of the vibrating object and the shape of the tested object can be calculated through speckle intensity fluctuation scanning technique or Fourier-transforming method. In this paper, we combine the analytical and numerical methods to simulate the properties of the time demodulation in temporal speckle patterns interferometry techniques. The performance of three kinds of temporal phase sequences, power, exponential and harmonic phase sequences, are studied with the parameters of temporal speckle intensity fluctuation, the value of the spatial phase term, optical integral time of the recording camera and the initial phase of the temporal speckle intensities. The results indicate that the normalized value and period change of the instantaneous intensity are nearly coincident with that of the integral intensity for the harmonic temporal phase sequences and are different for the power and exponential temporal phase sequences.     

Transmission processes in random patterns of subwavelength holes

The optical transmission of random patterns of holes is believed to depend on the transmission of the independent holes only. By comparing the transmission spectra of random patterns with different densities, we show that the quasi-cylindrical wave plays an important role in the transmission of samples with large hole densities. Furthermore, we report on a speckle pattern seen in the transmission of these arrays. By studying the degree of depolarization in this speckle pattern, as a function of hole density, we are able to quantify the role of surface plasmons to the transmission.     

Measurements of femtosecond temporal speckle field of a random medium

The femtosecond temporal speckle field of a random medium is studied theoretically and experimentally. Femtosecond temporal speckle arises from the interference of multiple randomly scattered electric fields. The femtosecond temporal speckle field is measured with a cross-correlation frequency-resolved optical gating method. The spatial average of the speckle field yields a smooth transmitted profile. The speckle field is a circular complex Gaussian variable because the scattered light beams from different trajectories have no correlation with each other. The field and the intensity profiles of individual speckle spots fluctuate randomly in time. The ensemble average of the temporal intensity profiles converges, thereby yielding the photon travel time probability distribution function.     

Experimental measurements of topological singularity screening in random paraxial scalar and vector optical fields

There exists a substantial body of theory that predicts mutual screening of signed topological singularities (topological charges) in random optical fields (speckle patterns). Such screening appears to be rather mysterious because there are neither energetic nor entropic reasons for its existence. We present the first experimental confirmation of mutual screening by the stationary points of the intensity, the canonical optical scalar field, and of mutual screening by C points in elliptically polarized light, the generic optical vector field. We also elucidate specific aspects of the geometry and topology of these fields that we argue give rise to screening.     

Mechanism of speckle reduction in laser-microscope images using a rotating optical fiber

The reduction mechanism of speckles appearing in laser-microscope images is studied theoretically and experimentally when an object is illuminated by laser light through a rotating multimode optical fiber. The principle of the speckle reduction is based on independent addition of microscope images with boiling-like speckles as a result of the rotational motion of the optical fiber used for illumination. Especially, the speckle reduction is evaluated from first-order statistics of the speckle intensity in which its saturation effect is taken into consideration.     

Encryption and decryption using a sandwich phase diffuser made by using two speckle patterns and placed in the Fourier plane: Simulation results

In the present paper, we describe the encryption and decryption of two-dimensional images. The encryption is done by employing a sandwich phase diffuser made by using two elongated speckle patterns, and placed in the Fourier plane of a double random phase encoding system. After encryption, the two constituent phase diffusers of such a sandwich diffuser are separated. During decryption, if the conjugate of either of the two elongated phase speckle patterns is used, the image cannot be retrieved. Correct decryption is also not possible if a sandwich diffuser with any of the phase speckle patterns is shifted in position with respect to the other. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the sandwich diffuser, and then the product is further Fourier transformed. It is possible to generate the image only if both the elongated phase speckle patterns are matched point-to-point and then the proper conjugate is made. The use of elongated speckle patterns in constituting a sandwich phase diffuser makes the system less complicated as compared to the use of a sandwich diffuser made with normal speckle patterns, enabling an easy alignment of the random phase diffuser at the time of rejoining the constituent diffusers for making the right key. The ease of alignment is due to the reduction of the requirement of 360° scanning at the time of rejoining these diffusers with little reduction in the security of the system. Simulation results are presented in support of the proposed idea. For optical implementation, the decrypted image may be obtained by generating a phase conjugate wave by the phase conjugation technique, and passing through the same sandwich phase diffuser. To evaluate the reliability of the technique, mean square error (MSE) between the decrypted and original image has been calculated.     

