Subpixel Speckle Displacement Measurement Using a Digital Processing Technique

Abstract

This paper deals with the optical measurement of deformations and displacements of diffusing rough surfaces using changes in the speckle pattern obtained by laser illumination. A digitized speckle signal is obtained using a linear charge-coupled device photodetector that produces samples of one-dimensional signals of N pixels. A sequential numerical processing procedure is applied to detect the relative displacement of two speckle signals, corresponding to two different states of the surface; the accuracy is better than one micrometre. The principles of the method and the corresponding algorithms are described. Experimental results are given and these include an analysis of the deformation of video structure under directional traction.     

Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics

Abstract

The paper describes the possibility of using the speckle pattern decorrelation for determination of small deformation tensor components of an elementary object surface area in an optical image field. The relationship between the small-deformation tensor and the speckle field displacement is analysed in detail. The studied problem is presented from the approximation viewpoint of both wave and geometrical optics.     

Digital speckle radiography—a new ballistic measurement technique

Abstract

Digital speckle radiography is a measurement technique which is capable of visualizing internal flow fields within an opaque material undergoing a ballistic impact. This recent development has been successfully applied to the study of polyester, cement, sand and glass targets. The technique is based on digital speckle photography but, instead of producing the required speckle pattern by traditional means, the specimen is seeded with a layer of X-ray opaque filings. By utilizing two X-ray heads and varying the delays and position of the seeded layer, a full three-dimensional displacement map can be built up. The theories behind the technique are introduced, and results presented from two-dimensional displacement measurements on sand subjected to rod impact and three-dimensional measurements of cement being impacted by a shaped charge jet.     

Phase shift calibration in speckle photography—a first step to practical real-time analysis of speckle correlation fringes

Abstract

The paper is focused on the implemention of phase shift calibration in speckle photography with a view to introducing the possibility of realtime analysis of displacement data obtained by the method. Phase reversal is accomplished by varying pressure within an air-filled quartz cell inserted in the pump beam in a conventional two-beam coupling arrangement. It is shown that phase reversal is achieved when a π-shifted speckle pattern overlaps on an unshifted speckle pattern at the observation plane. This phenomenon is exploited for calibration of the phase shift. Experimental results show good agreement with the theory.     

Fringe visibility analysis with different scale apertures in speckle photography

Abstract

The use of different scale aperture pupils for image recording in speckle photography is analysed. In particular a double-exposure specklegram is considered. The ensemble-average intensity in the Fourier plane is analytically derived and fringe visibility is investigated. The theoretical results are verified by in-plane displacement translation experiments.     

Composite Displacement Measurement by Speckle Technique

Abstract

We present a simple method for measuring composite movements which comprise a longitudinal displacement and a rotation of a rough surface. The method is based on the direct analysis of the double exposure photographic recording obtained from two speckle patterns produced by the diffuser, before and after it is translated and rotated.     

Real Time Pseudocolour Encoding of Depth Using White Light Processing

Abstract

An interferometer, consisting of a grating and a double exposed speckle pattern, used to perform pseudocolour encoding of depth in real time under white light illumination, is described. A theory of operation based on Fresnel diffraction is also given.     

Consideration of existence of phase information of object shape in zeroth-order diffraction beam using electromagnetic simulation with aperture in front of objective

ABSTRACT

It has been reported that the shape of a measured object can be determined by detecting the change in phase distribution generated by a lateral shift of the object using speckle interferometry. In speckle interferometry technique, it was also reported that the shape of the object beyond the diffraction limit can be measured. In this study, the principle of this method is discussed through experiments and electromagnetic analysis. Accordingly, the results of the experiments and electromagnetic analysis of phase change only under zeroth-order diffraction light through the lateral shift of the object are investigated by shutting out the higher harmonic diffraction lights using an aperture in front of the lens. The results indicate that even if the image of the object cannot be focused upon, three-dimensional shape measurement can be performed by analysing only the zeroth-order diffraction light from the object.     

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.     

Superposition of Two Dynamic Speckle Patterns

Abstract

A model is proposed to explain the influence of blood flow and moving surrounding tissue on laser light scattering. Blood and tissue are represented by two sets of scatterers which are moving in arbitrary directions with different velocities. The real dynamic speckle pattern is thought to be composed of the coherent superposition of the two speckle patterns due to the scattering on these two sets of scatterers. The model describes the spectrum of the speckle intensity in an arbitrary observation point. No special assumptions must be made concerning the geometry of illumination and the position of the observation point. A measuring value B for the determination of the blood flow is derived from the speckle intensity. The model also provides the dependence of B on density and mean velocity of each set of scatterers. It has been shown that the main contribution of the tissue movement on B can be compensated by a control measurement and that the sensitivity of B due to blood velocity variations depends on the density of both sets of scatterers and on the tissue velocity.     

