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.     

The effect of phase modulation of scattered radiation on the asymptotic behavior of the contrast ratio of partially coherent speckle fields

We analyze the influence of a weak phase modulation of multiply scattered partially coherent light fields on the variance of fluctuations of the scattered field intensity. It is suggested to perform diagnostics of scattering media by analyzing the probing radiation scattered from a “modulating” medium and determining the speckle intensity index (or contrast ratio) upon introduction of an object studied into the scheme of measurements. The proposed method is experimentally verified on model scattering media.     

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.     

Diffraction halo function of partially coherent speckle photography

We studied the diffraction halo function of partially coherent speckle photography, using the theory of partial coherence of light and speckle statistics. Numerical calculations were made on the basis of the derived expression. It was shown that the anisotropic coherence of the illumination induced by the source could lead to the inhomogeneity of the halo distribution. An experiment was performed to prove the theoretical predictions.     

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.     

Model-based inversion of speckle interferometer fringe patterns

Micrometer-scale rigid-body translations are determined fromelectronic speckle interferometric fringe patterns. An iterativeminimum error procedure employs the relative fringe order of pickedpositions of fringe maxima and minima within a single interferogram tocalculate the displacement field directly. The method does notcalculate the displacement at a single point but relies on theassumption that the character, but not the magnitudes or directions, ofthe displacements over the viewing area of the interferogram isknown. That is, a model of the displacements exists. Onperfect, noise-free forward modeled fringe patterns calculated for an 8.0-mum displacement, the phase error is less than 2 x10(-6) fringe orders (1.3 x 10(-5) rad)and probably results only from numerical noise in the inversion. Onreal fringe patterns obtained in electronic speckle interferometricexperiments, mean phase errors are generally less than 5 x10(-5) fringe orders (3.2 x 10(-4)rad), suggesting that the technique is robust despite errorsresulting from speckle noise, lack of accuracy in positioning ofexperimental components, and image-distortion corrections.     

Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry

A method for measurement of continuous displacements that uses phase-shifting speckle interferometry is presented. The initial random phase of the speckle pattern is evaluated by phase shifting before deformation. The changing phase thereafter is evaluated from only one image at a time by a least-squares algorithm. The technique can be used for measuring transients and other dynamic events, heat expansion as well as other phenomena, for which it is difficult to accomplish phase shifting during deformation. Theory along with computer simulations and experimental results are described.     

Wavelet transform analysis of dynamic speckle patterns texture

We propose the use of the wavelet transform to characterize the time evolution of dynamic speckle patterns. We describe it by using as an example a method used for the assessment of the drying of paint. Optimal texture features are determined and the time evolution is described in terms of the Mahalanobis distance to the final (dry) state. From the behavior of this distance function, two parameters are defined that characterize the evolution. Because detailed knowledge of the involved dynamics is not required, the methodology could be implemented for other complex or poorly understood dynamic phenomena.     

Electronic speckle pattern interferometry based on spatial information using only two sheets of speckle patterns

Abstract

Speckle interferometry is an important deformation measurement method for an object with a rough surface. In this paper, a novel fringe analysis method is proposed that uses a new optical system, which uses a plane wave as the reference beam of the speckle interferometer. When the optical system is employed in fringe analysis, the deformation information and the bias components of the speckle patterns are clearly separated in the frequency domain. Therefore, the deformation information can be readily extracted using a Fourier transform, which gives a pair of real and imaginary components concerning the information. The specklegram is calculated using such a pair of components, and the phase map is obtained from the specklegram. Experimental results confirmed that the resolution power of this measurement method is higher than 1/261 of the wavelength of the light source of the optical system.     

Wavelet analysis of speckle patterns with a temporal carrier

A novel temporal phase-analysis technique that is based on wavelet analysis and a temporal carrier is presented. To measure displacement on a vibrating object by using electronic speckle pattern interferometry, one captures a series of speckle patterns, using a high-speed CCD camera. To avoid ambiguity in phase estimation, a temporal carrier is generated by a piezoelectric transducer stage in the reference beam of the interferometer. The intensity variation of each pixel on recorded images is then analyzed along the time axis by a robust mathematical tool, i.e., a complex Morlet wavelet transform. After the temporal carrier is removed, the absolute displacement of a vibrating object is obtained without the need for temporal or spatial phase unwrapping. The results obtained by a wavelet transform are compared with those from a temporal Fourier transform.     