Enhanced wavefront reconstruction by random phase modulation with a phase diffuser

A phase retrieval technique for enhanced wavefront reconstruction using random phase modulation and a phase diffuser is proposed. The speckle field generated is sampled at multiple axially displaced planes and the speckle patterns are used in an iterative algorithm based on the optical wave propagation in free space. The presentation of this technique is carried out using two setups. In the first setup, a diffuser plate is placed at the image plane of a metallic test object. The benefit of randomizing the phase of the object wave is the enhanced intensity recording due to high dynamic range of the diffusely scattered beam. The use of demagnification optics will also allow the investigations of relatively large objects. In the second setup, a transparent object is illuminated using a wavefront with random phase and constant amplitude by positioning the phase diffuser close to the object. The benefit of phase-only modulation is the increased resolution of the phase structures of the transparent test objects.     

Speckle characteristics of simulated deep Fresnel region under shadowing effect

After the three-dimensional self-affine fractal random surface simulation, we use the optical scattering theory to calculate the deep Fresnel region speckle(DFRS) under consideration of the more strict shadowing effect. The evolution of DFRS with the scattering distance and the intensity probability distribution are studied. It is found that the morphology of the scatterer has an antisymmetric relationship with the intensity distribution of DFRS, and the effect of micro-lenses on the scattering surface causes the intensity probability distribution of DFRS to deviate from the Gaussian speckle in the high light intensity area.     

地面对激光雷达信号散射的统计研究

从理论角度研究了利用高斯光束照射远场目标时,激光散斑的统计特性.导出了散射光场的自相关函数和光强度的二阶矩的解析表达式,计算了激光散斑的面积.研究表明:在接收面上,光强的分布与目标表面高度的相关长度和均方根高度密切相关,激光散斑面积和散斑光强的相关系数只与激光束腰的尺度有关,与目标的均方根高度和相关长度无关. 关键词： 激光散斑 自相关函数 高斯分布 协方差     

Fractality of light's darkness

Natural light fields are threaded by lines of darkness. For monochromatic light, the phenomenon is familiar in laser speckle, i.e., the black points that appear in the scattered light. These black points are optical vortices that extend as lines throughout the volume of the field. We establish by numerical simulations, supported by experiments, that these vortex lines have the fractal properties of a Brownian random walk. Approximately 73% of the lines percolate through the optical beam, the remainder forming closed loops. Our statistical results are similar to those of vortices in random discrete lattice models of cosmic strings, implying that the statistics of singularities in random optical fields exhibit universal behavior.     

空间散斑的运动规律

相干光照明的漫射表面在空间中产生随机散斑。反射表面相对于光源运动,引起散斑的相应运动。当跟踪一个运动的斑,认为斑的强度不变,而位相是可以变化的。从Fresnel-Kirch-hoff积分,得到关于散斑运动的三个基本规则,即文中的(3),(4)和(5)式。第一和第二式类似于光栅方程。第三式类似于透镜定律。从这三个规则推导了当表面运动时散斑的运动公式(18)。这公式以矩阵形式表示,包括三个转动和三个平动。实验结果与公式非常符合。同时,三个基本规则适用于一般的空间衍射图。 关键词：     

The autocorrelation function of polychromatic laser speckle patterns near the image plane

The autocorrelation function of polychromatic speckle patterns produced near the image plane of a double diffraction imaging system is experimentally studied. The condition under which the polychromatic speckle field obeys Gaussian statistics is further investigated as a function of the numberN of scattering cells, using the average contrast of the speckle intensity fluctuations. The profile of the autocorrelation function is next investigated as a function ofN and the defocused distance from the image plane. It is found that the average contrast and autocorrelation function of the polychromatic speckle intensity fluctuations converge less rapidly with an increase inN than those of the monochromatic ones.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

A contrast variation of image speckle intensity under illumination of partially coherent light

Speckle patterns are formed by completely and partially coherent light at the image plane of a diffusing object. The general formula is derived for the contrast variation of the image speckle intensity distribution as a function of the spatial coherence of the illuminating light, the amplitude point-spread function of the optical imaging system and the statistical characteristic of the diffusing object. The effect of spatial coherence of the illuminating light on the contrast variations of the image speckle intensity distribution is theoretically evaluated under various statistical conditions of the diffusing object. The theoretical results are confirmed experimentally.     

Compressed ghost imaging based on differential speckle patterns

We propose a compressed ghost imaging scheme based on differential speckle patterns,named CGI-DSP.In the scheme,a series of bucket detector signals are acquired when a series of random speckle patterns are employed to illuminate an unknown object.Then the differential speckle patterns(differential bucket detector signals) are obtained by taking the difference between present random speckle patterns(present bucket detector signals) and previous random speckle patterns(previous bucket detector signals).Finally,the image of object can be obtained directly by performing the compressed sensing algorithm on the differential speckle patterns and differential bucket detector signals.The experimental and simulated results reveal that CGI-DSP can improve the imaging quality and reduce the number of measurements comparing with the traditional compressed ghost imaging schemes because our scheme can remove the environmental illuminations efficiently.