A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

As a practical and effective tool for quantitative in-plane deformation measurement of a planar object surface, two-dimensional digital image correlation (2D DIC) is now widely accepted and commonly used in the field of experimental mechanics. It directly provides full-field displacements to sub-pixel accuracy and full-field strains by comparing the digital images of a test object surface acquired before and after deformation. In this review, methodologies of the 2D DIC technique for displacement field measurement and strain field estimation are systematically reviewed and discussed. Detailed analyses of the measurement accuracy considering the influences of both experimental conditions and algorithm details are provided. Measures for achieving high accuracy deformation measurement using the 2D DIC technique are also recommended. Since microscale and nanoscale deformation measurement can easily be realized by combining the 2D DIC technique with high-spatial-resolution microscopes, the 2D DIC technique should find more applications in broad areas.

https://iopscience.iop.org/article/10.1088/0957-0233/20/6/062001/pdf

Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review

Review of experimental techniques for high rate deformation and shock studies

In digital image correlation (DIC), to obtain the displacements of each point of interest, a correlation criterion must be predefined to evaluate the similarity between the reference subset and the target subset. The correlation criterion is of fundamental importance in DIC, and various correlation criteria have been designed and used in literature. However, little research has been carried out to investigate their relations. In this paper, we first provide a comprehensive overview of various correlation criteria used in DIC. Then we focus on three robust and most widely used correlation criteria, i.e., a zero-mean normalized cross-correlation (ZNCC) criterion, a zero-mean normalized sum of squared difference (ZNSSD) criterion, and a parametric sum of squared difference (PSSD(ab)) criterion with two additional unknown parameters, since they are insensitive to the scale and offset changes of the target subset intensity and have been highly recommended for practical use in literature. The three correlation criteria are analyzed to establish their transversal relationships, and the theoretical analyses clearly indicate that the three correlation criteria are actually equivalent, which elegantly unifies these correlation criteria for pattern matching. Finally, the equivalence of these correlation criteria is further validated by numerical simulation and actual experiment.

/pdf/equivalence-of-digital-image-correlation-criteria-for-48454aa1h6.pdf

Equivalence of digital image correlation criteria for pattern matching.

An algorithm for unwrapping noisy phase maps has recently been proposed, based on the identification of discontinuity sources that mark the start or end of a 2π phase discontinuity Branch cuts between sources act as barriers to unwrapping, resulting in a unique phase map that is independent of the unwrapping route We investigate four methods for optimizing the placement of the cuts A modified nearest neighbor approach is found to be the most successful and can reliably unwrap unfiltered speckle-interferometry phase maps with discontinuity source densities of 005 sources pixel(-1)

Improved noise-immune phase-unwrapping algorithm.

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: analysis of an algorithm giving the displacement with subpixel accuracy.

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

Systematic and random errors in electronic speckle photography.

Improved quality of phase maps in pulsed digital holographic interferometry is demonstrated by finding the right reconstruction distance. The objective is to improve the optical phase information when the object under study is a phase object and when it is out of focus, leading to low contrast fringes in the phase map. A numerical refocusing is performed by introducing an ideal lens as a multiplication by a phase field in the Fourier domain, and then a region of maximum speckle correlation is found by comparing undisturbed and disturbed subimages in different refocused imaging planes. After finding the right reconstruction distance, a phase map of high visibility is constructed. By this technique a 30% reduction of the phase error for a flow of helium gas and a 50% reduction of the phase error for a weak thin lens were obtained, which resulted in a significant improvement of the visual appearance of the phase maps.

Improving the quality of phase maps in phase object digital holographic interferometry by finding the right reconstruction distance

Measurement of dynamic crack tip displacement field by speckle photography and interferometry

A method for noise reduction in double-exposure speckle interferometry is proposed, based on averaging independent spatially filtered correlation fringe patterns.

Lars Benckert

Papers

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

Systematic and random errors in electronic speckle photography.

Improving the quality of phase maps in phase object digital holographic interferometry by finding the right reconstruction distance

Measurement of dynamic crack tip displacement field by speckle photography and interferometry

Speckle interferometry: noise reduction by correlation fringe averaging