Phase-object detection by use of double-exposure fringe-modulated speckle patterns

We study the properties of a double-exposure image specklegram of a diffuse object obtained by use of a double-aperture pupil. A phase object is placed in front of one aperture during the first or the second exposure. Also, it is assumed that a uniform displacement of the diffuser between exposures is produced. The recorded specklegram is coherently illuminated and analyzed by Fourier transform operations. The average intensity distribution and the interference fringe visibility in the Fourier plane are investigated. On this basis, an alternative interference technique to detect phase objects is proposed.     

Anisotropic speckle patterns in the light scattered by rough cylindrical surfaces

Speckle patterns in the light field scattered from the rough surface of a cylindrical object are experimentally studied. The light speckles are elongated in the direction normal to the cylinder axis. A theoretical model explains the main features of the scattered light field. The dimensions of light speckles depend on both the surface roughness and the surface curvature.     

Speckle suppression in holographic projection displays using temporal integration of speckle images from diffractive optical elements

Speckles on images in holographic projection displays (HPDs) were efficiently suppressed by the temporal sum of two diffractive images generated from diffractive optical elements (DOEs). Using a modified iterative Fourier transform algorithm, we obtained pairs of phase-only DOEs that generated the diffractive images with high negative correlation coefficients of -0.827 and -0.490 in the one-dimensional and the two-dimensional simulations, respectively. The suppression ratios of the speckles in the two simulations were 0.301 and 0.457, which were 61% and 35% lower, respectively, than the sum of the two uncorrelated images. We have successfully demonstrated that the sum of two negatively correlated images from DOEs can effectively reduce the image speckles and improve the image quality in HPD systems.     

Role of caustics in the formation of networks of amplitude zeros for partially developed speckle fields

The topology of a partially developed speckle field was studied by use of interference techniques through computer simulation. Amplitude and phase structures in the vicinity of caustics for a coherent radiation field scattered at a surface with large inhomogeneities were investigated. It was confirmed that the caustics are indispensible components of the procedure for the formation of networks of amplitude zeros for a coherent field scattered by a rough surface with large inhomogeneities. It is shown that the formation of interference forklets in the field gives evidence of changes in the field's topology, as these forklets are a diagnostic sign of transition from a caustic to a three-dimensional pattern of a diffraction catastrophe.     

Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera

Recently, a new method to measure object shape and deformation with temporal evolution of speckles in speckle interferometry was reported. In this method, certain parameters, sensitive to shape or deformation are changed continuously, and the fluctuations in the irradiance of each speckle is recorded. The information over the whole object deformation is retrieved by Fourier-transformation techniques. We present a detailed theory and analyze the influence of decorrelation due to longitudinal and lateral size of the speckles. It is also shown that the method can be used to measure small deformations (less than 5 mum) with higher resolution. Further, the nonlinearity of the camera is shown to enhance the sensitivity.     

Method of direction-of-arrival estimation for uncorrelated, partially correlated and coherent sources

A new direction-of-arrival estimation method is proposed when uncorrelated, partially correlated and coherent sources coexist. These sources are estimated at two different stages. The uncorrelated and partially correlated sources are first estimated using conventional subspace methods. By exploiting the property of oblique projection, the contributions of uncorrelated and partially correlated sources are then eliminated from the covariance matrix and only the coherent sources remain. Finally, the coherent sources are estimated by the technique of spatial smoothing. The new method need not estimate the partially correlated sources repeatedly but can resolve more sources than the array elements. Simulation results demonstrate the effectiveness and efficiency of the new method.     

Three-dimensional mapping and range measurement by means of projected speckle patterns

We present a novel approach for three-dimensional (3D) measurements that includes the projection of coherent light through ground glass. Such a projection generates random speckle patterns on the object or on the camera, depending if the configuration is transmissive or reflective. In both cases the spatially random patterns are seen by the sensor. Different spatially random patterns are generated at different planes. The patterns are highly random and not correlated. This low correlation between different patterns is used for both 3D mapping of objects and range finding.