Mikael Sjödahl

Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy

Replacing photographic recording by electronic processing has some obvious advantages. An algorithm used for electronic speckle pattern photography is presented, and the reliability and accuracy is analyzed by using computer-generated speckle patterns. The algorithm is based on a two-dimensional discrete cross correlation between subimages from different images. Subpixel accuracy is obtained by a Fourier series expansion of the discrete correlation surface. The accuracy of the algorithm was found to vary in proportion to sigma/n(1 - delta)(2), where sigma is the speckle size, n is the subimage size, and delta is the amount of decorrelation, with negligible systematic errors. For typical values the uncertainty in the displacement is approximately 0.05 pixels. The uncertainty is found to increase with increased displacement gradients.

Electronic speckle photography: increased accuracy by nonintegral pixel shifting

Electronic speckle photography offers a simple and fast technique for measuring in-plane displacement fields in solid and fluid mechanics. An improved algorithm is presented and analyzed by use of both computer-simulated speckle patterns and real experiments. The idea of the improved algorithm is to maximize the correlation between correlated subimages from different images by shifting one of them by nonintegral pixel values. The improved algorithm was found to determine displacement components with an uncertainty of less than 1% of a pixel and with negligible systematic errors in ideal experimental conditions.

Accuracy in electronic speckle photography

Electronic speckle photography is an accurate, easy-to-use, video-based technique for the analysis of two- and three-dimensional deformation fields and in-plane strain fields, based on numerical cross correlation. Through the use of statistical optics, simulated speckle patterns, and experiments the accuracy in electronic speckle photography was found to depend on correlation, speckle size, window size, and correlation filter. The estimated correlation was found to be the combined effect of three mutually competing factors because of classical speckle correlation, subimage overlap, and displacement gradients. In many applications white-light speckle patterns provide a more accurate estimate of the displacement field than do laser speckle patterns.

A stereoscopic digital speckle photography system for 3-D displacement field measurements

Stereoscopic digital speckle photography offers a technique to measure object shapes and 3-D displacement fields in experimental mechanics. The system measures the displacement of a random white light speckle pattern, which somehow is present on the object surface, using digital correlation. This paper describes a general physical model for stereo imaging systems. A camera calibration algorithm, which takes the distortion in the lenses into account, is also presented and evaluated by real experiments. Standard deviations of small deformations as low as 1% of the pixel size for in-plane deformations and 6% of the pixel size for the out-of-plane component are reported. Using the calibration algorithm described, the main source of errors is random errors originating from the correlation algorithm.

Systematic and random errors in electronic speckle photography

Electronic speckle photography offers a simple and fast technique for measuring in-plane displacement fields in solid and fluid mechanics. Errors from undersampling, illumination divergence, and displacement magnitude have been analyzed and measured. The nature of the systematic error is such that a drift toward the closest integral pixel value is introduced. Because of the finite extent of the sensor area, considerable undersampling is tolerable before systematic errors occur. The random errors are mainly dependent on the effective ƒ-number of the imaging system and speckle decorrelation introduced by object displacement. When sampling at a rate of ~ 70% of the Nyquist frequency, we avoided systematic errors and minimized random errors.

Measurement of shape by using projected random patterns and temporal digital speckle photography

Projected random patterns have been used to measure the shape of discontinuous objects. A sequence of independent random patterns are projected onto the object. These images are analyzed by use of the technique called temporal digital speckle photography (DSP) that is introduced here. With temporal DSP the spatial resolution of the shape measurement is improved considerably compared with previously reported results with projected random patterns. A calibration procedure is described that uses a sequence of independent random patterns to calibrate measurement volume. As a result, independent space coordinates for each subimage are obtained. The accuracy is of the order of 1/1000 of the field of view where a subimage size of 8 pixels seems to be a good compromise between reliability and spatial resolution. The technique is illustrated with a measurement of an electrical plug and a 9-V battery.

Some recent advances in electronic speckle photography

Major advances in electronic speckle photography are reviewed. Topics include the correlation properties of laser speckles, the principles and expected accuracy of electronic speckle photography, the effect of the digital recording and evaluation, and some recent applications. These applications involve two techniques for the measurement of 3D deformation fields, measurement of the in-plane strain field components using defocused laser speckle, and measurement of object shape.

Microscopic 3-D displacement field measurements using digital speckle photography

Abstract A technique to measure object shape and 3-D displacement fields in micro-scale is offered by microscopic stereo digital speckle photography. The displacement of the random features that are often present on many engineering surfaces when viewed in a microscope is measured with the system, using image correlation. In this paper the equipment, physical model and calibration routines are described. The technique can be applied for sub-mm sized objects of arbitrary shape for small deformation fields. As a verifying experiment, an in-plane rotation of a flat calibration plate is presented. The expected in-plane errors are shown to be less than 0.1 μm and the corresponding out-of-plane errors about three times larger. As a pilot experiment, micro-structural paper expansion is studied, when exposed to humidity. The scaling properties of the microscope as well as the sampling criteria and reliability of the system are discussed in detail.

Electronic speckle photography: measurement of in-plane strain fields through the use of defocused laser speckle

High-accuracy, noncontact measurements of in-plane strain fields have been performed through the use of an electronic-speckle-photography system. The strain fields are extracted from the displacement of defocused laser speckle in a telecentric imaging system. Two different illumination configurations have been suggested, both of which use four illumination directions. Both configurations produce results of an accuracy according to Me/ΔL, where M is the demagnification of the telecentric imaging system, e is the random error in the speckle-displacement fields, and ΔL is the magnitude of the defocusing distance. The maximum defocusing distance possible was found to be restricted by the spatial resolution, especially at high magnifications. In experiments on a semicircularly and a rectangularly notched aluminum sheet, the principal strain field around the notch was measured with a random error in the strain field of less than 10 µstrain (µm/m).

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.