Comprehensive influence of in-plane displacement,double-aperture orientation and wedge-shearing direction on slope fringe formation in speckle shearing interferometry

Abstract

The comprehensive influence of the in-plane displacement, double-aperture orientation and wedge-shearing direction on the slope fringe formation in speckle shearing interferometry is discussed in this paper. The results show that the two in-plane displacement components have an influence on the slope fringe formation and that the double-aperture orientation and wedge-shearing direction also have an important influence on the slope fringe formation. A theoretical analysis and experimental results are given. The experimental results are in good agreement with the theoretical analysis.     

Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation

Laser-speckles show displacement accompanied by structure change when diffuse objects generating them undergo displacement and/or deformation. This behaviour is theoretically investigated by calculating the cross-correlation functions of speckle intensities before and after the deformation. The dependences of speckle displacement on geometries of object illumination and speckle observation as well as on deformation parameters are clarified. The relations derived are interpreted physically by introducing the shift in diffraction rays due to displacement and deformation of a grating. Distributions of speckle displacement are calculated numerically and shown graphically.     

Completely passive method of speckle reduction utilizing static multimode optical fibre and two-dimensional diffractive optical element

ABSTRACT

In this paper, we present experimental results on speckle noise suppression using a completely passive method. The passivity of the method is achieved owing to the absence of any mechanical, electronic, or other dynamic influences on the optical scheme elements. In the experiment, a multimode semiconductor 520?±?5-nm laser with a spectral bandwidth of 2?nm, static two-dimensional (2D) and 2?×?1D diffractive optical elements (DOEs), as well as multimode single-core optical fibre and multimode optical fibre bundle were used. The dependence of the speckle reduction efficiency as a function of the optical fibre type and optical fibre length was measured for different DOEs. A speckle contrast of 0.148 and speckle reduction coefficient of 2.38 were obtained for a 2.5-m-long multimode optical fibre bundle. The experimental results confirmed that it is possible to construct completely passive optical circuits with reduced speckle noises using static multimode optical fibres and diffraction optical elements.     

Speckle Patterns Generated by Rough Surfaces with a Periodic Component

Abstract

A real diffraction grating is replaced by a coordinate-dependent surface impedance that is constructed as the sum of two contributions: a perfectly periodic contribution and a randomly varying contributon. Numerical results obtained with this model show the presence of diffuse light bands on the speckle pattern that constitutes the diffuse background of the spectrum. We emphasize the role played by the electromagnetic surface waves supported by this structure on the generation of the bands.     

A partial hybrid stress model for the refined C1 higher‐order plate theory

Abstract

The partial hybrid stress model is applied to the refined C ¹ higher‐order plate theory in this paper. The displacement model is adopted in the flexural part and the hybrid stress model in the transverse shear part. The plate concept is introduced and the governing equations of plate are derived variationally from the modified Hellinger‐Reissner principle. This new plate element is demonstrated to be more accurate than displacement formulation in the analysis of orthotropic thick laminated plates. Moreover, the through thickness distribution of transverse shear stress is precisely predicted.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Complex Degree of Coherence Due to Tilted Planar Sources

Abstract

The complex degree of coherence (CDC) due to a quasi-monochromatic spatially incoherent source can be displayed by performing a two-step procedure. The CDC information is encoded in the spectral content of the speckle pattern produced via a diffuser placed at the plane where the CDC is to be studied. In a second step, the recorded speckle is Fourier analysed. We apply this method to the study of tilted incoherent sources, for which the CDC is no longer an homogeneous function. A relationship is found that links the size of the speckle halo in the Fourier plane (where CDC information exists), and the tilt angle of the source plane. Some experimental results are shown in order to illustrate the method. Finally, some possible extensions and applications of our study are mentioned.     

Fraunhofer diffraction by cantor fractals with variable lacunarity

Abstract

Optical diffraction by fractal openings is increasingly being studied because it allows the properties and parameters that characterize these objects to be determined. Allain and Cloitre published the first results showing that the resulting analysis of the distribution of intensity obtained from diffraction experiments through fractal deterministic pupils permits the self-similar dimension and other geometrical characteristic of these structures to be obtained directly. In this work the lacunarity effect ?, dimension d and order k of growth of the Cantor fractal about the distribution of intensities of the diffraction pattern are studied, solved analytically and characterized. In particular we note the influence of lacunarity because this is one of the first studies in which this geometric fractal parameter is taken into consideration. The selfsimilarity of the diffraction figure at different orders is also proved. The results of this study allow us to say that an intimate relation exists between the distribution of the diffracted waves and the parameters that describe this kind of fractal geometry.     

Carrier-modulated Object Step-loading Method of Automated Analysis in Digital Speckle Shearing Interferometry

Abstract

An object step-loading method has been recently reported to overcome the problems of phase unwrapping and decorrelation in digital speckle shearing interferometry. In this paper, a carrier modulation procedure is incorporated into the object step-loading method in order to improve the phase derivation accuracy. An added advantage with this approach is that the direction of deformation is also revealed.